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+ } else { + parent + .find("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + parent + .children(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + parent.siblings("section").slideToggle(); + }); + } +); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $("a.docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * RegX escape function from MDN + * Refer: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ + function escapeRegExp(string) { + return string.replace(/[.*+?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `

`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + searchstring = escapeRegExp(querystring); + let textindex = new RegExp(`${searchstring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(searchstring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + combineWith: "AND", + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
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Spin wave simulations of CoRh₂O₄\n", + "\n", + "This tutorial introduces Sunny through its features for performing\n", + "conventional spin wave theory calculations. We consider the crystal CoRh₂O₄\n", + "and reproduce the calculations of [Ge et al., Phys. Rev. B 96,\n", + "064413](https://doi.org/10.1103/PhysRevB.96.064413)." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Get Julia and Sunny\n", + "\n", + "Sunny is implemented in Julia, which allows for interactive development (like\n", + "Python or Matlab) while also providing high numerical efficiency (like C++ or\n", + "Fortran). New Julia users should begin with our **[Getting\n", + "Started](https://github.com/SunnySuite/Sunny.jl/wiki/Getting-started-with-Julia)**\n", + "guide. Sunny requires Julia 1.10 or later.\n", + "\n", + "From the Julia prompt, load Sunny and also [GLMakie](https://docs.makie.org/)\n", + "for graphics." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "If these packages are not yet installed, Julia will offer to install them. If\n", + "executing this tutorial gives an error, you may need to update Sunny and\n", + "GLMakie from the [built-in package\n", + "manager](https://github.com/SunnySuite/Sunny.jl/wiki/Getting-started-with-Julia#the-built-in-julia-package-manager)." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Units" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "The `Units` object selects reference energy and length\n", + "scales, and uses these to provide physical constants. For example, `units.K`\n", + "returns one kelvin as 0.086 meV, where the Boltzmann constant is implicit." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom);" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Crystal cell\n", + "\n", + "A crystallographic cell may be loaded from a `.cif` file, or specified from\n", + "atom positions and types.\n", + "\n", + "Start by defining the shape of the conventional chemical cell. CoRh₂O₄ has\n", + "cubic spacegroup 227 (Fd-3m). Its lattice constants are 8.5 Å, and the cell\n", + "angles are 90°. With this information, `lattice_vectors` constructs a\n", + "3×3 matrix `latvecs`. Columns of `latvecs` define the lattice vectors $(𝐚_1,\n", + "𝐚_2, 𝐚_3)$ in the global Cartesian coordinate system. Conversely, columns\n", + "of `inv(latvecs)` define the global Cartesian axes $(\\hat{x}, \\hat{y},\n", + "\\hat{z})$ in components of the lattice vectors." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "a = 8.5031 # (Å)\n", + "latvecs = lattice_vectors(a, a, a, 90, 90, 90)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct the `Crystal` cell from the spacegroup number 227 and one\n", + "representative atom of each occupied Wyckoff. In the standard setting of\n", + "spacegroup 227, position `[0, 0, 0]` belongs to Wyckoff 8a, which is the\n", + "diamond cubic crystal." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "positions = [[0, 0, 0]]\n", + "cryst = Crystal(latvecs, positions, 227; types=[\"Co\"], setting=\"1\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "`view_crystal` launches an interface for interactive inspection and\n", + "symmetry analysis." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Spin system" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "A `System` will define the spin model. Each cobalt atom carries\n", + "quantum spin $s = 3/2$, with a $g$-factor of 2. Specify this\n", + "`Moment` data for cobalt atom 1. By symmetry, the same moment data\n", + "also applies to cobalt atoms 2, 3, ... 7. The option `:dipole` indicates a\n", + "traditional model type, for which quantum spin is modeled as a dipole\n", + "expectation value." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=3/2, g=2)], :dipole)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Ge et al. demonstrated that inelastic neutron scattering data for CoRh₂O₄ is\n", + "well modeled by antiferromagnetic nearest neighbor exchange, `J = 0.63` meV.\n", + "Call `set_exchange!` with the bond that connects atom 1 to atom 3, and\n", + "has zero displacement between chemical cells. Consistent with the symmetries\n", + "of spacegroup 227, this interaction will be propagated to all other\n", + "nearest-neighbor bonds. Calling `view_crystal` with `sys` now shows\n", + "the antiferromagnetic Heisenberg interactions as blue polkadot spheres." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "J = +0.63 # (meV)\n", + "set_exchange!(sys, J, Bond(1, 3, [0, 0, 0]))\n", + "view_crystal(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Optimizing spins" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "To search for the ground state, call `randomize_spins!` and\n", + "`minimize_energy!` in sequence. For this problem, optimization\n", + "converges rapidly to the expected Néel order. See this with\n", + "`plot_spins`, where spins are colored according to their global\n", + "$z$-component." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; color=[S[3] for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The diamond lattice is bipartite, allowing each spin to perfectly anti-align\n", + "with its 4 nearest-neighbors. Each of these 4 bonds contribute $-J s^2$ to\n", + "the total energy. Two sites participate in each bond, so the energy per site\n", + "is $-2 J s^2$. Check this by calling `energy_per_site`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "@assert energy_per_site(sys) ≈ -2J*(3/2)^2" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Reshaping the magnetic cell" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "The most compact magnetic cell for this Néel order is a primitive unit cell.\n", + "Reduce the magnetic cell size using `reshape_supercell`, where columns\n", + "of the `shape` matrix are primitive lattice vectors as multiples of the\n", + "conventional cubic lattice vectors $(𝐚_1, 𝐚_2, 𝐚_3)$. One could\n", + "alternatively use `shape = cryst.latvecs \\ cryst.prim_latvecs`. Verify that\n", + "the energy per site is unchanged after the reshaping the supercell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "shape = [0 1 1;\n", + " 1 0 1;\n", + " 1 1 0] / 2\n", + "sys_prim = reshape_supercell(sys, shape)\n", + "@assert energy_per_site(sys_prim) ≈ -2J*(3/2)^2" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plotting `sys_prim` shows the two spins within the primitive cell, as well as\n", + "the larger conventional cubic cell for context." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "plot_spins(sys_prim; color=[S[3] for S in sys_prim.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Spin wave theory" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "With this primitive cell, we will perform a `SpinWaveTheory`\n", + "calculation of the structure factor $\\mathcal{S}(𝐪,ω)$. The measurement\n", + "`ssf_perp` indicates projection of the spin structure factor\n", + "$\\mathcal{S}(𝐪,ω)$ perpendicular to the direction of momentum transfer, as\n", + "appropriate for unpolarized neutron scattering. The isotropic\n", + "`FormFactor` for Co²⁺ dampens intensities at large $𝐪$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "formfactors = [1 => FormFactor(\"Co2\")]\n", + "measure = ssf_perp(sys_prim; formfactors)\n", + "swt = SpinWaveTheory(sys_prim; measure)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Select `lorentzian` broadening with a full-width at half-maximum\n", + "(FWHM) of 0.8 meV." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "kernel = lorentzian(fwhm=0.8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define a `q_space_path` that connects high-symmetry points in\n", + "reciprocal space. The $𝐪$-points are given in reciprocal lattice units\n", + "(RLU) for the _original_ cubic cell. For example, `[1/2, 1/2, 0]` denotes the\n", + "sum of the first two reciprocal lattice vectors, $𝐛_1/2 + 𝐛_2/2$. A total\n", + "of 500 $𝐪$-points will be sampled along the path." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0, 0, 0], [1/2, 0, 0], [1/2, 1/2, 0], [0, 0, 0]]\n", + "path = q_space_path(cryst, qs, 500)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate single-crystal scattering `intensities` along this path, for\n", + "energies between 0 and 6 meV. Use `plot_intensities` to visualize the\n", + "result." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "energies = range(0, 6, 300)\n", + "res = intensities(swt, path; energies, kernel)\n", + "plot_intensities(res; units, title=\"CoRh₂O₄ LSWT\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Sometimes experimental data is only available as a powder average, i.e., as an\n", + "average over all possible crystal orientations. Use `powder_average`\n", + "to simulate these intensities. Each $𝐪$-magnitude defines a spherical shell\n", + "in reciprocal space. Consider 200 radii from 0 to 3 inverse angstroms, and\n", + "collect `2000` random samples per spherical shell. As configured, this\n", + "calculation completes in about two seconds. Had we used the conventional cubic\n", + "cell, the calculation would be an order of magnitude slower." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 3, 200) # (1/Å)\n", + "res = powder_average(cryst, radii, 2000) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units, saturation=1.0, title=\"CoRh₂O₄ Powder Average\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "This result can be compared to experimental neutron scattering data\n", + "from Fig. 5 of [Ge et al.](https://doi.org/10.1103/PhysRevB.96.064413)\n", + "\n", + "" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### What's next?\n", + "\n", + "* For more spin wave calculations of this type, browse the SpinW tutorials\n", + " ported to Sunny.\n", + "* Spin wave theory neglects thermal fluctuations of the magnetic order. The\n", + " next CoRh₂O₄ tutorial demonstrates how to sample spins in thermal equilibrium, and\n", + " measure dynamical correlations from the classical spin dynamics.\n", + "* Sunny also offers features that go beyond the dipole approximation of a\n", + " quantum spin via the theory of SU(_N_) coherent states. This can be\n", + " especially useful for systems with strong single-ion anisotropy, as\n", + " demonstrated in the FeI₂ tutorial." + ], + "metadata": {} + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/02_LLD_CoRh2O4.ipynb b/previews/PR319/assets/notebooks/02_LLD_CoRh2O4.ipynb new file mode 100644 index 000000000..f26e19efc --- /dev/null +++ b/previews/PR319/assets/notebooks/02_LLD_CoRh2O4.ipynb @@ -0,0 +1,427 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 2. Landau-Lifshitz dynamics of CoRh₂O₄ at finite *T*\n", + "\n", + "In the previous tutorial, we\n", + "used spin wave theory to calculate the dynamical spin structure factor of\n", + "CoRh₂O₄. Here, we perform a similar calculation using equilibrium samples from\n", + "the Boltzmann distribution at finite $T$. For each sampled spin\n", + "configuration, we will simulate the classical Landau-Lifshitz spin dynamics\n", + "and extract dynamical spin-spin correlations. After applying a\n", + "classical-to-quantum correction factor, the resulting intensities can be\n", + "compared to inelastic neutron scattering data." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Construct the system as in the previous tutorial. For this antiferromagnetic model on the diamond\n", + "cubic lattice, the ground state is unfrustrated Néel order." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie\n", + "\n", + "units = Units(:meV, :angstrom)\n", + "a = 8.5031 # (Å)\n", + "latvecs = lattice_vectors(a, a, a, 90, 90, 90)\n", + "cryst = Crystal(latvecs, [[0,0,0]], 227, setting=\"1\")\n", + "\n", + "sys = System(cryst, [1 => Moment(s=3/2, g=2)], :dipole)\n", + "J = 0.63 # (meV)\n", + "set_exchange!(sys, J, Bond(1, 3, [0,0,0]))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; color=[S[3] for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `repeat_periodically` to extend the system to 10×10×10 chemical\n", + "unit cells. The ground state Néel order is retained. Increasing the system\n", + "size further would reduce finite-size artifacts and increase momentum-space\n", + "resolution, but would also make the simulations slower." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = repeat_periodically(sys, (10, 10, 10))\n", + "plot_spins(sys; color=[S[3] for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Langevin dynamics for sampling" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "We will be using a `Langevin` spin dynamics to thermalize the system.\n", + "This dynamics is a variant of the Landau-Lifshitz equation that incorporates\n", + "noise and dissipation terms, which are linked by a fluctuation-dissipation\n", + "theorem. The temperature 6 K ≈ 1.38 meV is slightly above ordering for this\n", + "model. The dimensionless `damping` magnitude sets a timescale for coupling to\n", + "the implicit thermal bath; 0.2 is usually a good choice." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "langevin = Langevin(; damping=0.2, kT=16*units.K)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `suggest_timestep` to select an integration timestep. A\n", + "dimensionless error tolerance of `1e-2` is usually a good choice. The\n", + "suggested timestep will vary according to the magnetic configuration. It is\n", + "reasonable to start from an energy-minimized configuration." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "suggest_timestep(sys, langevin; tol=1e-2)\n", + "langevin.dt = 0.025;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Now run a Langevin trajectory to sample spin configurations. Keep track of the\n", + "energy per site at each time step." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "energies = [energy_per_site(sys)]\n", + "for _ in 1:1000\n", + " step!(sys, langevin)\n", + " push!(energies, energy_per_site(sys))\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "From the relaxed spin configuration, we can learn that `dt` was a little\n", + "smaller than necessary; increasing it will make the remaining simulations\n", + "faster." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "suggest_timestep(sys, langevin; tol=1e-2)\n", + "langevin.dt = 0.042;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot energy versus time using the [Makie `lines`\n", + "function](https://docs.makie.org/stable/reference/plots/lines). The plateau\n", + "suggests that the system has reached thermal equilibrium." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "lines(energies, color=:blue, figure=(size=(600,300),), axis=(xlabel=\"Timesteps\", ylabel=\"Energy (meV)\"))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the spins colored by their alignment with a reference spin at the origin.\n", + "The field `sys.dipoles` is a 4D array storing the spin dipole data. The first\n", + "three indices of label the chemical cell, while the fourth index labels an\n", + "atom within the cell. Note that Julia arrays use 1-based indexing. Thermal\n", + "fluctuations are apparent in the plot." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "S0 = sys.dipoles[1,1,1,1]\n", + "plot_spins(sys; color=[S'*S0 for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Static structure factor" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Use `SampledCorrelationsStatic` to estimate spatial correlations for\n", + "configurations in classical thermal equilibrium. Each call to\n", + "`add_sample!` will accumulate data for the current spin snapshot." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "formfactors = [1 => FormFactor(\"Co2\")]\n", + "measure = ssf_perp(sys; formfactors)\n", + "sc = SampledCorrelationsStatic(sys; measure)\n", + "add_sample!(sc, sys) # Accumulate the newly sampled structure factor into `sf`" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Collect 20 additional samples. Perform 100 Langevin time-steps between\n", + "measurements to approximately decorrelate the sample in thermal equilibrium." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "for _ in 1:20\n", + " for _ in 1:100\n", + " step!(sys, langevin)\n", + " end\n", + " add_sample!(sc, sys)\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `q_space_grid` to define a slice of momentum space $[H, K, 0]$,\n", + "where $H$ and $K$ each range from -10 to 10 in RLU. This command produces\n", + "a 200×200 grid of sample points." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "grid = q_space_grid(cryst, [1, 0, 0], range(-10, 10, 200), [0, 1, 0], (-10, 10))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the instantaneous structure factor on the slice by\n", + "integrating over all energy values ω. We employ the appropriate\n", + "`FormFactor` for Co2⁺. Selecting `saturation = 1.0` sets the color\n", + "saturation point to the maximum intensity value. This is reasonable because we\n", + "are above the ordering temperature, and do not have sharp Bragg peaks." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "res = intensities_static(sc, grid)\n", + "plot_intensities(res; saturation=1.0, title=\"Static Intensities at T = 16 K\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Dynamical structure factor" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "To collect statistics for the _dynamical_ structure factor intensities\n", + "$\\mathcal{S}(𝐪,ω)$ at finite temperature, use\n", + "`SampledCorrelations`. It requires a range of `energies` to resolve,\n", + "which will be associated with frequencies of the classical spin dynamics. The\n", + "integration timestep `dt` can be somewhat larger than that used by the\n", + "Langevin dynamics." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "dt = 2*langevin.dt\n", + "energies = range(0, 6, 50)\n", + "sc = SampledCorrelations(sys; dt, energies, measure=ssf_perp(sys))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Like before, use Langevin dynamics to sample spin configurations from thermal\n", + "equilibrium. Now, however, each call to `add_sample!` will run a\n", + "classical spin dynamics trajectory and measure dynamical correlations. To make\n", + "the tutorial run quickly, we average over just 5 trajectories. To make a\n", + "publication quality figure, this number should be significantly increased for\n", + "better statistics." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "for _ in 1:5\n", + " for _ in 1:100\n", + " step!(sys, langevin)\n", + " end\n", + " add_sample!(sc, sys)\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Select points that define a piecewise-linear path through reciprocal space,\n", + "and a sampling density." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[3/4, 3/4, 0],\n", + " [ 0, 0, 0],\n", + " [ 0, 1/2, 1/2],\n", + " [1/2, 1, 0],\n", + " [ 0, 1, 0],\n", + " [1/4, 1, 1/4],\n", + " [ 0, 1, 0],\n", + " [ 0, -4, 0]]\n", + "path = q_space_path(cryst, qs, 500)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the intensities along this path." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "res = intensities(sc, path; energies, langevin.kT)\n", + "plot_intensities(res; units, title=\"Intensities at 16 K\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Powder averaged intensity" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Define spherical shells in reciprocal space via their radii, in absolute units\n", + "of 1/Å. For each shell, calculate and average the intensities at 350\n", + "$𝐪$-points" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 3.5, 200) # (1/Å)\n", + "res = powder_average(cryst, radii, 350) do qs\n", + " intensities(sc, qs; energies, langevin.kT)\n", + "end\n", + "plot_intensities(res; units, title=\"Powder Average at 16 K\")" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/03_LSWT_SU3_FeI2.ipynb b/previews/PR319/assets/notebooks/03_LSWT_SU3_FeI2.ipynb new file mode 100644 index 000000000..3999b17c1 --- /dev/null +++ b/previews/PR319/assets/notebooks/03_LSWT_SU3_FeI2.ipynb @@ -0,0 +1,491 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 3. Multi-flavor spin wave simulations of FeI₂\n", + "\n", + "This tutorial illustrates various advanced features such as symmetry analysis,\n", + "energy minimization, and spin wave theory with multi-flavor bosons.\n", + "\n", + "Our context will be FeI₂, an effective spin-1 material with strong single-ion\n", + "anisotropy. Quadrupolar fluctuations give rise to a single-ion bound state\n", + "that is observable in neutron scattering, and cannot be described by a\n", + "dipole-only model. We will use the linear spin wave theory of SU(3) coherent\n", + "states (i.e. 2-flavor bosons) to model the magnetic spectrum of FeI₂. The\n", + "original study was performed in [Bai et al., Nature Physics 17, 467–472\n", + "(2021)](https://doi.org/10.1038/s41567-020-01110-1).\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "The Fe atoms are arranged in stacked triangular layers. The effective spin\n", + "Hamiltonian takes the form,\n", + "\n", + "$$\n", + "\\mathcal{H}=\\sum_{(i,j)} 𝐒_i ⋅ J_{ij} 𝐒_j - D\\sum_i \\left(S_i^z\\right)^2,\n", + "$$\n", + "\n", + "where the exchange matrices $J_{ij}$ between bonded sites $(i,j)$ include\n", + "competing ferromagnetic and antiferromagnetic interactions. This model also\n", + "includes a strong easy axis anisotropy, $D > 0$." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load packages." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct the chemical cell of FeI₂ by specifying the lattice vectors and the\n", + "full set of atoms." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "a = b = 4.05012 # Lattice constants for triangular lattice (Å)\n", + "c = 6.75214 # Spacing between layers (Å)\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 120)\n", + "positions = [[0, 0, 0], [1/3, 2/3, 1/4], [2/3, 1/3, 3/4]]\n", + "types = [\"Fe\", \"I\", \"I\"]\n", + "cryst = Crystal(latvecs, positions; types)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Observe that the space group 'P -3 m 1' (164) has been inferred, as well as\n", + "point group symmetries. Only the Fe atoms are magnetic, so we focus on them\n", + "with `subcrystal`. Importantly, the new crystal retains the symmetry\n", + "information for spacegroup 164." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "cryst = subcrystal(cryst, \"Fe\")\n", + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Symmetry analysis\n", + "\n", + "The command `print_symmetry_table` provides a list of all the\n", + "symmetry-allowed interactions out to 8 Å." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "print_symmetry_table(cryst, 8.0)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The allowed $g$-tensor is expressed as a 3×3 matrix in the free coefficients\n", + "`A`, `B`, ... The allowed single-ion anisotropy is expressed as a linear\n", + "combination of Stevens operators. The latter correspond to polynomials of the\n", + "spin operators, as we will describe below.\n", + "\n", + "The allowed exchange interactions are given as 3×3 matrices for representative\n", + "bonds. The notation `Bond(i, j, n)` indicates a bond between atom indices `i`\n", + "and `j`, with cell offset `n`. Note that the order of the pair $(i, j)$ is\n", + "significant if the exchange tensor contains antisymmetric\n", + "Dzyaloshinskii–Moriya (DM) interactions.\n", + "\n", + "The bonds can be visualized in the `view_crystal` interface. By default,\n", + "`Bond(1, 1, [1,0,0])` is toggled on, to show the 6 nearest-neighbor Fe-Fe\n", + "bonds on a triangular lattice layer. Toggling `Bond(1, 1, [0,0,1])` shows the\n", + "Fe-Fe bond between layers, etc." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "### Defining the spin model" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Construct a `System` with spin $s=1$ and $g=2$ for the Fe ions.\n", + "\n", + "Recall that quantum spin-1 is, in reality, a linear combination of basis\n", + "states $|m⟩$ with well-defined angular momentum $m = -1, 0, 1$. FeI₂ has a\n", + "strong easy-axis anisotropy, which stabilizes a single-ion bound state of zero\n", + "angular momentum, $|m=0⟩$. Such a bound state is inaccessible to traditional\n", + "spin wave theory, which works with dipole expectation values of fixed\n", + "magnitude. This physics is, however, well captured with a theory of SU(_N_)\n", + "coherent states, where $N = 2S+1 = 3$ is the number of levels. Activate this\n", + "generalized theory by selecting `:SUN` mode instead of `:dipole` mode.\n", + "\n", + "An optional random number `seed` will make the calculations exactly\n", + "reproducible." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :SUN, seed=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Set the exchange interactions for FeI₂ following the fits of [Bai et\n", + "al.](https://doi.org/10.1038/s41567-020-01110-1)" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "J1pm = -0.236 # (meV)\n", + "J1pmpm = -0.161\n", + "J1zpm = -0.261\n", + "J2pm = 0.026\n", + "J3pm = 0.166\n", + "J′0pm = 0.037\n", + "J′1pm = 0.013\n", + "J′2apm = 0.068\n", + "\n", + "J1zz = -0.236\n", + "J2zz = 0.113\n", + "J3zz = 0.211\n", + "J′0zz = -0.036\n", + "J′1zz = 0.051\n", + "J′2azz = 0.073\n", + "\n", + "J1xx = J1pm + J1pmpm\n", + "J1yy = J1pm - J1pmpm\n", + "J1yz = J1zpm\n", + "\n", + "set_exchange!(sys, [J1xx 0.0 0.0;\n", + " 0.0 J1yy J1yz;\n", + " 0.0 J1yz J1zz], Bond(1,1,[1,0,0]))\n", + "set_exchange!(sys, [J2pm 0.0 0.0;\n", + " 0.0 J2pm 0.0;\n", + " 0.0 0.0 J2zz], Bond(1,1,[1,2,0]))\n", + "set_exchange!(sys, [J3pm 0.0 0.0;\n", + " 0.0 J3pm 0.0;\n", + " 0.0 0.0 J3zz], Bond(1,1,[2,0,0]))\n", + "set_exchange!(sys, [J′0pm 0.0 0.0;\n", + " 0.0 J′0pm 0.0;\n", + " 0.0 0.0 J′0zz], Bond(1,1,[0,0,1]))\n", + "set_exchange!(sys, [J′1pm 0.0 0.0;\n", + " 0.0 J′1pm 0.0;\n", + " 0.0 0.0 J′1zz], Bond(1,1,[1,0,1]))\n", + "set_exchange!(sys, [J′2apm 0.0 0.0;\n", + " 0.0 J′2apm 0.0;\n", + " 0.0 0.0 J′2azz], Bond(1,1,[1,2,1]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The function `set_onsite_coupling!` assigns a single-ion anisotropy.\n", + "The argument can be constructed using `spin_matrices` or\n", + "`stevens_matrices`. Here we use Julia's anonymous function syntax to\n", + "assign an easy-axis anisotropy along the direction $\\hat{z}$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "D = 2.165 # (meV)\n", + "set_onsite_coupling!(sys, S -> -D*S[3]^2, 1)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Finding the ground state" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "This model has been fitted so that energy minimization yields the physically\n", + "correct ground state. Knowing this, we could set the magnetic configuration\n", + "manually by calling `set_dipole!` on each site in the system. Another\n", + "approach, as we will demonstrate, is to search for the ground-state via\n", + "`minimize_energy!`.\n", + "\n", + "To reduce bias in the search, use `resize_supercell` to create a\n", + "relatively large system of 4×4×4 chemical cells. Randomize all spins\n", + "(represented as SU(3) coherent states) and minimize the energy." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = resize_supercell(sys, (4, 4, 4))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "A positive number above indicates that the procedure has converged to a local\n", + "energy minimum. The configuration, however, may still have defects. This can\n", + "be checked by visualizing the expected spin dipoles, colored according to\n", + "their $z$-components." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "plot_spins(sys; color=[S[3] for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To better understand the spin configuration, we could inspect the static\n", + "structure factor $\\mathcal{S}(𝐪)$ in the 3D space of momenta $𝐪$. The\n", + "general tool for this analysis is `SampledCorrelationsStatic`. For the\n", + "present purposes, however, it is more convenient to use\n", + "`print_wrapped_intensities`, which reports $\\mathcal{S}(𝐪)$ with\n", + "periodic wrapping of all commensurate $𝐪$ wavevectors into the first\n", + "Brillouin zone." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "print_wrapped_intensities(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The known zero-field energy-minimizing magnetic structure of FeI₂ is a two-up,\n", + "two-down order. It can be described as a generalized spiral with a single\n", + "propagation wavevector $𝐤$. Rotational symmetry allows for three equivalent\n", + "orientations: $±𝐤 = [0, -1/4, 1/4]$, $[1/4, 0, 1/4]$, or\n", + "$[-1/4,1/4,1/4]$. Small systems can spontaneously break this symmetry, but\n", + "for larger systems, defects and competing domains are to be expected.\n", + "Nonetheless, `print_wrapped_intensities` shows large intensities consistent\n", + "with a subset of the known ordering wavevectors.\n", + "\n", + "Let's break the three-fold symmetry by hand. The function\n", + "`suggest_magnetic_supercell` takes one or more $𝐤$ modes, and\n", + "suggests a magnetic cell shape that is commensurate." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "suggest_magnetic_supercell([[0, -1/4, 1/4]])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calling `reshape_supercell` yields a much smaller system, making it\n", + "much easier to find the global energy minimum. Plot the system again, now\n", + "including \"ghost\" spins out to 12Å, to verify that the magnetic order is\n", + "consistent with FeI₂." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys_min = reshape_supercell(sys, [1 0 0; 0 2 1; 0 -2 1])\n", + "randomize_spins!(sys_min)\n", + "minimize_energy!(sys_min);\n", + "plot_spins(sys_min; color=[S[3] for S in sys_min.dipoles], ghost_radius=12)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Spin wave theory\n", + "\n", + "Now that the system has been relaxed to an energy minimized ground state, we\n", + "can calculate the spin wave spectrum. Because we are working with a system of\n", + "SU(3) coherent states, this calculation will require a multi-flavor boson\n", + "generalization of the usual spin wave theory." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys_min; measure=ssf_perp(sys_min))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the spectrum along a momentum-space path that connects a\n", + "sequence of high-symmetry $𝐪$-points. This interface abstracts over the\n", + "underlying calculator type." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0,0,0], [1,0,0], [0,1,0], [1/2,0,0], [0,1,0], [0,0,0]]\n", + "path = q_space_path(cryst, qs, 500)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units, title=\"Single Crystal Bands\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To make direct comparison with inelastic neutron scattering (INS) data, we\n", + "must account for empirical broadening of the data. Model this using a\n", + "`lorentzian` kernel, with a full-width at half-maximum of 0.3 meV." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "kernel = lorentzian(fwhm=0.3)\n", + "energies = range(0, 10, 300); # 0 < ω < 10 (meV)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Also, a real FeI₂ sample will exhibit competing magnetic domains. We use\n", + "`domain_average` to average over the three possible domain\n", + "orientations. This involves 120° rotations about the axis $\\hat{z} = [0, 0,\n", + "1]$ in global Cartesian coordinates." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "rotations = [([0,0,1], n*(2π/3)) for n in 0:2]\n", + "weights = [1, 1, 1]\n", + "res = domain_average(cryst, path; rotations, weights) do path_rotated\n", + " intensities(swt, path_rotated; energies, kernel)\n", + "end\n", + "plot_intensities(res; units, colormap=:viridis, title=\"Domain Averaged Intensities\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "This result can be directly compared to experimental neutron scattering data\n", + "from [Bai et al.](https://doi.org/10.1038/s41567-020-01110-1)\n", + "\n", + "\n", + "\n", + "\n", + "(The publication figure used a non-standard coordinate system to label the\n", + "wave vectors.)\n", + "\n", + "To get this agreement, the theory of SU(3) coherent states is essential. The\n", + "lower band has large quadrupolar character, and arises from the strong\n", + "easy-axis anisotropy of FeI₂.\n", + "\n", + "An interesting exercise is to repeat the same study, but using `:dipole` mode\n", + "instead of `:SUN`. That alternative choice would constrain the coherent state\n", + "dynamics to the space of dipoles only, and the flat band of single-ion bound\n", + "states would be missing." + ], + "metadata": {} + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/04_GSD_FeI2.ipynb b/previews/PR319/assets/notebooks/04_GSD_FeI2.ipynb new file mode 100644 index 000000000..3c8fd6130 --- /dev/null +++ b/previews/PR319/assets/notebooks/04_GSD_FeI2.ipynb @@ -0,0 +1,398 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 4. Generalized spin dynamics of FeI₂ at finite *T*" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "The previous FeI₂ tutorial used multi-flavor spin wave theory to calculate the dynamical spin\n", + "structure factor. This tutorial performs an analogous calculation at finite\n", + "temperature using the [classical dynamics of SU(_N_) coherent\n", + "states](https://doi.org/10.1103/PhysRevB.106.054423).\n", + "\n", + "Compared to spin wave theory, classical spin dynamics in real-space is\n", + "typically much slower, and is limited in $𝐪$-space resolution. The\n", + "approach, however, allows for thermal fluctuations, can be used to explore\n", + "[finite temperature phases](https://doi.org/10.1103/PhysRevB.109.014427), and\n", + "enables the study of [highly non-equilibrium\n", + "processes](https://doi.org/10.1103/PhysRevB.106.235154).\n", + "\n", + "The structure of this tutorial largely follows the previous study of CoRh₂O₄\n", + "at finite *T*.\n", + "The main difference is that CoRh₂O₄ can be well described with `:dipole` mode,\n", + "whereas FeI₂ is best modeled using `:SUN` mode, owing to its strong easy-axis\n", + "anisotropy.\n", + "\n", + "Construct the FeI₂ system as previously described." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie\n", + "\n", + "units = Units(:meV, :angstrom)\n", + "a = b = 4.05012\n", + "c = 6.75214\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 120)\n", + "cryst = Crystal(latvecs, [[0,0,0]], 164; types=[\"Fe\"])\n", + "\n", + "sys = System(cryst, [1 => Moment(s=1, g=2)], :SUN)\n", + "J1pm = -0.236\n", + "J1pmpm = -0.161\n", + "J1zpm = -0.261\n", + "J2pm = 0.026\n", + "J3pm = 0.166\n", + "J′0pm = 0.037\n", + "J′1pm = 0.013\n", + "J′2apm = 0.068\n", + "J1zz = -0.236\n", + "J2zz = 0.113\n", + "J3zz = 0.211\n", + "J′0zz = -0.036\n", + "J′1zz = 0.051\n", + "J′2azz = 0.073\n", + "J1xx = J1pm + J1pmpm\n", + "J1yy = J1pm - J1pmpm\n", + "J1yz = J1zpm\n", + "set_exchange!(sys, [J1xx 0.0 0.0; 0.0 J1yy J1yz; 0.0 J1yz J1zz], Bond(1,1,[1,0,0]))\n", + "set_exchange!(sys, [J2pm 0.0 0.0; 0.0 J2pm 0.0; 0.0 0.0 J2zz], Bond(1,1,[1,2,0]))\n", + "set_exchange!(sys, [J3pm 0.0 0.0; 0.0 J3pm 0.0; 0.0 0.0 J3zz], Bond(1,1,[2,0,0]))\n", + "set_exchange!(sys, [J′0pm 0.0 0.0; 0.0 J′0pm 0.0; 0.0 0.0 J′0zz], Bond(1,1,[0,0,1]))\n", + "set_exchange!(sys, [J′1pm 0.0 0.0; 0.0 J′1pm 0.0; 0.0 0.0 J′1zz], Bond(1,1,[1,0,1]))\n", + "set_exchange!(sys, [J′2apm 0.0 0.0; 0.0 J′2apm 0.0; 0.0 0.0 J′2azz], Bond(1,1,[1,2,1]))\n", + "D = 2.165\n", + "set_onsite_coupling!(sys, S -> -D*S[3]^2, 1)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Thermalization" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "To study thermal fluctuations in real-space, use a large system size with\n", + "16×16×4 copies of the chemical cell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = resize_supercell(sys, (16, 16, 4))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Direct optimization via `minimize_energy!` is susceptible to trapping\n", + "in a local minimum. An alternative approach is to simulate the system using\n", + "`Langevin` spin dynamics. This requires a bit more set-up, but allows\n", + "sampling from thermal equilibrium at any target temperature. Select the\n", + "temperature 2.3 K ≈ 0.2 meV. This temperature is small enough to magnetically\n", + "order, but large enough so that the dynamics can readily overcome local energy\n", + "barriers and annihilate defects." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "langevin = Langevin(; damping=0.2, kT=2.3*units.K)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `suggest_timestep` to select an integration timestep for the error\n", + "tolerance `tol=1e-2`. Initializing `sys` to some low-energy configuration\n", + "usually works well." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys; maxiters=10)\n", + "suggest_timestep(sys, langevin; tol=1e-2)\n", + "langevin.dt = 0.03;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Run a Langevin trajectory for 10,000 time-steps and plot the spins. The\n", + "magnetic order is present, but may be difficult to see." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "for _ in 1:10_000\n", + " step!(sys, langevin)\n", + "end\n", + "plot_spins(sys; color=[S[3] for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Verify the expected two-up, two-down spiral magnetic order by calling\n", + "`print_wrapped_intensities`. A single propagation wavevector $±𝐤$\n", + "dominates the static intensity in $\\mathcal{S}(𝐪)$, indicating the expected\n", + "2 up, 2 down magnetic spiral order. A smaller amount of intensity is spread\n", + "among many other wavevectors due to thermal fluctuations." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "print_wrapped_intensities(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Thermalization has not substantially altered the suggested `dt`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "suggest_timestep(sys, langevin; tol=1e-2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "### Structure factor in the paramagnetic phase" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "The remainder of this tutorial will focus on the paramagnetic phase.\n", + "Re-thermalize the system to the temperature of 3.5 K ≈ 0.30 meV." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "langevin.kT = 3.5 * units.K\n", + "for _ in 1:10_000\n", + " step!(sys, langevin)\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The suggested timestep has increased slightly. Following this suggestion will\n", + "make the simulations a bit faster." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "suggest_timestep(sys, langevin; tol=1e-2)\n", + "langevin.dt = 0.040;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Collect dynamical spin structure factor data using\n", + "`SampledCorrelations`. This procedure involves sampling spin\n", + "configurations from thermal equilibrium and using the [spin dynamics of\n", + "SU(_N_) coherent states](https://arxiv.org/abs/2204.07563) to estimate\n", + "dynamical correlations. With proper classical-to-quantum corrections, the\n", + "associated structure factor intensities $S^{αβ}(q,ω)$ can be compared with\n", + "finite-temperature inelastic neutron scattering data. Incorporate the\n", + "`FormFactor` appropriate to Fe²⁺." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "dt = 2*langevin.dt\n", + "energies = range(0, 7.5, 120)\n", + "formfactors = [1 => FormFactor(\"Fe2\"; g_lande=3/2)]\n", + "sc = SampledCorrelations(sys; dt, energies, measure=ssf_perp(sys; formfactors))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The function `add_sample!` will collect data by running a dynamical\n", + "trajectory starting from the current system configuration." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "add_sample!(sc, sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To collect additional data, it is required to re-sample the spin configuration\n", + "from the thermal distribution. Statistical error is reduced by fully\n", + "decorrelating the spin configurations between calls to `add_sample!`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "for _ in 1:2\n", + " for _ in 1:1000 # Enough steps to decorrelate spins\n", + " step!(sys, langevin)\n", + " end\n", + " add_sample!(sc, sys)\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Perform an intensity calculation for two special $𝐪$-points in reciprocal\n", + "lattice units (RLU). A classical-to-quantum rescaling of normal mode\n", + "occupations will be performed according to the temperature `kT`. The large\n", + "statistical noise could be reduced by averaging over more thermal samples." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "res = intensities(sc, [[0, 0, 0], [0.5, 0.5, 0.5]]; energies, langevin.kT)\n", + "fig = lines(res.energies, res.data[:, 1]; axis=(xlabel=\"meV\", ylabel=\"Intensity\"), label=\"(0,0,0)\")\n", + "lines!(res.energies, res.data[:, 2]; label=\"(π,π,π)\")\n", + "axislegend()\n", + "fig" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Next, we will measure intensities along a `q_space_path` that connects\n", + "high symmetry points. Because this is a real-space calculation, data is only\n", + "available for discrete $𝐪$ modes, with resolution that scales inversely to\n", + "linear system size. Intensities at $ω = 0$ dominate, so to enhance\n", + "visibility, we restrict the color range empirically." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0, 0, 0], # List of wave vectors that define a path\n", + " [1, 0, 0],\n", + " [0, 1, 0],\n", + " [1/2, 0, 0],\n", + " [0, 1, 0],\n", + " [0, 0, 0]]\n", + "qpath = q_space_path(cryst, qs, 500)\n", + "res = intensities(sc, qpath; energies, langevin.kT)\n", + "plot_intensities(res; colorrange=(0.0, 1.0), title=\"Intensities at T = 2.3 K\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "One can also view the intensity along a `q_space_grid` for a fixed\n", + "energy value. Alternatively, use `intensities_static` to integrate\n", + "over all available energies." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "grid = q_space_grid(cryst, [1, 0, 0], range(-1.5, 1.5, 300), [0, 1, 0], (-1.5, 1.5); orthogonalize=true)\n", + "res = intensities(sc, grid; energies=[3.5], langevin.kT)\n", + "plot_intensities(res; title=\"Intensity slice at ω = 3.5 meV\")" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/05_MC_Ising.ipynb b/previews/PR319/assets/notebooks/05_MC_Ising.ipynb new file mode 100644 index 000000000..cee21b663 --- /dev/null +++ b/previews/PR319/assets/notebooks/05_MC_Ising.ipynb @@ -0,0 +1,169 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 5. Monte Carlo sampling of the Ising model\n", + "\n", + "This tutorial illustrates simulation of the classical 2D Ising model." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To model the 2D square lattice, create an elongated tetragonal cell with one\n", + "atom." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "latvecs = lattice_vectors(1, 1, 10, 90, 90, 90)\n", + "crystal = Crystal(latvecs, [[0, 0, 0]])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a `System` of spin dipoles. Following the Ising convention, we\n", + "will restrict the dipoles to $±1$ along the global $\\hat{z}$-axis. Select\n", + "$g=-1$ so that the Zeeman coupling between external field $𝐁$ and spin\n", + "dipole $𝐬$ is $-𝐁⋅𝐬$. The system size is 128×128." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "L = 128\n", + "sys = System(crystal, [1 => Moment(s=1, g=-1)], :dipole; dims=(L, L, 1), seed=0)\n", + "polarize_spins!(sys, (0, 0, 1))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `set_exchange!` to include a ferromagnetic Heisenberg interaction\n", + "along nearest-neighbor bonds. The `Bond` below connects two spins\n", + "displaced by the lattice vector $𝐚₁$. This interaction will be propagated\n", + "to all nearest-neighbors bonds in the system, consistent with the symmetries\n", + "of the square lattice." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "set_exchange!(sys, -1.0, Bond(1, 1, (1, 0, 0)))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "If an external field is desired, it can be set using `set_field!`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "B = 0\n", + "set_field!(sys, (0, 0, B))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The critical temperature for the Ising model is known analytically." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "Tc = 2/log(1+√2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use a `LocalSampler` to perform `nsweeps` Monte Carlo sweeps. A sweep\n", + "consists of, on average, one trial update per spin in the system. Each\n", + "proposed update is accepted or rejected according to the Metropolis acceptance\n", + "probability. As its name suggests, the `propose_flip` function will\n", + "only propose pure spin flips, $𝐬 \\rightarrow -𝐬$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "nsweeps = 4000\n", + "sampler = LocalSampler(kT=Tc, propose=propose_flip)\n", + "for i in 1:nsweeps\n", + " step!(sys, sampler)\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the Ising spins by extracting the $z$-component of the dipoles" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "heatmap(reshape([S[3] for S in sys.dipoles], (L, L)))" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/06_CP2_Skyrmions.ipynb b/previews/PR319/assets/notebooks/06_CP2_Skyrmions.ipynb new file mode 100644 index 000000000..b5fe38f42 --- /dev/null +++ b/previews/PR319/assets/notebooks/06_CP2_Skyrmions.ipynb @@ -0,0 +1,267 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 6. Dynamical quench into CP² skyrmion liquid\n", + "\n", + "This example demonstrates a non-equilibrium study of SU(3) spin dynamics\n", + "leading to the formation of a CP² skyrmion liquid. As proposed in [Zhang et\n", + "al., Nature Communications **14**, 3626\n", + "(2023)](https://www.nature.com/articles/s41467-023-39232-8), CP² skyrmions are\n", + "topological defects that involve both the dipolar and quadrupolar parts of\n", + "quantum spin-1, and can be studied using the formalism SU(3) coherent states.\n", + "\n", + "This study uses the SU(N) generalization of Landau-Lifshitz spin dynamics,\n", + "with Langevin coupling to a thermal bath, as described in [Dahlbom et al.,\n", + "Phys. Rev. B **106**, 235154\n", + "(2022)](https://doi.org/10.1103/PhysRevB.106.235154). Beginning from an\n", + "initial high-temperature state, the dynamics following a rapid quench in\n", + "temperature gives rise a disordered liquid of CP² skyrmions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Begin with a `Crystal` cell for the triangular lattice." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "lat_vecs = lattice_vectors(1, 1, 10, 90, 90, 120)\n", + "positions = [[0, 0, 0]]\n", + "cryst = Crystal(lat_vecs, positions)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a spin `System` containing $L×L$ cells. Following previous\n", + "worse, select $g=-1$ so that the Zeeman coupling has the form $-𝐁⋅𝐬$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "L = 40\n", + "sys = System(cryst, [1 => Moment(s=1, g=-1)], :SUN; dims=(L, L, 1))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The Hamiltonian,\n", + "$$\n", + "\\mathcal{H} = \\sum_{\\langle i,j \\rangle} J_{ij}( \\hat{S}_i^x \\hat{S}_j^x + \\hat{S}_i^y \\hat{S}_j^y + \\Delta\\hat{S}_i^z \\hat{S}_j^z) - h\\sum_{i}\\hat{S}_i^z + D\\sum_{i}(\\hat{S}_i^z)^2,\n", + "$$\n", + "contains competing ferromagnetic first-neighbor and antiferromagnetic\n", + "second-neighbor exchange terms on a triangular lattice. Both exchange matrices\n", + "include anisotropy in the $\\hat{z}$ direction. Additionally, there is an\n", + "external magnetic field $h$ and an easy-plane single-ion anisotropy $D$.\n", + "Select parameters for a point in the [Zhang et\n", + "al.](https://www.nature.com/articles/s41467-023-39232-8) phase diagram where\n", + "the CP² skyrmions are stable." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "J1 = -1 # Nearest-neighbor ferromagnetic\n", + "J2 = (2.0/(1+√5)) # Tune competing exchange to set skyrmion scale length\n", + "Δ = 2.6 # Exchange anisotropy\n", + "\n", + "ex1 = J1 * [1 0 0;\n", + " 0 1 0;\n", + " 0 0 Δ]\n", + "ex2 = J2 * [1 0 0;\n", + " 0 1 0;\n", + " 0 0 Δ]\n", + "set_exchange!(sys, ex1, Bond(1, 1, [1, 0, 0]))\n", + "set_exchange!(sys, ex2, Bond(1, 1, [1, 2, 0]))\n", + "\n", + "h = 15.5 # External field in energy units\n", + "field = set_field!(sys, [0, 0, h])\n", + "\n", + "D = 19.0 # Easy-plane anisotropy\n", + "set_onsite_coupling!(sys, S -> D*S[3]^2, 1)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Initialize system to an infinite temperature (fully randomized) initial\n", + "condition." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "We will study a temperature quench process using a generalized\n", + "`Langevin` spin dynamics. In this SU(3) treatment of quantum spin-1,\n", + "the dynamics include coupled dipoles and quadrupoles. Select a relatively\n", + "small damping magnitude to overcome local minima, and disable thermal\n", + "fluctuations." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "damping = 0.05\n", + "kT = 0;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The first step is to estimate a reasonable integration timestep `dt`. In this\n", + "case, a random spin configuration gives a tighter bound than does an\n", + "energy-minimized configuration. A relatively large error tolerance is OK for\n", + "this phenomenological study." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "integrator = Langevin(; damping, kT)\n", + "suggest_timestep(sys, integrator; tol=0.05)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Apply the suggested timestep." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "integrator.dt = 0.01;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Now run the dynamical quench starting from a randomized configuration. The\n", + "field `frames` stores the system spin configuration, as SU(3) coherent states,\n", + "at three different times during the quenching process." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "τs = [4, 16, 256] # Times to record snapshots\n", + "frames = [] # Empty array to store snapshots\n", + "for i in eachindex(τs)\n", + " dur = i == 1 ? τs[1] : τs[i] - τs[i-1] # Determine the length of time to simulate\n", + " numsteps = round(Int, dur/integrator.dt)\n", + " for _ in 1:numsteps # Perform the integration\n", + " step!(sys, integrator)\n", + " end\n", + " push!(frames, copy(sys.coherents)) # Save a snapshot spin configuration\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Visualize the state of the system contained in each snapshot by plotting the\n", + "SU(3) Berry phase curvature over triangular plaquettes. This is a measure of\n", + "CP² skyrmion density. The function `plot_triangular_plaquettes` is not part of\n", + "the core Sunny package, but rather something you could define yourself using\n", + "Makie. Find this helper function at\n", + "[`examples/extra/Plotting/`](https://github.com/SunnySuite/Sunny.jl/tree/main/examples/extra/Plotting)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "include(pkgdir(Sunny, \"examples\", \"extra\", \"Plotting\", \"plotting2d.jl\"))\n", + "\n", + "function sun_berry_curvature(z₁, z₂, z₃)\n", + " z₁, z₂, z₃ = normalize.((z₁, z₂, z₃))\n", + " n₁ = z₁ ⋅ z₂\n", + " n₂ = z₂ ⋅ z₃\n", + " n₃ = z₃ ⋅ z₁\n", + " return angle(n₁ * n₂ * n₃)\n", + "end\n", + "\n", + "plot_triangular_plaquettes(sun_berry_curvature, frames; size=(600, 200),\n", + " offset_spacing=10, texts=[\"\\tt = \"*string(τ) for τ in τs], text_offset=(0, 6)\n", + ")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The times are given in $\\hbar/|J_1|$. The white background corresponds to a\n", + "quantum paramagnetic state, where the local spin exhibits a strong quadrupole\n", + "moment and little or no dipole moment. At late times, there are well-formed\n", + "skyrmions of positive (red) and negative (blue) charge, and various metastable\n", + "spin configurations. A full-sized version of this figure is available in\n", + "[Dahlbom et al.](https://doi.org/10.1103/PhysRevB.106.235154)." + ], + "metadata": {} + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/07_Dipole_Dipole.ipynb b/previews/PR319/assets/notebooks/07_Dipole_Dipole.ipynb new file mode 100644 index 000000000..6b6cac6a3 --- /dev/null +++ b/previews/PR319/assets/notebooks/07_Dipole_Dipole.ipynb @@ -0,0 +1,212 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 7. Long-range dipole interactions\n", + "\n", + "This example shows how long-range dipole-dipole interactions can affect a spin\n", + "wave calculation. These interactions can be included two ways: Ewald summation\n", + "or in real-space with a distance cutoff. The study follows [Del Maestro and\n", + "Gingras, J. Phys.: Cond. Matter, **16**, 3339\n", + "(2004)](https://arxiv.org/abs/cond-mat/0403494)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a pyrochlore crystal from spacegroup 227." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:K, :angstrom)\n", + "latvecs = lattice_vectors(10.19, 10.19, 10.19, 90, 90, 90)\n", + "positions = [[1/8, 1/8, 1/8]]\n", + "cryst = Crystal(latvecs, positions, 227, setting=\"1\")\n", + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a system and reshape to the primitive cell, which contains four atoms.\n", + "Add antiferromagnetic nearest neighbor exchange interactions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "primitive_cell = [1/2 1/2 0; 0 1/2 1/2; 1/2 0 1/2]\n", + "sys = System(cryst, [1 => Moment(s=7/2, g=2)], :dipole; seed=0)\n", + "sys = reshape_supercell(sys, primitive_cell)\n", + "J1 = 0.304 # (K)\n", + "set_exchange!(sys, J1, Bond(1, 2, [0,0,0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a copy of the system and enable long-range dipole-dipole interactions\n", + "using Ewald summation." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys_lr = clone_system(sys)\n", + "enable_dipole_dipole!(sys_lr, units.vacuum_permeability)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a copy of the system and add long-range dipole-dipole interactions up\n", + "to a 5 Å cutoff distance." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys_lr_cut = clone_system(sys)\n", + "modify_exchange_with_truncated_dipole_dipole!(sys_lr_cut, 5.0, units.vacuum_permeability)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Find an energy minimizing spin configuration accounting for the long-range\n", + "dipole-dipole interactions. This will arbitrarily select from a discrete set\n", + "of possible ground states based on the system `seed`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys_lr)\n", + "minimize_energy!(sys_lr)\n", + "plot_spins(sys_lr; ghost_radius=8, color=[:red, :blue, :yellow, :purple])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Copy this configuration to the other two systems. Note that the original `sys`\n", + "has a _continuum_ of degenerate ground states." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys.dipoles .= sys_lr.dipoles\n", + "sys_lr_cut.dipoles .= sys_lr.dipoles;" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate dispersions for the three systems. The high-symmetry $𝐪$-points\n", + "are specified in reciprocal lattice units with respect to the conventional\n", + "cubic cell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0,0,0], [0,1,0], [1,1/2,0], [1/2,1/2,1/2], [3/4,3/4,0], [0,0,0]]\n", + "labels = [\"Γ\", \"X\", \"W\", \"L\", \"K\", \"Γ\"]\n", + "path = q_space_path(cryst, qs, 500; labels)\n", + "\n", + "measure = ssf_trace(sys)\n", + "swt = SpinWaveTheory(sys; measure)\n", + "res1 = intensities_bands(swt, path)\n", + "\n", + "swt = SpinWaveTheory(sys_lr; measure)\n", + "res2 = intensities_bands(swt, path)\n", + "\n", + "swt = SpinWaveTheory(sys_lr_cut; measure)\n", + "res3 = intensities_bands(swt, path);" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a panel corresponding to Fig. 2 of [Del Maestro and\n", + "Gingras](https://arxiv.org/abs/cond-mat/0403494). Dashed lines show the effect\n", + "of truncating dipole-dipole interactions at 5 Å. The Del Maestro and Gingras\n", + "paper underreported the energy scale by a factor of two, and requires slight\n", + "corrections to its third dispersion band." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "fig = Figure(size=(768, 300))\n", + "plot_intensities!(fig[1, 1], res1; units, title=\"Without long-range dipole\")\n", + "ax = plot_intensities!(fig[1, 2], res2; units, title=\"With long-range dipole\")\n", + "for c in eachrow(res3.disp)\n", + " lines!(ax, eachindex(c), c; linestyle=:dash, color=:black)\n", + "end\n", + "fig" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/08_Momentum_Conventions.ipynb b/previews/PR319/assets/notebooks/08_Momentum_Conventions.ipynb new file mode 100644 index 000000000..77038e9ee --- /dev/null +++ b/previews/PR319/assets/notebooks/08_Momentum_Conventions.ipynb @@ -0,0 +1,219 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# 8. Momentum transfer conventions\n", + "\n", + "This example illustrates Sunny's conventions for dynamical structure factor\n", + "intensities, $\\mathcal{S}(𝐪,ω)$, as documented in the page Structure\n", + "Factor Conventions. The variables $𝐪$ and $ω$ describe momentum\n", + "and energy transfer _to_ the sample.\n", + "\n", + "For systems without inversion-symmetry, the structure factor intensities at\n", + "$± 𝐪$ may be inequivalent. To highlight this, consider a simple 1D chain\n", + "that includes only Dzyaloshinskii–Moriya interactions between neighboring\n", + "sites. Coupling to an external field then breaks time-reversal symmetry,\n", + "giving rise to an inequivalence of intensities $\\mathcal{S}(±𝐪,ω)$" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Selecting the P1 spacegroup will effectively disable all symmetry analysis.\n", + "This can be a convenient way to avoid symmetry-imposed constraints on the\n", + "couplings. A disadvantage is that all bonds are treated as inequivalent, and\n", + "Sunny will therefore not be able to propagate any couplings between bonds." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "latvecs = lattice_vectors(2, 2, 1, 90, 90, 90)\n", + "cryst = Crystal(latvecs, [[0,0,0]], \"P1\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a 1D chain system that extends along the global Cartesian $ẑ$\n", + "axis. The Hamiltonian includes DM and Zeeman coupling terms, $ℋ = ∑_j D ẑ ⋅\n", + "(𝐒_j × 𝐒_{j+1}) - ∑_j 𝐁 ⋅ μ_j$, where $μ_j = - g 𝐒_j$ is the\n", + "`magnetic_moment` and $𝐁 ∝ ẑ$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(1, 1, 25))\n", + "D = 0.1\n", + "B = 5D\n", + "set_exchange!(sys, dmvec([0, 0, D]), Bond(1, 1, [0, 0, 1]))\n", + "set_field!(sys, [0, 0, B])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The large external field fully polarizes the system. Here, the DM coupling\n", + "contributes nothing, leaving only Zeeman coupling." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "@assert energy_per_site(sys) ≈ -10D" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Sample from the classical Boltzmann distribution at a low temperature." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "dt = 0.1\n", + "kT = 0.02\n", + "damping = 0.1\n", + "langevin = Langevin(dt; kT, damping)\n", + "suggest_timestep(sys, langevin; tol=1e-2)\n", + "for _ in 1:10_000\n", + " step!(sys, langevin)\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The Zeeman coupling polarizes the magnetic moments in the $𝐁 ∝ ẑ$\n", + "direction. The spin dipoles, however, are anti-aligned with the magnetic\n", + "moments, and therefore point towards $-ẑ$. This is shown below." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "plot_spins(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Estimate the dynamical structure factor using classical dynamics." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sc = SampledCorrelations(sys; dt, energies=range(0, 15D, 100), measure=ssf_trace(sys))\n", + "add_sample!(sc, sys)\n", + "nsamples = 100\n", + "for _ in 1:nsamples\n", + " for _ in 1:1_000\n", + " step!(sys, langevin)\n", + " end\n", + " add_sample!(sc, sys)\n", + "end\n", + "path = q_space_path(cryst, [[0,0,-1/2], [0,0,+1/2]], 400)\n", + "res1 = intensities(sc, path; energies=:available, kT)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate the same quantity with linear spin wave theory at $T = 0$. Because\n", + "the ground state is fully polarized, the required magnetic cell is a $1×1×1$\n", + "grid of chemical unit cells." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys_small = resize_supercell(sys, (1,1,1))\n", + "minimize_energy!(sys_small)\n", + "swt = SpinWaveTheory(sys_small; measure=ssf_trace(sys_small))\n", + "res2 = intensities_bands(swt, path)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "This model system has a single magnon band with dispersion $ϵ(𝐪) = 1 - D/B\n", + "\\sin(2πq₃)$ and uniform intensity. Both calculation methods reproduce this\n", + "analytical solution. Observe that $𝐪$ and $-𝐪$ are inequivalent. The\n", + "structure factor calculated from classical dynamics additionally shows an\n", + "elastic peak at $𝐪 = [0,0,0]$, reflecting the ferromagnetic ground state." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "fig = Figure(size=(768, 300))\n", + "plot_intensities!(fig[1, 1], res1; title=\"Classical dynamics\")\n", + "plot_intensities!(fig[1, 2], res2; title=\"Spin wave theory\")\n", + "fig" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW01_FM_Heseinberg_chain.ipynb b/previews/PR319/assets/notebooks/SW01_FM_Heseinberg_chain.ipynb new file mode 100644 index 000000000..46c5cb418 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW01_FM_Heseinberg_chain.ipynb @@ -0,0 +1,269 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW01 - FM Heisenberg chain\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "1](https://spinw.org/tutorials/01tutorial), originally authored by Goran\n", + "Nilsen and Sandor Toth. It calculates the spin wave spectrum of the\n", + "ferromagnetic Heisenberg nearest-neighbor spin chain." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define a chemical cell for the spin chain lattice. It is tetrahedral, with a\n", + "short dimension of 3 Å and two long dimensions of 8 Å. Observe that Sunny\n", + "infers the spacegroup 'P 4/m m m' (123)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "a = 3.0\n", + "b = 8.0\n", + "c = 8.0\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 90)\n", + "positions = [[0, 0, 0]]\n", + "cryst = Crystal(latvecs, positions)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "View the crystal in 2D. The nearest neighbor bond along the chain is visible,\n", + "and labeled `Bond(1, 1, [1, 0, 0])`. The first two atom indices must be 1,\n", + "because there is only a single atom in the chemical cell. The vector `[1, 0,\n", + "0]` indicates that the bond includes a displacement of $1 𝐚_1 + 0 𝐚_2 + 0\n", + "𝐚_3$ between chemical cells." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "view_crystal(cryst; ndims=2, ghost_radius=8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Sunny will always perform symmetry analysis based on the provided\n", + "crystallographic information. For example, one can see that there are three\n", + "different symmetry-equivalent classes of bonds up to a distance of 8 Å, and\n", + "the symmetry-allowed exchange matrices are strongly constrained." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "print_symmetry_table(cryst, 8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use the chemical cell to create a spin `System` with spin $s = 1$\n", + "and a magnetic form factor for Cu¹⁺. In this case, it is only necessary to\n", + "simulate a single chemical cell. The option `:dipole` indicates that,\n", + "following traditional spin wave theory, we are modeling quantum spins using\n", + "only their expected dipole moments." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Set a nearest neighbor exchange interaction of $J = -1$ meV between\n", + "neighboring atoms. That is, the total energy along each bond is $J S_i\n", + "S_{i+1}$. The exchange interaction will be propagated to all symmetry\n", + "equivalent bonds in the system." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "J = -1\n", + "set_exchange!(sys, J, Bond(1, 1, [1, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Find the energy minimum, which is ferromagnetic. The energy per site is $-J$\n", + "for this unfrustrated FM order." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "energy_per_site(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Because the interaction is Heisenberg (isotropic), the minimization procedure\n", + "selects an arbitrary direction in spin-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "plot_spins(sys; ndims=2, ghost_radius=8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build a `SpinWaveTheory` object to measure the dynamical spin-spin\n", + "structure factor (SSF). Select `ssf_perp` to project intensities onto\n", + "the space perpendicular to the momentum transfer $𝐪$, which is appropriate\n", + "for an unpolarized neutron beam." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define a path from $[0,0,0]$ to $[1,0,0]$ in reciprocal lattice units\n", + "(RLU) containing 400 sampled $𝐪$-points." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0,0,0], [1,0,0]]\n", + "path = q_space_path(cryst, qs, 400)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the intensities along this path." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Perform a powder average over the intensities for 200 radii between 0 and 2.5\n", + "inverse Å. Each radial distance defines a spherical shell in recripocal space,\n", + "which will be sampled approximately uniformly, involving 1000 sample points.\n", + "Measure intensities for 200 energy values between 0 and 5 meV. Gaussian\n", + "line-broadening is applied with a full-width at half-maximum (FWHM) of 0.1\n", + "meV. With the above parameters, this calculation takes about a second on a\n", + "modern laptop. To decrease stochastic error, one can increase the number of\n", + "sample points on each spherical shell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2.5, 200) # 1/Å\n", + "energies = range(0, 5, 200) # meV\n", + "kernel = gaussian(fwhm=0.1)\n", + "res = powder_average(cryst, radii, 1000) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW02_AFM_Heisenberg_chain.ipynb b/previews/PR319/assets/notebooks/SW02_AFM_Heisenberg_chain.ipynb new file mode 100644 index 000000000..fe1f84808 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW02_AFM_Heisenberg_chain.ipynb @@ -0,0 +1,162 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW02 - AFM Heisenberg chain\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "2](https://spinw.org/tutorials/02tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the antiferromagnetic\n", + "Heisenberg nearest-neighbor spin chain." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell for a 1D chain following the [previous tutorial](@ref\n", + "\"SW01 - FM Heisenberg chain\")." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(3, 8, 8, 90, 90, 90)\n", + "cryst = Crystal(latvecs, [[0, 0, 0]])\n", + "view_crystal(cryst; ndims=2, ghost_radius=8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Unlike in the previous tutorial, here the magnetic cell should include 2×1×1\n", + "chemical cells to support antiferromagnetic (Néel) order along the chain." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(2, 1, 1))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Set a nearest neighbor interaction of $J = +1$ meV along the chain, and find\n", + "the energy-minimizing Néel order. As before, a global rotation in spin-space\n", + "is arbitrary." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "J = 1\n", + "set_exchange!(sys, J, Bond(1, 1, [1, 0, 0]))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2, ghost_radius=8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Perform a `SpinWaveTheory` calculation for a path between $[0,0,0]$\n", + "and $[1,0,0]$ in RLU." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[0,0,0], [1,0,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "This system includes two bands that are fully degenerate in their dispersion." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "isapprox(res.disp[1, :], res.disp[2, :])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the intensities summed over the two degenerate bands using the [Makie\n", + "`lines` function](https://docs.makie.org/stable/reference/plots/lines)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "xs = [q[1] for q in path.qs]\n", + "ys = log10.(res.data[1, :] + res.data[2, :])\n", + "lines(xs, ys; axis=(; xlabel=\"[H, 0, 0]\", ylabel=\"Log intensity (dimensionless)\"))" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW03_Frustrated_chain.ipynb b/previews/PR319/assets/notebooks/SW03_Frustrated_chain.ipynb new file mode 100644 index 000000000..3c051042d --- /dev/null +++ b/previews/PR319/assets/notebooks/SW03_Frustrated_chain.ipynb @@ -0,0 +1,167 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW03 - Frustrated J1-J2 chain\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "3](https://spinw.org/tutorials/03tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the frustrated J1-J2\n", + "chain." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell for a 1D chain following the [SW01 tutorial](@ref\n", + "\"SW01 - FM Heisenberg chain\")." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(3, 8, 8, 90, 90, 90)\n", + "cryst = Crystal(latvecs, [[0, 0, 0]])\n", + "view_crystal(cryst; ndims=2, ghost_radius=8)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with competing nearest-neighbor (FM) and\n", + "next-nearest-neighbor (AFM) interactions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)\n", + "J1 = -1\n", + "J2 = +2 * abs(J1)\n", + "set_exchange!(sys, J1, Bond(1, 1, [1, 0, 0]))\n", + "set_exchange!(sys, J2, Bond(1, 1, [2, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Assuming a spiral order, optimize the propagation wavevector $𝐤$ starting\n", + "from a random initial guess. Because all interactions are isotropic in spin\n", + "space, the polarization `axis` is arbitrary." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "axis = [0, 0, 1]\n", + "randomize_spins!(sys)\n", + "k = minimize_spiral_energy!(sys, axis; k_guess=randn(3))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The first component of the order wavevector $𝐤$ has a unique value up to\n", + "reflection symmetry, $𝐤 → -𝐤$. The second and third components of $𝐤$\n", + "are arbitrary for this 1D chain system. In all cases, the minimized energy has\n", + "a precise value of -33/16 in units of $|J₁|$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "@assert k[1] ≈ 0.2300534561 || k[1] ≈ 1 - 0.2300534561\n", + "@assert spiral_energy_per_site(sys; k, axis) ≈ -33/16 * abs(J1)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To view part of the incommensurate spiral spin structure, one can construct an\n", + "enlarged system with `repeat_periodically_as_spiral`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys_enlarged = repeat_periodically_as_spiral(sys, (8, 1, 1); k, axis)\n", + "plot_spins(sys_enlarged; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `SpinWaveTheorySpiral` on the original `sys` to calculate the\n", + "dispersion and intensities for the incommensurate ordering wavevector." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheorySpiral(sys; measure=ssf_perp(sys), k, axis)\n", + "qs = [[0,0,0], [1,0,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW04_Frustrated_square.ipynb b/previews/PR319/assets/notebooks/SW04_Frustrated_square.ipynb new file mode 100644 index 000000000..92ad330ec --- /dev/null +++ b/previews/PR319/assets/notebooks/SW04_Frustrated_square.ipynb @@ -0,0 +1,112 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW04 - Frustrated square lattice\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "4](https://spinw.org/tutorials/04tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the frustrated square\n", + "lattice." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To model the 2D square lattice, create an elongated tetragonal cell with one\n", + "atom." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(3.0, 3.0, 6.0, 90, 90, 90)\n", + "cryst = Crystal(latvecs, [[0, 0, 0]])\n", + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with competing nearest-neighbor (AFM) and\n", + "next-nearest-neighbor (FM) interactions. The Néel magnetic order requires a\n", + "supercell of 2×2 chemical cells." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(2, 2, 1))\n", + "J1 = 1.0\n", + "J2 = -0.1\n", + "set_exchange!(sys, J1, Bond(1, 1, [1, 0, 0]))\n", + "set_exchange!(sys, J2, Bond(1, 1, [1, 1, 0]))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot intensities for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[0, 0, 0], [1/2, 0, 0], [1/2, 1/2, 0], [0, 0, 0]]\n", + "path = q_space_path(cryst, qs, 400);\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW05_Simple_kagome_FM.ipynb b/previews/PR319/assets/notebooks/SW05_Simple_kagome_FM.ipynb new file mode 100644 index 000000000..166cb4958 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW05_Simple_kagome_FM.ipynb @@ -0,0 +1,195 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW05 - Simple kagome ferromagnet\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "5](https://spinw.org/tutorials/05tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the kagome lattice\n", + "with a nearest-neighbor ferromagnetic coupling." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell. By specifying spacegroup 147 (P-3), Sunny will\n", + "propagate the position [1/2, 0, 0] to the three symmetry-equivalent sites of\n", + "the kagome unit cell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(6, 6, 5, 90, 90, 120)\n", + "positions = [[1/2, 0, 0]]\n", + "cryst = Crystal(latvecs, positions, 147)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Another way to construct the kagome lattice is to provide all three site\n", + "positions of the chemical cell, and allow Sunny to infer the largest possible\n", + "group of symmetry operations. In this case, Sunny infers spacegroup 191\n", + "(P6/mmm). Because 191 has more symmetry operations than 147, it will impose\n", + "more constraints on the allowed 3×3 exchange matrices. Isotropic Heisenberg\n", + "exchange, however, is always allowed." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "positions = [[1/2, 0, 0], [0, 1/2, 0], [1/2, 1/2, 0]]\n", + "cryst2 = Crystal(latvecs, positions)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "View the kagome lattice" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with nearest-neighbor ferromagnetic interactions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)\n", + "J = -1.0\n", + "set_exchange!(sys, J, Bond(2, 3, [0, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Energy minimization yields the expected ferromagnetic order. Each site\n", + "participates in 4 bonds, which contributes energy 4J/2." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "energy_per_site(sys)\n", + "@assert energy_per_site(sys) ≈ 4J/2\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot intensities for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[-1/2, 0, 0], [0, 0, 0], [1/2, 1/2, 0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the powder average with two different magnitudes of\n", + "Gaussian line-broadening. Pick an explicit intensity `colorrange` (as a\n", + "density in meV) so that the two color scales are consistent." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2.5, 200)\n", + "energies = range(0, 6.5, 200)\n", + "res1 = powder_average(cryst, radii, 1000) do qs\n", + " intensities(swt, qs; energies, kernel=gaussian(fwhm=0.02))\n", + "end\n", + "res2 = powder_average(cryst, radii, 1000) do qs\n", + " intensities(swt, qs; energies, kernel=gaussian(fwhm=0.25))\n", + "end\n", + "\n", + "fig = Figure(size=(768, 800))\n", + "plot_intensities!(fig[1, 1], res1; units, colorrange=(0,10), title=\"FWHM 0.02 meV\")\n", + "plot_intensities!(fig[2, 1], res2; units, colorrange=(0,10), title=\"FWHM 0.25 meV\")\n", + "fig" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW06_Complex_kagome_FM.ipynb b/previews/PR319/assets/notebooks/SW06_Complex_kagome_FM.ipynb new file mode 100644 index 000000000..e4f569fbe --- /dev/null +++ b/previews/PR319/assets/notebooks/SW06_Complex_kagome_FM.ipynb @@ -0,0 +1,174 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW06 - Complex kagome ferromagnet\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "6](https://spinw.org/tutorials/06tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the kagome lattice\n", + "with multiple competing interactions." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell of a kagome lattice with spacegroup 147 (P-3)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(6, 6, 8, 90, 90, 120)\n", + "cryst = Crystal(latvecs, [[1/2, 0, 0]], 147)\n", + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with strongly ferromagnetic nearest-neighbor\n", + "interactions, and two additional interactions. There are two\n", + "symmetry-inequivalent exchange types at distance 6 Å (3rd nearest neighbor).\n", + "The first type, associated with `J3a`, is a bond from atom 2 to atom 2 that\n", + "passes over atom 3. The second type, associated with `J3b`, is a bond from\n", + "atom 1 to atom 1 that passes through the center of an \"empty\" hexagon of the\n", + "kagome lattice." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)\n", + "J1 = -1.0\n", + "J2 = 0.1\n", + "J3a = 0.00\n", + "J3b = 0.17\n", + "set_exchange!(sys, J1, Bond(2, 3, [0, 0, 0]))\n", + "set_exchange!(sys, J2, Bond(2, 1, [0, 0, 0]))\n", + "set_exchange!(sys, J3a, Bond(2, 2, [1, 0, 0]))\n", + "set_exchange!(sys, J3b, Bond(1, 1, [1, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Interactively visualize the specified interactions. Red (blue) color indicates\n", + "FM (AFM)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "view_crystal(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Energy minimization favors ferromagnetic order." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot intensities for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the powder averaged spectrum. Select an empirical\n", + "`colorrange` that brings the lower-intensity features into focus." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2.5, 200)\n", + "energies = range(0, 6.5, 200)\n", + "kernel = gaussian(fwhm=0.02)\n", + "res = powder_average(cryst, radii, 1000) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units, colorrange=(0,10))" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW07_k0_kagome_AFM.ipynb b/previews/PR319/assets/notebooks/SW07_k0_kagome_AFM.ipynb new file mode 100644 index 000000000..bd0dc3798 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW07_k0_kagome_AFM.ipynb @@ -0,0 +1,135 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW07 - k=0 kagome antiferromagnet\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "7](https://spinw.org/tutorials/07tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the kagome lattice\n", + "with antiferromagnetic interactions, with ordering wavevector of $𝐤 = 0$,\n", + "and relative rotation 120° between sublattices" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell of a kagome lattice with spacegroup 147 (P-3)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(6, 6, 8, 90, 90, 120)\n", + "cryst = Crystal(latvecs, [[1/2, 0, 0]], 147)\n", + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with nearest and next-nearest neighbor\n", + "antiferromagnetic interactions. Energy minimization determines a $𝐤 = 0$\n", + "magnetic order with 120° rotation between the three sublattices. The overall\n", + "global rotation in spin-space is arbitrary." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)\n", + "J1 = 1.0\n", + "J2 = 0.11\n", + "set_exchange!(sys, J1, Bond(2, 3, [0, 0, 0]))\n", + "set_exchange!(sys, J2, Bond(2, 1, [0, 0, 0]))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot intensities for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the powder averaged spectrum" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2.5, 200)\n", + "energies = range(0, 2.5, 200)\n", + "kernel = gaussian(fwhm=0.02)\n", + "res = powder_average(cryst, radii, 1000) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW08_sqrt3_kagome_AFM.ipynb b/previews/PR319/assets/notebooks/SW08_sqrt3_kagome_AFM.ipynb new file mode 100644 index 000000000..20d12e09a --- /dev/null +++ b/previews/PR319/assets/notebooks/SW08_sqrt3_kagome_AFM.ipynb @@ -0,0 +1,179 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW08 - √3×√3 kagome antiferromagnet\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "8](https://spinw.org/tutorials/08tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the linear spin wave theory spectrum for the\n", + "$\\sqrt{3} \\times \\sqrt{3}$ order of a kagome antiferromagnet." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell of a kagome lattice with spacegroup 147 (P-3)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(6, 6, 40, 90, 90, 120)\n", + "cryst = Crystal(latvecs, [[1/2, 0, 0]], 147)\n", + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with nearest neighbor antiferromagnetic exchange." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)\n", + "J = 1.0\n", + "set_exchange!(sys, J, Bond(2, 3, [0, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Initialize to an energy minimizing magnetic structure, for which\n", + "nearest-neighbor spins are at 120° angles." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "set_dipole!(sys, [cos(0), sin(0), 0], (1, 1, 1, 1))\n", + "set_dipole!(sys, [cos(0), sin(0), 0], (1, 1, 1, 2))\n", + "set_dipole!(sys, [cos(2π/3), sin(2π/3), 0], (1, 1, 1, 3))\n", + "k = [-1/3, -1/3, 0]\n", + "axis = [0, 0, 1]\n", + "sys_enlarged = repeat_periodically_as_spiral(sys, (3, 3, 1); k, axis)\n", + "plot_spins(sys_enlarged; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Check energy per site. Each site participates in 4 bonds with energy\n", + "$J\\cos(2π/3)$. Factor of 1/2 avoids double counting. The two calculation\n", + "methods agree." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "@assert energy_per_site(sys_enlarged) ≈ (4/2)*J*cos(2π/3)\n", + "@assert spiral_energy_per_site(sys; k, axis) ≈ (4/2)*J*cos(2π/3)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot intensities for a path through $𝐪$-space using two\n", + "calculation methods. The two methods agree in intensity, but the \"supercell\n", + "method\" gives rise to ghost modes in the dispersion that have zero intensity." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "\n", + "fig = Figure(size=(768, 300))\n", + "swt = SpinWaveTheory(sys_enlarged; measure=ssf_perp(sys_enlarged))\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities!(fig[1, 1], res; units, saturation=0.5,title=\"Supercell method\")\n", + "swt = SpinWaveTheorySpiral(sys; measure=ssf_perp(sys), k, axis)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities!(fig[1, 2], res; units, saturation=0.5, title=\"Spiral method\")\n", + "fig" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the powder averaged spectrum. Continuing to use the \"spiral\n", + "method\", this calculation executes in about two seconds. Because the\n", + "intensities are dominated by a flat band at zero energy transfer, select an\n", + "empirical `colorrange` that brings the lower-intensity features into focus." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2.5, 200)\n", + "energies = range(0, 3, 200)\n", + "kernel = gaussian(fwhm=0.05)\n", + "res = powder_average(cryst, radii, 200) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units, colorrange=(0,20))" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW09_k0_kagome_AFM_DM.ipynb b/previews/PR319/assets/notebooks/SW09_k0_kagome_AFM_DM.ipynb new file mode 100644 index 000000000..81b351855 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW09_k0_kagome_AFM_DM.ipynb @@ -0,0 +1,155 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW09 - k=0 kagome AFM and DM\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "9](https://spinw.org/tutorials/09tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. It calculates the spin wave spectrum of the kagome lattice\n", + "with antiferromagnetic and DM interactions, with ordering wavevector of $𝐤 =\n", + "0$, and relative rotation 120° between sublattices" + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie, LinearAlgebra" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell of a kagome lattice with spacegroup 147 (P-3)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(6, 6, 8, 90, 90, 120)\n", + "cryst = Crystal(latvecs, [[1/2, 0, 0]], 147)\n", + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with antiferromagnetic exchange and a\n", + "Dzyaloshinskii-Moriya interaction along the first neighbor bond. The symbol\n", + "`I` comes from Julia's LinearAlgebra package, and is used to promote the\n", + "scalar exchange strength 1 meV to a 3×3 exchange matrix. The function\n", + "`dmvec` promotes the DM interaction vector $[0, 0, -0.08]$ meV to a\n", + "3×3 antisymmetric matrix with nonzero $(x,y)$ components, defined with\n", + "respect to the global Cartesian coordinate system." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole)\n", + "J = 1.0*I + dmvec([0, 0, -0.08])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "As in in Tutorial 7, energy\n", + "minimization determines a $𝐤 = 0$ magnetic order with 120° rotation between\n", + "the three sublattices." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "set_exchange!(sys, J, Bond(2, 3, [0, 0, 0]))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot intensities for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot the powder averaged spectrum. Because the intensities are\n", + "dominated by a flat band at about 0.97 meV, select an empirical `colorrange`\n", + "that brings the lower-intensity features into focus." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2.5, 200)\n", + "energies = range(0, 2.5, 200)\n", + "kernel = gaussian(fwhm=0.02)\n", + "res = powder_average(cryst, radii, 1000) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units, colorrange=(0,20))" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW10_Energy_cut.ipynb b/previews/PR319/assets/notebooks/SW10_Energy_cut.ipynb new file mode 100644 index 000000000..0a7446080 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW10_Energy_cut.ipynb @@ -0,0 +1,141 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW10 - Energy cut on square lattice\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "10](https://spinw.org/tutorials/10tutorial), originally authored by Sandor\n", + "Toth. It calculates the spin wave spectrum on a constant energy cut of the\n", + "frustrated square lattice." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load Sunny and the GLMakie plotting package" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the chemical cell for the 2D square lattice." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(1.0, 1.0, 3.0, 90, 90, 90)\n", + "cryst = Crystal(latvecs, [[0, 0, 0]])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Construct a spin system with nearest-neighbor antiferomagnetic interactions of\n", + "1.0 meV. Energy minimization yields the expected Néel order on the 2×2\n", + "magnetic cell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(2, 2, 1))\n", + "set_exchange!(sys, 1.0, Bond(1, 1, [1, 0, 0]))\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define a 2D slice through $𝐪$-space with `q_space_grid`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "grid = q_space_grid(cryst, [1, 0, 0], range(0, 2, 201), [0, 1, 0], range(0, 2, 201))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate and plot a constant energy cut at the precise value of 3.75 meV.\n", + "Apply a line broadening with a full-width half-max of 0.2 meV to approximately\n", + "capture intensities between 3.5 and 4.0 meV." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "res = intensities(swt, grid; energies=[3.75], kernel=gaussian(fwhm=0.2))\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Integrate intensities between 3.5 and 4 meV using `intensities_static`\n", + "with the `bounds` option." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "res = intensities_static(swt, grid; bounds=(3.5, 4.01))\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW11_La2CuO4.ipynb b/previews/PR319/assets/notebooks/SW11_La2CuO4.ipynb new file mode 100644 index 000000000..bb8f5e7d8 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW11_La2CuO4.ipynb @@ -0,0 +1,151 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW11 - La₂CuO₄\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "11](https://spinw.org/tutorials/11tutorial), originally authored by Sandor\n", + "Toth. It calculates the spin wave spectrum of La₂CuO₄." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load packages" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build a square lattice for the the Cu²⁺ atoms. The lattice constant 1 Å is\n", + "selected arbitrarily." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(1, 1, 10, 90, 90, 90)\n", + "positions = [[0, 0, 0]]\n", + "types = [\"Cu\"]\n", + "cryst = Crystal(latvecs, positions; types)\n", + "view_crystal(cryst; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build a spin system using the exchange parameters from [R. Coldea, Phys. Rev.\n", + "Lett. **86**, 5377 (2001)](https://doi.org/10.1103/PhysRevLett.86.5377)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1/2, g=2)], :dipole; dims=(2, 2, 1))\n", + "J = 138.3\n", + "Jp = 2\n", + "Jpp = 2\n", + "Jc = 38\n", + "set_exchange!(sys, J-Jc/2, Bond(1, 1, [1, 0, 0]))\n", + "set_exchange!(sys, Jp-Jc/4, Bond(1, 1, [1, 1, 0]))\n", + "set_exchange!(sys, Jpp, Bond(1, 1, [2, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Energy minimization yields the expected Néel order" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the spin wave spectrum for a path through $𝐪$-space. Apply a manual\n", + "\"quantum correction\" that adjusts energy scale by the factor 1.18." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[3/4,1/4,0], [1/2, 1/2, 0], [1/2, 0, 0], [3/4, 1/4, 0], [1,0,0], [1/2 0 0]]\n", + "labels = [\"P\", \"M\", \"X\", \"P\", \"Γ\", \"X\"]\n", + "path = q_space_path(cryst, qs, 400; labels)\n", + "energies = range(0, 320, 400)\n", + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "res = intensities(swt, path; energies, kernel=gaussian(fwhm=35))\n", + "res.energies .*= 1.18\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot instantaneous itensities, integrated over ω." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "res = intensities_static(swt, path)\n", + "plot_intensities(res; colorrange=(0,20), units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW12_Triangular_easy_plane.ipynb b/previews/PR319/assets/notebooks/SW12_Triangular_easy_plane.ipynb new file mode 100644 index 000000000..436599f40 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW12_Triangular_easy_plane.ipynb @@ -0,0 +1,177 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW12 - Triangular lattice with easy plane\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "12](https://spinw.org/tutorials/12tutorial), originally authored by Sandor\n", + "Toth. It calculates the spin wave dispersion of a triangular lattice model\n", + "with antiferromagnetic interactions and easy-plane single-ion anisotropy." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load packages" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build a triangular lattice with arbitrary lattice constant of 3 Å." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "latvecs = lattice_vectors(3, 3, 4, 90, 90, 120)\n", + "cryst = Crystal(latvecs, [[0, 0, 0]])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build a system with exchange +1 meV along nearest neighbor bonds. Set the\n", + "lattice size in anticipation of a magnetic ordering with 3×3 cells." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "s = 3/2\n", + "J1 = +1.0\n", + "sys = System(cryst, [1 => Moment(; s, g=2)], :dipole; dims=(3, 3, 1))\n", + "set_exchange!(sys, J1, Bond(1, 1, [1, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Set an easy-axis anisotropy operator $+D S_z^2$ using\n", + "`set_onsite_coupling!`. **Important note**: When introducing a\n", + "single-ion anisotropy in `:dipole` mode, Sunny will automatically include a\n", + "classical-to-quantum correction factor, as described in the document\n", + "Interaction Renormalization. For an anisotropy operator that is\n", + "quadratic in the spin operators, Sunny will automatically renormalize the\n", + "interaction strength as $D → (1 - 1/2s) D$. We must \"undo\" Sunny's\n", + "classical-to-quantum rescaling factor to reproduce the SpinW calculation.\n", + "Alternatively, renormalization can be disabled by selecting the system mode\n", + "`:dipole_large_s` instead of `:dipole`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "undo_classical_to_quantum_rescaling = 1 / (1 - 1/2s)\n", + "D = 0.2 * undo_classical_to_quantum_rescaling\n", + "set_onsite_coupling!(sys, S -> D*S[3]^2, 1)\n", + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the spin wave spectrum for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0, 0, 0], [1, 1, 0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "To select a specific linear combination of spin structure factor (SSF)\n", + "components in global Cartesian coordinates, one can use `ssf_custom`.\n", + "Here we calculate and plot the real part of $\\mathcal{S}^{zz}(𝐪, ω)$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "measure = ssf_custom(sys) do q, ssf\n", + " return real(ssf[3, 3])\n", + "end\n", + "swt = SpinWaveTheory(sys; measure)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "It's also possible to get data for the full 3×3 SSF. For example, this is the\n", + "SSF for the 7th energy band, at the 10th $𝐪$-point along the path." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "measure = ssf_custom((q, ssf) -> ssf, sys)\n", + "swt = SpinWaveTheory(sys; measure)\n", + "res = intensities_bands(swt, path)\n", + "res.data[7, 10]" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW13_LiNiPO4.ipynb b/previews/PR319/assets/notebooks/SW13_LiNiPO4.ipynb new file mode 100644 index 000000000..499077578 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW13_LiNiPO4.ipynb @@ -0,0 +1,203 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW13 - LiNiPO₄\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "13](https://spinw.org/tutorials/13tutorial), originally authored by Sandor\n", + "Toth. It calculates the spin wave spectrum of LiNiPO₄." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load packages" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build an orthorhombic lattice and populate the Ni atoms according to\n", + "spacegroup 62 (Pnma)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "a = 10.02\n", + "b = 5.86\n", + "c = 4.68\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 90)\n", + "positions = [[1/4, 1/4, 0]]\n", + "types = [\"Ni\"]\n", + "cryst = Crystal(latvecs, positions, 62, setting=\"\"; types)\n", + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a system with exchange parameters taken from [T. Jensen, et al., PRB\n", + "**79**, 092413 (2009)](https://doi.org/10.1103/PhysRevB.79.092413). The\n", + "corrected anisotropy values are taken from the thesis of T. Jensen. The mode\n", + "`:dipole_large_s` avoids a [classical-to-quantum rescaling factor](@ref\n", + "\"Interaction Renormalization\") of anisotropy strengths, as needed for\n", + "consistency with the original fits." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "S = 3/2\n", + "sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole_large_s)\n", + "Jbc = 1.036\n", + "Jb = 0.6701\n", + "Jc = -0.0469\n", + "Jac = -0.1121\n", + "Jab = 0.2977\n", + "Da = 0.1969\n", + "Db = 0.9097\n", + "set_exchange!(sys, Jbc, Bond(2, 3, [0, 0, 0]))\n", + "set_exchange!(sys, Jc, Bond(1, 1, [0, 0, -1]))\n", + "set_exchange!(sys, Jb, Bond(1, 1, [0, 1, 0]))\n", + "set_exchange!(sys, Jab, Bond(1, 2, [0, 0, 0]))\n", + "set_exchange!(sys, Jab, Bond(3, 4, [0, 0, 0]))\n", + "set_exchange!(sys, Jac, Bond(3, 1, [0, 0, 0]))\n", + "set_exchange!(sys, Jac, Bond(4, 2, [0, 0, 0]))\n", + "set_onsite_coupling!(sys, S -> Da*S[1]^2 + Db*S[2]^2, 1)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Energy minimization yields a co-linear order along the $c$ axis." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys; color=[S[3] for S in sys.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate the spectrum along path [ξ, 1, 0]" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[0, 1, 0], [2, 1, 0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "fig = Figure(size=(768, 300))\n", + "plot_intensities!(fig[1, 1], res; units);" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "There are two physical bands with nonvanishing intensity. To extract these\n", + "intensity curves, we must filter out the additional bands with zero intensity.\n", + "One way is to sort the data along dimension 1 (the band index) with the\n", + "comparison operator \"is intensity less than $10^{-12}$\". Doing so moves the\n", + "physical bands to the end of the array axis. Call the [Makie `lines!`\n", + "function](https://docs.makie.org/stable/reference/plots/lines) to make a\n", + "custom plot." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "data_sorted = sort(res.data; dims=1, by= >(1e-12))\n", + "ax = Axis(fig[1, 2], xlabel=\"Momentum (r.l.u.)\", ylabel=\"Intensity\",\n", + " xticks=res.qpts.xticks, xticklabelrotation=π/6)\n", + "lines!(ax, data_sorted[end, :]; label=\"Lower band\")\n", + "lines!(ax, data_sorted[end-1, :]; label=\"Upper band\")\n", + "axislegend(ax)\n", + "fig" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Make the same plots along path [0, 1, ξ]" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0, 1, 0], [0, 1, 2]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "fig = Figure(size=(768, 300))\n", + "plot_intensities!(fig[1, 1], res; units)\n", + "\n", + "data_sorted = sort(res.data; dims=1, by=x->abs(x)>1e-12)\n", + "ax = Axis(fig[1, 2], xlabel=\"Momentum (r.l.u.)\", ylabel=\"Intensity\",\n", + " xticks=res.qpts.xticks, xticklabelrotation=π/6)\n", + "lines!(ax, data_sorted[end, :]; label=\"Lower band\")\n", + "lines!(ax, data_sorted[end-1, :]; label=\"Upper band\")\n", + "axislegend(ax)\n", + "fig" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW14_YVO3.ipynb b/previews/PR319/assets/notebooks/SW14_YVO3.ipynb new file mode 100644 index 000000000..698f85492 --- /dev/null +++ b/previews/PR319/assets/notebooks/SW14_YVO3.ipynb @@ -0,0 +1,166 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW14 - YVO₃\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "14](https://spinw.org/tutorials/14tutorial), originally authored by Sandor\n", + "Toth. It calculates the spin wave spectrum of YVO₃." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load packages" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build an orthorhombic lattice and populate the V atoms according to the\n", + "pseudocubic unit cell, doubled along the c-axis. The listed spacegroup of the\n", + "YVO₃ chemical cell is international number 62. It has been observed, however,\n", + "that the exchange interactions break this symmetry. For this reason, disable\n", + "all symmetry analysis by selecting spacegroup 1 (P1)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "a = 5.2821 / sqrt(2)\n", + "b = 5.6144 / sqrt(2)\n", + "c = 7.5283\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 90)\n", + "positions = [[0, 0, 0], [0, 0, 1/2]]\n", + "types = [\"V\", \"V\"]\n", + "cryst = Crystal(latvecs, positions, 1; types)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a system following the model of [C. Ulrich, et al. PRL **91**, 257202\n", + "(2003)](https://doi.org/10.1103/PhysRevLett.91.257202). The mode\n", + "`:dipole_large_s` avoids a [classical-to-quantum rescaling factor](@ref\n", + "\"Interaction Renormalization\") of anisotropy strengths, as needed for\n", + "consistency with the original fits." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=1/2, g=2), 2 => Moment(s=1/2, g=2)], :dipole_large_s; dims=(2,2,1))\n", + "Jab = 2.6\n", + "Jc = 3.1\n", + "δ = 0.35\n", + "K1 = 0.90\n", + "K2 = 0.97\n", + "d = 1.15\n", + "Jc1 = [-Jc*(1+δ)+K2 0 -d; 0 -Jc*(1+δ) 0; +d 0 -Jc*(1+δ)]\n", + "Jc2 = [-Jc*(1-δ)+K2 0 +d; 0 -Jc*(1-δ) 0; -d 0 -Jc*(1-δ)]\n", + "set_exchange!(sys, Jab, Bond(1, 1, [1, 0, 0]))\n", + "set_exchange!(sys, Jab, Bond(2, 2, [1, 0, 0]))\n", + "set_exchange!(sys, Jc1, Bond(1, 2, [0, 0, 0]))\n", + "set_exchange!(sys, Jc2, Bond(2, 1, [0, 0, 1]))\n", + "set_exchange!(sys, Jab, Bond(1, 1, [0, 1, 0]))\n", + "set_exchange!(sys, Jab, Bond(2, 2, [0, 1, 0]))\n", + "set_onsite_coupling!(sys, S -> -K1*S[1]^2, 1)\n", + "set_onsite_coupling!(sys, S -> -K1*S[1]^2, 2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "When using spacegroup P1, there is no symmetry-propagation of interactions\n", + "because all bonds are considered inequivalent. One can visualize the\n", + "interactions in the system by clicking the toggles in the\n", + "`view_crystal` GUI." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "view_crystal(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Energy minimization yields a Néel order with canting" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the spin wave spectrum along a path" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n", + "qs = [[0.75, 0.75, 0], [0.5, 0.5, 0], [0.5, 0.5, 1]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW15_Ba3NbFe3Si2O14.ipynb b/previews/PR319/assets/notebooks/SW15_Ba3NbFe3Si2O14.ipynb new file mode 100644 index 000000000..a7b45831c --- /dev/null +++ b/previews/PR319/assets/notebooks/SW15_Ba3NbFe3Si2O14.ipynb @@ -0,0 +1,233 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW15 - Ba₃NbFe₃Si₂O₁₄\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "15](https://spinw.org/tutorials/15tutorial), originally authored by Sandor\n", + "Toth. It calculates the linear spin wave theory spectrum of Ba₃NbFe₃Si₂O₁₄." + ], + "metadata": {} + }, + { + "cell_type": "markdown", + "source": [ + "Load packages" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Specify the Ba₃NbFe₃Si₂O₁₄ `Crystal` cell following [Marty et al.,\n", + "Phys. Rev. Lett. **101**, 247201\n", + "(2008)](http://dx.doi.org/10.1103/PhysRevLett.101.247201)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "a = b = 8.539 # (Å)\n", + "c = 5.2414\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 120)\n", + "types = [\"Fe\", \"Nb\", \"Ba\", \"Si\", \"O\", \"O\", \"O\"]\n", + "positions = [[0.24964,0,0.5], [0,0,0], [0.56598,0,0], [2/3,1/3,0.5220],\n", + " [2/3,1/3,0.2162], [0.5259,0.7024,0.3536], [0.7840,0.9002,0.7760]]\n", + "langasite = Crystal(latvecs, positions, 150; types)\n", + "cryst = subcrystal(langasite, \"Fe\")\n", + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Create a `System` and set exchange interactions as parametrized in\n", + "[Loire et al., Phys. Rev. Lett. **106**, 207201\n", + "(2011)](http://dx.doi.org/10.1103/PhysRevLett.106.207201)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys = System(cryst, [1 => Moment(s=5/2, g=2)], :dipole; seed=0)\n", + "J₁ = 0.85\n", + "J₂ = 0.24\n", + "J₃ = 0.053\n", + "J₄ = 0.017\n", + "J₅ = 0.24\n", + "set_exchange!(sys, J₁, Bond(3, 2, [1,1,0]))\n", + "set_exchange!(sys, J₄, Bond(1, 1, [0,0,1]))\n", + "set_exchange!(sys, J₂, Bond(1, 3, [0,0,0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "The final two exchanges are setting according to the desired chirality $ϵ_T$\n", + "of the magnetic structure." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "ϵT = -1\n", + "if ϵT == -1\n", + " set_exchange!(sys, J₃, Bond(2, 3, [-1,-1,1]))\n", + " set_exchange!(sys, J₅, Bond(3, 2, [1,1,1]))\n", + "elseif ϵT == 1\n", + " set_exchange!(sys, J₅, Bond(2, 3, [-1,-1,1]))\n", + " set_exchange!(sys, J₃, Bond(3, 2, [1,1,1]))\n", + "else\n", + " error(\"Chirality must be ±1\")\n", + "end" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "This compound is known to have a spiral order with approximate propagation\n", + "wavevector $𝐤 ≈ [0, 0, 1/7]$. Search for this magnetic order with\n", + "`minimize_spiral_energy!`. Due to reflection symmetry, one of two\n", + "possible propagation wavevectors may appear, $𝐤 = ± [0, 0, 0.1426…]$.\n", + "Note that $k_z = 0.1426…$ is very close to $1/7 = 0.1428…$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "axis = [0, 0, 1]\n", + "randomize_spins!(sys)\n", + "k = minimize_spiral_energy!(sys, axis)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "We can visualize the full magnetic cell using `repeat_periodically_as_spiral`,\n", + "which includes 7 rotated copies of the chemical cell." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "sys_enlarged = repeat_periodically_as_spiral(sys, (1, 1, 7); k, axis)\n", + "plot_spins(sys_enlarged; color=[S[1] for S in sys_enlarged.dipoles])" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "One could perform a spin wave calculation using either\n", + "`SpinWaveTheory` on `sys_enlarged`, or `SpinWaveTheorySpiral`\n", + "on the original `sys`. The latter has some restrictions on the interactions,\n", + "but allows for our slightly incommensurate wavevector $𝐤$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "measure = ssf_perp(sys)\n", + "swt = SpinWaveTheorySpiral(sys; measure, k, axis)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate broadened intensities for a path $[0, 1, L]$ through reciprocal\n", + "space" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0, 1, -1], [0, 1, -1+1], [0, 1, -1+2], [0, 1, -1+3]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "energies = range(0, 6, 400)\n", + "res = intensities(swt, path; energies, kernel=gaussian(fwhm=0.25))\n", + "plot_intensities(res; units, saturation=0.7, colormap=:jet, title=\"Scattering intensities\")" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `ssf_custom_bm` to calculate the imaginary part of\n", + "$\\mathcal{S}^{2, 3}(𝐪, ω) - \\mathcal{S}^{3, 2}(𝐪, ω)$. In polarized\n", + "neutron scattering, it is conventional to express the 3×3 structure factor\n", + "matrix $\\mathcal{S}^{α, β}(𝐪, ω)$ in the Blume-Maleev polarization axis\n", + "system. Specify the scattering plane $[0, K, L]$ via the spanning vectors\n", + "$𝐮 = [0, 1, 0]$ and $𝐯 = [0, 0, 1]$." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "measure = ssf_custom_bm(sys; u=[0, 1, 0], v=[0, 0, 1]) do q, ssf\n", + " imag(ssf[2,3] - ssf[3,2])\n", + "end\n", + "swt = SpinWaveTheorySpiral(sys; measure, k, axis)\n", + "res = intensities(swt, path; energies, kernel=gaussian(fwhm=0.25))\n", + "plot_intensities(res; units, saturation=0.8, allpositive=false,\n", + " title=\"Im[S²³(q, ω) - S³²(q, ω)]\")" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW18_Distorted_kagome.ipynb b/previews/PR319/assets/notebooks/SW18_Distorted_kagome.ipynb new file mode 100644 index 000000000..1477af2ed --- /dev/null +++ b/previews/PR319/assets/notebooks/SW18_Distorted_kagome.ipynb @@ -0,0 +1,238 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW18 - Distorted kagome\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "18](https://spinw.org/tutorials/18tutorial), originally authored by Goran\n", + "Nilsen and Sandor Toth. This tutorial illustrates spin wave calculations for\n", + "KCu₃As₂O₇(OD)₃. The Cu ions are arranged in a distorted kagome lattice, and\n", + "exhibit an incommensurate helical magnetic order, as described in [G. J.\n", + "Nilsen, et al., Phys. Rev. B **89**, 140412\n", + "(2014)](https://doi.org/10.1103/PhysRevB.89.140412). The model follows [Toth\n", + "and Lake, J. Phys.: Condens. Matter **27**, 166002\n", + "(2015)](https://arxiv.org/abs/1402.6069)." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build the distorted kagome crystal, with spacegroup 12." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "latvecs = lattice_vectors(10.2, 5.94, 7.81, 90, 117.7, 90)\n", + "positions = [[0, 0, 0], [1/4, 1/4, 0]]\n", + "types = [\"Cu1\", \"Cu2\"]\n", + "cryst = Crystal(latvecs, positions, 12; types, setting=\"b1\")\n", + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define the interactions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "moments = [1 => Moment(s=1/2, g=2), 3 => Moment(s=1/2, g=2)]\n", + "sys = System(cryst, moments, :dipole, seed=0)\n", + "J = -2\n", + "Jp = -1\n", + "Jab = 0.75\n", + "Ja = -J/.66 - Jab\n", + "Jip = 0.01\n", + "set_exchange!(sys, J, Bond(1, 3, [0, 0, 0]))\n", + "set_exchange!(sys, Jp, Bond(3, 5, [0, 0, 0]))\n", + "set_exchange!(sys, Ja, Bond(3, 4, [0, 0, 0]))\n", + "set_exchange!(sys, Jab, Bond(1, 2, [0, 0, 0]))\n", + "set_exchange!(sys, Jip, Bond(3, 4, [0, 0, 1]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Use `minimize_spiral_energy!` to optimize the generalized spiral\n", + "order. This determines the propagation wavevector `k`, and fits the spin\n", + "values within the unit cell. One must provide a fixed `axis` perpendicular to\n", + "the polarization plane. For this system, all interactions are rotationally\n", + "invariant, and the `axis` vector is arbitrary. In other cases, a good `axis`\n", + "will frequently be determined from symmetry considerations." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "axis = [0, 0, 1]\n", + "randomize_spins!(sys)\n", + "k = minimize_spiral_energy!(sys, axis; k_guess=randn(3))\n", + "plot_spins(sys; ndims=2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "If successful, the optimization process will find one two propagation\n", + "wavevectors, `±k_ref`, with opposite chiralities. In this system, the\n", + "`spiral_energy_per_site` is independent of chirality." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "k_ref = [0.785902495, 0.0, 0.107048756]\n", + "k_ref_alt = [1, 0, 1] - k_ref\n", + "@assert isapprox(k, k_ref; atol=1e-6) || isapprox(k, k_ref_alt; atol=1e-6)\n", + "@assert spiral_energy_per_site(sys; k, axis) ≈ -0.78338383838" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Check the energy with a real-space calculation using a large magnetic cell.\n", + "First, we must determine a lattice size for which k becomes approximately\n", + "commensurate." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "suggest_magnetic_supercell([k_ref]; tol=1e-3)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Resize the system as suggested, and perform a real-space calculation. Working\n", + "with a commensurate wavevector increases the energy slightly. The precise\n", + "value might vary from run-to-run due to trapping in a local energy minimum." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "new_shape = [14 0 1; 0 1 0; 0 0 2]\n", + "sys2 = reshape_supercell(sys, new_shape)\n", + "randomize_spins!(sys2)\n", + "minimize_energy!(sys2)\n", + "energy_per_site(sys2)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Return to the original system (with a single chemical cell) and construct\n", + "`SpinWaveTheorySpiral` for calculations on the incommensurate spiral\n", + "phase." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "measure = ssf_perp(sys; apply_g=false)\n", + "swt = SpinWaveTheorySpiral(sys; measure, k, axis)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot intensities for a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0,0,0], [1,0,0]]\n", + "path = q_space_path(cryst, qs, 400)\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot the powder-averaged intensities" + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "radii = range(0, 2, 100) # (1/Å)\n", + "energies = range(0, 6, 200)\n", + "kernel = gaussian(fwhm=0.05)\n", + "res = powder_average(cryst, radii, 400) do qs\n", + " intensities(swt, qs; energies, kernel)\n", + "end\n", + "plot_intensities(res; units)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/notebooks/SW19_Different_Ions.ipynb b/previews/PR319/assets/notebooks/SW19_Different_Ions.ipynb new file mode 100644 index 000000000..c23d053cc --- /dev/null +++ b/previews/PR319/assets/notebooks/SW19_Different_Ions.ipynb @@ -0,0 +1,180 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "source": [ + "# SW19 - Different magnetic ions\n", + "\n", + "This is a Sunny port of [SpinW Tutorial\n", + "19](https://spinw.org/tutorials/19tutorial), originally authored by Bjorn Fak\n", + "and Sandor Toth. This tutorial illustrates how to eliminate magnetic\n", + "contributions from a subset of ions via the special value `zero(FormFactor)`." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "using Sunny, GLMakie" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Build a crystal with Cu²⁺ and Fe²⁺ ions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "units = Units(:meV, :angstrom)\n", + "a = 3.0\n", + "b = 8.0\n", + "c = 4.0\n", + "latvecs = lattice_vectors(a, b, c, 90, 90, 90)\n", + "positions = [[0, 0, 0], [0, 1/2, 0]]\n", + "types = [\"Cu2\", \"Fe2\"]\n", + "cryst = Crystal(latvecs, positions, 1; types)\n", + "view_crystal(cryst)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Set exchange interactions." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "J_Cu_Cu = 1.0\n", + "J_Fe_Fe = 1.0\n", + "J_Cu_Fe = -0.1\n", + "moments = [1 => Moment(s=1/2, g=2), 2 => Moment(s=2, g=2)]\n", + "sys = System(cryst, moments, :dipole; dims=(2, 1, 1), seed=0)\n", + "set_exchange!(sys, J_Cu_Cu, Bond(1, 1, [-1, 0, 0]))\n", + "set_exchange!(sys, J_Fe_Fe, Bond(2, 2, [-1, 0, 0]))\n", + "set_exchange!(sys, J_Cu_Fe, Bond(2, 1, [0, 1, 0]))\n", + "set_exchange!(sys, J_Cu_Fe, Bond(1, 2, [0, 0, 0]))" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Find and plot a minimum energy configuration." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "randomize_spins!(sys)\n", + "minimize_energy!(sys)\n", + "plot_spins(sys)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Define a path through $𝐪$-space." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "qs = [[0,0,0], [1,0,0]]\n", + "path = q_space_path(cryst, qs, 400)" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Plot different pair correlation intensities by varying the\n", + "`FormFactor` on different atom types. Indices 1 and 2 refer to atoms\n", + "in the original chemical, and are propagated by symmetry. The special \"zero\"\n", + "form factor effectively removes the spin moment from the calculation." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "fig = Figure(size=(768,600))\n", + "\n", + "formfactors = [1 => FormFactor(\"Cu2\"), 2 => FormFactor(\"Fe2\")]\n", + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys; formfactors))\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities!(fig[1, 1], res; units, title=\"All correlations\")\n", + "\n", + "formfactors = [1 => FormFactor(\"Cu2\"), 2 => zero(FormFactor)]\n", + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys; formfactors))\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities!(fig[1, 2], res; units, title=\"Cu-Cu correlations\")\n", + "\n", + "formfactors = [1 => zero(FormFactor), 2 => FormFactor(\"Fe2\")]\n", + "swt = SpinWaveTheory(sys; measure=ssf_perp(sys; formfactors))\n", + "res = intensities_bands(swt, path)\n", + "plot_intensities!(fig[2, 2], res; units, title=\"Fe-Fe correlations\")\n", + "\n", + "fig" + ], + "metadata": {}, + "execution_count": null + }, + { + "cell_type": "markdown", + "source": [ + "Calculate quantum corrections $δS$ to spin magnitude, which arise from the\n", + "zero-point energy of the spin waves. The outputs are ordered following the\n", + "`Site` indexing scheme for the system `sys`: `(cell1, cell2, cell3,\n", + "sublattice)`, with left-most indices fastest. The two corrections $δS ≈\n", + "-0.137$ and $δS ≈ -0.578$ apply to the Cu and Fe ions, respectively. The\n", + "larger correction on Fe is due to the relatively weak interchain coupling." + ], + "metadata": {} + }, + { + "outputs": [], + "cell_type": "code", + "source": [ + "Sunny.magnetization_lswt_correction_dipole(swt; atol=1e-4)" + ], + "metadata": {}, + "execution_count": null + } + ], + "nbformat_minor": 3, + "metadata": { + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "1.10.5" + }, + "kernelspec": { + "name": "julia-1.10", + "display_name": "Julia 1.10.5", + "language": "julia" + } + }, + "nbformat": 4 +} diff --git a/previews/PR319/assets/paraviewcolormap.png b/previews/PR319/assets/paraviewcolormap.png new file mode 100644 index 0000000000000000000000000000000000000000..1d1073abe36ddf9a3a8ebfdf6c61f1277291bf22 GIT binary patch literal 27585 zcmbUJWmH^k&@GBWaJOI~xCeLF;0_6Hfgr)%f(CcD;K3b&I|O%kcXy|O?z4EmbI#rS zj(z{!jKK)Ky4UJQW>w9qXBJ^9O44Y^ACRG-pwMJxB-Egwpk1J#-bo_91Flq{T~-1A 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z-S7P1nCS4I2GeI-^FzF;7T&LNI!XL7iDs={>`ka5ihZHlePxDnJ`za1Enmyg?=Jcl z*lyN34KFv>ByJ}A+3F6v2ph2b8!nh_`)YV*d*v0UWN>K`2InienPk5+j2CQ8mL^*A zPCXt9QzVN`*|3`{yQaT6E1e|{+;ec?Zan?*``mmCm518htg0?u(?n%4`gyGnE*(2< zY#YA81_$aNeMd9-Q`K(b>d338Q2b++)KpKn37&WpLs#A}8-0DI+dAFR>5_(ui(^RV zdDl(~XB5TcRQ8}5h%kt+@$!P;nDl1;A)WFkVaqyqq~ii?MzP!taEcfbrT_d_MCO(379yVn4BD5 zu-8U!n4A*ZAW8 z7Z7-HUdx({iRom{jnLK+%>Lz}a*G}Q@b9pE6YuzzJU;?<;nYyzNN?}FT52IhX54>x z3UPLJ$cDIbb#Xb#NKRf*@`>6=b*o8PY-B#8VEoeDdoxqr-gB5$U$He^ac&*DyJyH# zevULN7k5N+t6cOZhR2nN34j=Y_L%z4cm8B+%cfh1;4PBOG!~(1X7=J16K|U~%qF(s zYKWGg10R*=^72C!7FJdY^77d^Id3~j<*MPJBGlaXjJo}SI+gLog62;*jFG$&A3J7d zU%*XmgL`z4xwQmP3G0U7cMH}?x9HVFp(UpSnUj~jt_XfQqYZPCV2&Nt*{ zhxZxK7!I5@$So($D`3Jo*b(51p%x3xCNYPSZf(k})u#V1wNg=0=`aJxV05CzaS+P$SoiJQhv`pVS{~|l z{=uhsG_(U@_B_0(5WFKo)<~PDPo6R_@oB7MvM*>p>fY+70Gd0odzcy&io9n;?zK5l zjA=}?x65c$`rh(1HUJTELfXziij}S|d*y16aii1KBI=r03H<^8wuI?c{oN(0V5q8| zCuU<+$2S2w=jB^unsU6MZ~Qaeh^o=YK4Em3+l3pFMB_e`Y6P+@xt-HB02ppNG^J4W z2XlbUJEt^GR--wvuXHIhZyK3Z*hdzhSFKeYRNa(O@zOmF7}x=Zj#TdU4p18JuznbW zc)ObIe(`p Moment(s=3/2, g=2)], :dipole) + +J = +0.63 # (meV) +set_exchange!(sys, J, Bond(1, 3, [0, 0, 0])) +view_crystal(sys) + +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; color=[S[3] for S in sys.dipoles]) + +@assert energy_per_site(sys) ≈ -2J*(3/2)^2 + +shape = [0 1 1; + 1 0 1; + 1 1 0] / 2 +sys_prim = reshape_supercell(sys, shape) +@assert energy_per_site(sys_prim) ≈ -2J*(3/2)^2 + +plot_spins(sys_prim; color=[S[3] for S in sys_prim.dipoles]) + +formfactors = [1 => FormFactor("Co2")] +measure = ssf_perp(sys_prim; formfactors) +swt = SpinWaveTheory(sys_prim; measure) + +kernel = lorentzian(fwhm=0.8) + +qs = [[0, 0, 0], [1/2, 0, 0], [1/2, 1/2, 0], [0, 0, 0]] +path = q_space_path(cryst, qs, 500) + +energies = range(0, 6, 300) +res = intensities(swt, path; energies, kernel) +plot_intensities(res; units, title="CoRh₂O₄ LSWT") + +radii = range(0, 3, 200) # (1/Å) +res = powder_average(cryst, radii, 2000) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units, saturation=1.0, title="CoRh₂O₄ Powder Average") diff --git a/previews/PR319/assets/scripts/02_LLD_CoRh2O4.jl b/previews/PR319/assets/scripts/02_LLD_CoRh2O4.jl new file mode 100644 index 000000000..d98a3f212 --- /dev/null +++ b/previews/PR319/assets/scripts/02_LLD_CoRh2O4.jl @@ -0,0 +1,82 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = 8.5031 # (Å) +latvecs = lattice_vectors(a, a, a, 90, 90, 90) +cryst = Crystal(latvecs, [[0,0,0]], 227, setting="1") + +sys = System(cryst, [1 => Moment(s=3/2, g=2)], :dipole) +J = 0.63 # (meV) +set_exchange!(sys, J, Bond(1, 3, [0,0,0])) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; color=[S[3] for S in sys.dipoles]) + +sys = repeat_periodically(sys, (10, 10, 10)) +plot_spins(sys; color=[S[3] for S in sys.dipoles]) + +langevin = Langevin(; damping=0.2, kT=16*units.K) + +suggest_timestep(sys, langevin; tol=1e-2) +langevin.dt = 0.025; + +energies = [energy_per_site(sys)] +for _ in 1:1000 + step!(sys, langevin) + push!(energies, energy_per_site(sys)) +end + +suggest_timestep(sys, langevin; tol=1e-2) +langevin.dt = 0.042; + +lines(energies, color=:blue, figure=(size=(600,300),), axis=(xlabel="Timesteps", ylabel="Energy (meV)")) + +S0 = sys.dipoles[1,1,1,1] +plot_spins(sys; color=[S'*S0 for S in sys.dipoles]) + +formfactors = [1 => FormFactor("Co2")] +measure = ssf_perp(sys; formfactors) +sc = SampledCorrelationsStatic(sys; measure) +add_sample!(sc, sys) # Accumulate the newly sampled structure factor into `sf` + +for _ in 1:20 + for _ in 1:100 + step!(sys, langevin) + end + add_sample!(sc, sys) +end + +grid = q_space_grid(cryst, [1, 0, 0], range(-10, 10, 200), [0, 1, 0], (-10, 10)) + +res = intensities_static(sc, grid) +plot_intensities(res; saturation=1.0, title="Static Intensities at T = 16 K") + +dt = 2*langevin.dt +energies = range(0, 6, 50) +sc = SampledCorrelations(sys; dt, energies, measure=ssf_perp(sys)) + +for _ in 1:5 + for _ in 1:100 + step!(sys, langevin) + end + add_sample!(sc, sys) +end + +qs = [[3/4, 3/4, 0], + [ 0, 0, 0], + [ 0, 1/2, 1/2], + [1/2, 1, 0], + [ 0, 1, 0], + [1/4, 1, 1/4], + [ 0, 1, 0], + [ 0, -4, 0]] +path = q_space_path(cryst, qs, 500) + +res = intensities(sc, path; energies, langevin.kT) +plot_intensities(res; units, title="Intensities at 16 K") + +radii = range(0, 3.5, 200) # (1/Å) +res = powder_average(cryst, radii, 350) do qs + intensities(sc, qs; energies, langevin.kT) +end +plot_intensities(res; units, title="Powder Average at 16 K") diff --git a/previews/PR319/assets/scripts/03_LSWT_SU3_FeI2.jl b/previews/PR319/assets/scripts/03_LSWT_SU3_FeI2.jl new file mode 100644 index 000000000..2383ecc2e --- /dev/null +++ b/previews/PR319/assets/scripts/03_LSWT_SU3_FeI2.jl @@ -0,0 +1,90 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = b = 4.05012 # Lattice constants for triangular lattice (Å) +c = 6.75214 # Spacing between layers (Å) +latvecs = lattice_vectors(a, b, c, 90, 90, 120) +positions = [[0, 0, 0], [1/3, 2/3, 1/4], [2/3, 1/3, 3/4]] +types = ["Fe", "I", "I"] +cryst = Crystal(latvecs, positions; types) + +cryst = subcrystal(cryst, "Fe") +view_crystal(cryst) + +print_symmetry_table(cryst, 8.0) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :SUN, seed=2) + +J1pm = -0.236 # (meV) +J1pmpm = -0.161 +J1zpm = -0.261 +J2pm = 0.026 +J3pm = 0.166 +J′0pm = 0.037 +J′1pm = 0.013 +J′2apm = 0.068 + +J1zz = -0.236 +J2zz = 0.113 +J3zz = 0.211 +J′0zz = -0.036 +J′1zz = 0.051 +J′2azz = 0.073 + +J1xx = J1pm + J1pmpm +J1yy = J1pm - J1pmpm +J1yz = J1zpm + +set_exchange!(sys, [J1xx 0.0 0.0; + 0.0 J1yy J1yz; + 0.0 J1yz J1zz], Bond(1,1,[1,0,0])) +set_exchange!(sys, [J2pm 0.0 0.0; + 0.0 J2pm 0.0; + 0.0 0.0 J2zz], Bond(1,1,[1,2,0])) +set_exchange!(sys, [J3pm 0.0 0.0; + 0.0 J3pm 0.0; + 0.0 0.0 J3zz], Bond(1,1,[2,0,0])) +set_exchange!(sys, [J′0pm 0.0 0.0; + 0.0 J′0pm 0.0; + 0.0 0.0 J′0zz], Bond(1,1,[0,0,1])) +set_exchange!(sys, [J′1pm 0.0 0.0; + 0.0 J′1pm 0.0; + 0.0 0.0 J′1zz], Bond(1,1,[1,0,1])) +set_exchange!(sys, [J′2apm 0.0 0.0; + 0.0 J′2apm 0.0; + 0.0 0.0 J′2azz], Bond(1,1,[1,2,1])) + +D = 2.165 # (meV) +set_onsite_coupling!(sys, S -> -D*S[3]^2, 1) + +sys = resize_supercell(sys, (4, 4, 4)) +randomize_spins!(sys) +minimize_energy!(sys) + +plot_spins(sys; color=[S[3] for S in sys.dipoles]) + +print_wrapped_intensities(sys) + +suggest_magnetic_supercell([[0, -1/4, 1/4]]) + +sys_min = reshape_supercell(sys, [1 0 0; 0 2 1; 0 -2 1]) +randomize_spins!(sys_min) +minimize_energy!(sys_min); +plot_spins(sys_min; color=[S[3] for S in sys_min.dipoles], ghost_radius=12) + +swt = SpinWaveTheory(sys_min; measure=ssf_perp(sys_min)) + +qs = [[0,0,0], [1,0,0], [0,1,0], [1/2,0,0], [0,1,0], [0,0,0]] +path = q_space_path(cryst, qs, 500) +res = intensities_bands(swt, path) +plot_intensities(res; units, title="Single Crystal Bands") + +kernel = lorentzian(fwhm=0.3) +energies = range(0, 10, 300); # 0 < ω < 10 (meV) + +rotations = [([0,0,1], n*(2π/3)) for n in 0:2] +weights = [1, 1, 1] +res = domain_average(cryst, path; rotations, weights) do path_rotated + intensities(swt, path_rotated; energies, kernel) +end +plot_intensities(res; units, colormap=:viridis, title="Domain Averaged Intensities") diff --git a/previews/PR319/assets/scripts/04_GSD_FeI2.jl b/previews/PR319/assets/scripts/04_GSD_FeI2.jl new file mode 100644 index 000000000..9c6621d2b --- /dev/null +++ b/previews/PR319/assets/scripts/04_GSD_FeI2.jl @@ -0,0 +1,94 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = b = 4.05012 +c = 6.75214 +latvecs = lattice_vectors(a, b, c, 90, 90, 120) +cryst = Crystal(latvecs, [[0,0,0]], 164; types=["Fe"]) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :SUN) +J1pm = -0.236 +J1pmpm = -0.161 +J1zpm = -0.261 +J2pm = 0.026 +J3pm = 0.166 +J′0pm = 0.037 +J′1pm = 0.013 +J′2apm = 0.068 +J1zz = -0.236 +J2zz = 0.113 +J3zz = 0.211 +J′0zz = -0.036 +J′1zz = 0.051 +J′2azz = 0.073 +J1xx = J1pm + J1pmpm +J1yy = J1pm - J1pmpm +J1yz = J1zpm +set_exchange!(sys, [J1xx 0.0 0.0; 0.0 J1yy J1yz; 0.0 J1yz J1zz], Bond(1,1,[1,0,0])) +set_exchange!(sys, [J2pm 0.0 0.0; 0.0 J2pm 0.0; 0.0 0.0 J2zz], Bond(1,1,[1,2,0])) +set_exchange!(sys, [J3pm 0.0 0.0; 0.0 J3pm 0.0; 0.0 0.0 J3zz], Bond(1,1,[2,0,0])) +set_exchange!(sys, [J′0pm 0.0 0.0; 0.0 J′0pm 0.0; 0.0 0.0 J′0zz], Bond(1,1,[0,0,1])) +set_exchange!(sys, [J′1pm 0.0 0.0; 0.0 J′1pm 0.0; 0.0 0.0 J′1zz], Bond(1,1,[1,0,1])) +set_exchange!(sys, [J′2apm 0.0 0.0; 0.0 J′2apm 0.0; 0.0 0.0 J′2azz], Bond(1,1,[1,2,1])) +D = 2.165 +set_onsite_coupling!(sys, S -> -D*S[3]^2, 1) + +sys = resize_supercell(sys, (16, 16, 4)) + +langevin = Langevin(; damping=0.2, kT=2.3*units.K) + +randomize_spins!(sys) +minimize_energy!(sys; maxiters=10) +suggest_timestep(sys, langevin; tol=1e-2) +langevin.dt = 0.03; + +for _ in 1:10_000 + step!(sys, langevin) +end +plot_spins(sys; color=[S[3] for S in sys.dipoles]) + +print_wrapped_intensities(sys) + +suggest_timestep(sys, langevin; tol=1e-2) + +langevin.kT = 3.5 * units.K +for _ in 1:10_000 + step!(sys, langevin) +end + +suggest_timestep(sys, langevin; tol=1e-2) +langevin.dt = 0.040; + +dt = 2*langevin.dt +energies = range(0, 7.5, 120) +formfactors = [1 => FormFactor("Fe2"; g_lande=3/2)] +sc = SampledCorrelations(sys; dt, energies, measure=ssf_perp(sys; formfactors)) + +add_sample!(sc, sys) + +for _ in 1:2 + for _ in 1:1000 # Enough steps to decorrelate spins + step!(sys, langevin) + end + add_sample!(sc, sys) +end + +res = intensities(sc, [[0, 0, 0], [0.5, 0.5, 0.5]]; energies, langevin.kT) +fig = lines(res.energies, res.data[:, 1]; axis=(xlabel="meV", ylabel="Intensity"), label="(0,0,0)") +lines!(res.energies, res.data[:, 2]; label="(π,π,π)") +axislegend() +fig + +qs = [[0, 0, 0], # List of wave vectors that define a path + [1, 0, 0], + [0, 1, 0], + [1/2, 0, 0], + [0, 1, 0], + [0, 0, 0]] +qpath = q_space_path(cryst, qs, 500) +res = intensities(sc, qpath; energies, langevin.kT) +plot_intensities(res; colorrange=(0.0, 1.0), title="Intensities at T = 2.3 K") + +grid = q_space_grid(cryst, [1, 0, 0], range(-1.5, 1.5, 300), [0, 1, 0], (-1.5, 1.5); orthogonalize=true) +res = intensities(sc, grid; energies=[3.5], langevin.kT) +plot_intensities(res; title="Intensity slice at ω = 3.5 meV") diff --git a/previews/PR319/assets/scripts/05_MC_Ising.jl b/previews/PR319/assets/scripts/05_MC_Ising.jl new file mode 100644 index 000000000..34b26fd80 --- /dev/null +++ b/previews/PR319/assets/scripts/05_MC_Ising.jl @@ -0,0 +1,23 @@ +using Sunny, GLMakie + +latvecs = lattice_vectors(1, 1, 10, 90, 90, 90) +crystal = Crystal(latvecs, [[0, 0, 0]]) + +L = 128 +sys = System(crystal, [1 => Moment(s=1, g=-1)], :dipole; dims=(L, L, 1), seed=0) +polarize_spins!(sys, (0, 0, 1)) + +set_exchange!(sys, -1.0, Bond(1, 1, (1, 0, 0))) + +B = 0 +set_field!(sys, (0, 0, B)) + +Tc = 2/log(1+√2) + +nsweeps = 4000 +sampler = LocalSampler(kT=Tc, propose=propose_flip) +for i in 1:nsweeps + step!(sys, sampler) +end + +heatmap(reshape([S[3] for S in sys.dipoles], (L, L))) diff --git a/previews/PR319/assets/scripts/06_CP2_Skyrmions.jl b/previews/PR319/assets/scripts/06_CP2_Skyrmions.jl new file mode 100644 index 000000000..84321f24d --- /dev/null +++ b/previews/PR319/assets/scripts/06_CP2_Skyrmions.jl @@ -0,0 +1,62 @@ +using Sunny, GLMakie + +lat_vecs = lattice_vectors(1, 1, 10, 90, 90, 120) +positions = [[0, 0, 0]] +cryst = Crystal(lat_vecs, positions) + +L = 40 +sys = System(cryst, [1 => Moment(s=1, g=-1)], :SUN; dims=(L, L, 1)) + +J1 = -1 # Nearest-neighbor ferromagnetic +J2 = (2.0/(1+√5)) # Tune competing exchange to set skyrmion scale length +Δ = 2.6 # Exchange anisotropy + +ex1 = J1 * [1 0 0; + 0 1 0; + 0 0 Δ] +ex2 = J2 * [1 0 0; + 0 1 0; + 0 0 Δ] +set_exchange!(sys, ex1, Bond(1, 1, [1, 0, 0])) +set_exchange!(sys, ex2, Bond(1, 1, [1, 2, 0])) + +h = 15.5 # External field in energy units +field = set_field!(sys, [0, 0, h]) + +D = 19.0 # Easy-plane anisotropy +set_onsite_coupling!(sys, S -> D*S[3]^2, 1) + +damping = 0.05 +kT = 0; + +randomize_spins!(sys) +integrator = Langevin(; damping, kT) +suggest_timestep(sys, integrator; tol=0.05) + +integrator.dt = 0.01; + +randomize_spins!(sys) +τs = [4, 16, 256] # Times to record snapshots +frames = [] # Empty array to store snapshots +for i in eachindex(τs) + dur = i == 1 ? τs[1] : τs[i] - τs[i-1] # Determine the length of time to simulate + numsteps = round(Int, dur/integrator.dt) + for _ in 1:numsteps # Perform the integration + step!(sys, integrator) + end + push!(frames, copy(sys.coherents)) # Save a snapshot spin configuration +end + +include(pkgdir(Sunny, "examples", "extra", "Plotting", "plotting2d.jl")) + +function sun_berry_curvature(z₁, z₂, z₃) + z₁, z₂, z₃ = normalize.((z₁, z₂, z₃)) + n₁ = z₁ ⋅ z₂ + n₂ = z₂ ⋅ z₃ + n₃ = z₃ ⋅ z₁ + return angle(n₁ * n₂ * n₃) +end + +plot_triangular_plaquettes(sun_berry_curvature, frames; size=(600, 200), + offset_spacing=10, texts=["\tt = "*string(τ) for τ in τs], text_offset=(0, 6) +) diff --git a/previews/PR319/assets/scripts/07_Dipole_Dipole.jl b/previews/PR319/assets/scripts/07_Dipole_Dipole.jl new file mode 100644 index 000000000..f4668ade7 --- /dev/null +++ b/previews/PR319/assets/scripts/07_Dipole_Dipole.jl @@ -0,0 +1,48 @@ +using Sunny, GLMakie + +units = Units(:K, :angstrom) +latvecs = lattice_vectors(10.19, 10.19, 10.19, 90, 90, 90) +positions = [[1/8, 1/8, 1/8]] +cryst = Crystal(latvecs, positions, 227, setting="1") +view_crystal(cryst) + +primitive_cell = [1/2 1/2 0; 0 1/2 1/2; 1/2 0 1/2] +sys = System(cryst, [1 => Moment(s=7/2, g=2)], :dipole; seed=0) +sys = reshape_supercell(sys, primitive_cell) +J1 = 0.304 # (K) +set_exchange!(sys, J1, Bond(1, 2, [0,0,0])) + +sys_lr = clone_system(sys) +enable_dipole_dipole!(sys_lr, units.vacuum_permeability) + +sys_lr_cut = clone_system(sys) +modify_exchange_with_truncated_dipole_dipole!(sys_lr_cut, 5.0, units.vacuum_permeability) + +randomize_spins!(sys_lr) +minimize_energy!(sys_lr) +plot_spins(sys_lr; ghost_radius=8, color=[:red, :blue, :yellow, :purple]) + +sys.dipoles .= sys_lr.dipoles +sys_lr_cut.dipoles .= sys_lr.dipoles; + +qs = [[0,0,0], [0,1,0], [1,1/2,0], [1/2,1/2,1/2], [3/4,3/4,0], [0,0,0]] +labels = ["Γ", "X", "W", "L", "K", "Γ"] +path = q_space_path(cryst, qs, 500; labels) + +measure = ssf_trace(sys) +swt = SpinWaveTheory(sys; measure) +res1 = intensities_bands(swt, path) + +swt = SpinWaveTheory(sys_lr; measure) +res2 = intensities_bands(swt, path) + +swt = SpinWaveTheory(sys_lr_cut; measure) +res3 = intensities_bands(swt, path); + +fig = Figure(size=(768, 300)) +plot_intensities!(fig[1, 1], res1; units, title="Without long-range dipole") +ax = plot_intensities!(fig[1, 2], res2; units, title="With long-range dipole") +for c in eachrow(res3.disp) + lines!(ax, eachindex(c), c; linestyle=:dash, color=:black) +end +fig diff --git a/previews/PR319/assets/scripts/08_Momentum_Conventions.jl b/previews/PR319/assets/scripts/08_Momentum_Conventions.jl new file mode 100644 index 000000000..b20290c8b --- /dev/null +++ b/previews/PR319/assets/scripts/08_Momentum_Conventions.jl @@ -0,0 +1,47 @@ +using Sunny, GLMakie + +latvecs = lattice_vectors(2, 2, 1, 90, 90, 90) +cryst = Crystal(latvecs, [[0,0,0]], "P1") + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(1, 1, 25)) +D = 0.1 +B = 5D +set_exchange!(sys, dmvec([0, 0, D]), Bond(1, 1, [0, 0, 1])) +set_field!(sys, [0, 0, B]) + +randomize_spins!(sys) +minimize_energy!(sys) +@assert energy_per_site(sys) ≈ -10D + +dt = 0.1 +kT = 0.02 +damping = 0.1 +langevin = Langevin(dt; kT, damping) +suggest_timestep(sys, langevin; tol=1e-2) +for _ in 1:10_000 + step!(sys, langevin) +end + +plot_spins(sys) + +sc = SampledCorrelations(sys; dt, energies=range(0, 15D, 100), measure=ssf_trace(sys)) +add_sample!(sc, sys) +nsamples = 100 +for _ in 1:nsamples + for _ in 1:1_000 + step!(sys, langevin) + end + add_sample!(sc, sys) +end +path = q_space_path(cryst, [[0,0,-1/2], [0,0,+1/2]], 400) +res1 = intensities(sc, path; energies=:available, kT) + +sys_small = resize_supercell(sys, (1,1,1)) +minimize_energy!(sys_small) +swt = SpinWaveTheory(sys_small; measure=ssf_trace(sys_small)) +res2 = intensities_bands(swt, path) + +fig = Figure(size=(768, 300)) +plot_intensities!(fig[1, 1], res1; title="Classical dynamics") +plot_intensities!(fig[1, 2], res2; title="Spin wave theory") +fig diff --git a/previews/PR319/assets/scripts/SW01_FM_Heseinberg_chain.jl b/previews/PR319/assets/scripts/SW01_FM_Heseinberg_chain.jl new file mode 100644 index 000000000..906284252 --- /dev/null +++ b/previews/PR319/assets/scripts/SW01_FM_Heseinberg_chain.jl @@ -0,0 +1,40 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = 3.0 +b = 8.0 +c = 8.0 +latvecs = lattice_vectors(a, b, c, 90, 90, 90) +positions = [[0, 0, 0]] +cryst = Crystal(latvecs, positions) + +view_crystal(cryst; ndims=2, ghost_radius=8) + +print_symmetry_table(cryst, 8) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) + +J = -1 +set_exchange!(sys, J, Bond(1, 1, [1, 0, 0])) + +randomize_spins!(sys) +minimize_energy!(sys) +energy_per_site(sys) + +plot_spins(sys; ndims=2, ghost_radius=8) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) + +qs = [[0,0,0], [1,0,0]] +path = q_space_path(cryst, qs, 400) + +res = intensities_bands(swt, path) +plot_intensities(res; units) + +radii = range(0, 2.5, 200) # 1/Å +energies = range(0, 5, 200) # meV +kernel = gaussian(fwhm=0.1) +res = powder_average(cryst, radii, 1000) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW02_AFM_Heisenberg_chain.jl b/previews/PR319/assets/scripts/SW02_AFM_Heisenberg_chain.jl new file mode 100644 index 000000000..6c9a541b4 --- /dev/null +++ b/previews/PR319/assets/scripts/SW02_AFM_Heisenberg_chain.jl @@ -0,0 +1,26 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(3, 8, 8, 90, 90, 90) +cryst = Crystal(latvecs, [[0, 0, 0]]) +view_crystal(cryst; ndims=2, ghost_radius=8) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(2, 1, 1)) + +J = 1 +set_exchange!(sys, J, Bond(1, 1, [1, 0, 0])) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2, ghost_radius=8) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[0,0,0], [1,0,0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) + +isapprox(res.disp[1, :], res.disp[2, :]) + +xs = [q[1] for q in path.qs] +ys = log10.(res.data[1, :] + res.data[2, :]) +lines(xs, ys; axis=(; xlabel="[H, 0, 0]", ylabel="Log intensity (dimensionless)")) diff --git a/previews/PR319/assets/scripts/SW03_Frustrated_chain.jl b/previews/PR319/assets/scripts/SW03_Frustrated_chain.jl new file mode 100644 index 000000000..0a4c2b37a --- /dev/null +++ b/previews/PR319/assets/scripts/SW03_Frustrated_chain.jl @@ -0,0 +1,28 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(3, 8, 8, 90, 90, 90) +cryst = Crystal(latvecs, [[0, 0, 0]]) +view_crystal(cryst; ndims=2, ghost_radius=8) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) +J1 = -1 +J2 = +2 * abs(J1) +set_exchange!(sys, J1, Bond(1, 1, [1, 0, 0])) +set_exchange!(sys, J2, Bond(1, 1, [2, 0, 0])) + +axis = [0, 0, 1] +randomize_spins!(sys) +k = minimize_spiral_energy!(sys, axis; k_guess=randn(3)) + +@assert k[1] ≈ 0.2300534561 || k[1] ≈ 1 - 0.2300534561 +@assert spiral_energy_per_site(sys; k, axis) ≈ -33/16 * abs(J1) + +sys_enlarged = repeat_periodically_as_spiral(sys, (8, 1, 1); k, axis) +plot_spins(sys_enlarged; ndims=2) + +swt = SpinWaveTheorySpiral(sys; measure=ssf_perp(sys), k, axis) +qs = [[0,0,0], [1,0,0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW04_Frustrated_square.jl b/previews/PR319/assets/scripts/SW04_Frustrated_square.jl new file mode 100644 index 000000000..1ab9450b3 --- /dev/null +++ b/previews/PR319/assets/scripts/SW04_Frustrated_square.jl @@ -0,0 +1,21 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(3.0, 3.0, 6.0, 90, 90, 90) +cryst = Crystal(latvecs, [[0, 0, 0]]) +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(2, 2, 1)) +J1 = 1.0 +J2 = -0.1 +set_exchange!(sys, J1, Bond(1, 1, [1, 0, 0])) +set_exchange!(sys, J2, Bond(1, 1, [1, 1, 0])) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[0, 0, 0], [1/2, 0, 0], [1/2, 1/2, 0], [0, 0, 0]] +path = q_space_path(cryst, qs, 400); +res = intensities_bands(swt, path) +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW05_Simple_kagome_FM.jl b/previews/PR319/assets/scripts/SW05_Simple_kagome_FM.jl new file mode 100644 index 000000000..50d5a8013 --- /dev/null +++ b/previews/PR319/assets/scripts/SW05_Simple_kagome_FM.jl @@ -0,0 +1,41 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(6, 6, 5, 90, 90, 120) +positions = [[1/2, 0, 0]] +cryst = Crystal(latvecs, positions, 147) + +positions = [[1/2, 0, 0], [0, 1/2, 0], [1/2, 1/2, 0]] +cryst2 = Crystal(latvecs, positions) + +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) +J = -1.0 +set_exchange!(sys, J, Bond(2, 3, [0, 0, 0])) + +randomize_spins!(sys) +minimize_energy!(sys) +energy_per_site(sys) +@assert energy_per_site(sys) ≈ 4J/2 +plot_spins(sys; ndims=2) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[-1/2, 0, 0], [0, 0, 0], [1/2, 1/2, 0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) + +radii = range(0, 2.5, 200) +energies = range(0, 6.5, 200) +res1 = powder_average(cryst, radii, 1000) do qs + intensities(swt, qs; energies, kernel=gaussian(fwhm=0.02)) +end +res2 = powder_average(cryst, radii, 1000) do qs + intensities(swt, qs; energies, kernel=gaussian(fwhm=0.25)) +end + +fig = Figure(size=(768, 800)) +plot_intensities!(fig[1, 1], res1; units, colorrange=(0,10), title="FWHM 0.02 meV") +plot_intensities!(fig[2, 1], res2; units, colorrange=(0,10), title="FWHM 0.25 meV") +fig diff --git a/previews/PR319/assets/scripts/SW06_Complex_kagome_FM.jl b/previews/PR319/assets/scripts/SW06_Complex_kagome_FM.jl new file mode 100644 index 000000000..97fedb53c --- /dev/null +++ b/previews/PR319/assets/scripts/SW06_Complex_kagome_FM.jl @@ -0,0 +1,36 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(6, 6, 8, 90, 90, 120) +cryst = Crystal(latvecs, [[1/2, 0, 0]], 147) +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) +J1 = -1.0 +J2 = 0.1 +J3a = 0.00 +J3b = 0.17 +set_exchange!(sys, J1, Bond(2, 3, [0, 0, 0])) +set_exchange!(sys, J2, Bond(2, 1, [0, 0, 0])) +set_exchange!(sys, J3a, Bond(2, 2, [1, 0, 0])) +set_exchange!(sys, J3b, Bond(1, 1, [1, 0, 0])) + +view_crystal(sys; ndims=2) + +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) + +radii = range(0, 2.5, 200) +energies = range(0, 6.5, 200) +kernel = gaussian(fwhm=0.02) +res = powder_average(cryst, radii, 1000) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units, colorrange=(0,10)) diff --git a/previews/PR319/assets/scripts/SW07_k0_kagome_AFM.jl b/previews/PR319/assets/scripts/SW07_k0_kagome_AFM.jl new file mode 100644 index 000000000..b34d2815e --- /dev/null +++ b/previews/PR319/assets/scripts/SW07_k0_kagome_AFM.jl @@ -0,0 +1,29 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(6, 6, 8, 90, 90, 120) +cryst = Crystal(latvecs, [[1/2, 0, 0]], 147) +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) +J1 = 1.0 +J2 = 0.11 +set_exchange!(sys, J1, Bond(2, 3, [0, 0, 0])) +set_exchange!(sys, J2, Bond(2, 1, [0, 0, 0])) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) + +radii = range(0, 2.5, 200) +energies = range(0, 2.5, 200) +kernel = gaussian(fwhm=0.02) +res = powder_average(cryst, radii, 1000) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW08_sqrt3_kagome_AFM.jl b/previews/PR319/assets/scripts/SW08_sqrt3_kagome_AFM.jl new file mode 100644 index 000000000..f9668b41e --- /dev/null +++ b/previews/PR319/assets/scripts/SW08_sqrt3_kagome_AFM.jl @@ -0,0 +1,41 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(6, 6, 40, 90, 90, 120) +cryst = Crystal(latvecs, [[1/2, 0, 0]], 147) +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) +J = 1.0 +set_exchange!(sys, J, Bond(2, 3, [0, 0, 0])) + +set_dipole!(sys, [cos(0), sin(0), 0], (1, 1, 1, 1)) +set_dipole!(sys, [cos(0), sin(0), 0], (1, 1, 1, 2)) +set_dipole!(sys, [cos(2π/3), sin(2π/3), 0], (1, 1, 1, 3)) +k = [-1/3, -1/3, 0] +axis = [0, 0, 1] +sys_enlarged = repeat_periodically_as_spiral(sys, (3, 3, 1); k, axis) +plot_spins(sys_enlarged; ndims=2) + +@assert energy_per_site(sys_enlarged) ≈ (4/2)*J*cos(2π/3) +@assert spiral_energy_per_site(sys; k, axis) ≈ (4/2)*J*cos(2π/3) + +qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]] +path = q_space_path(cryst, qs, 400) + +fig = Figure(size=(768, 300)) +swt = SpinWaveTheory(sys_enlarged; measure=ssf_perp(sys_enlarged)) +res = intensities_bands(swt, path) +plot_intensities!(fig[1, 1], res; units, saturation=0.5,title="Supercell method") +swt = SpinWaveTheorySpiral(sys; measure=ssf_perp(sys), k, axis) +res = intensities_bands(swt, path) +plot_intensities!(fig[1, 2], res; units, saturation=0.5, title="Spiral method") +fig + +radii = range(0, 2.5, 200) +energies = range(0, 3, 200) +kernel = gaussian(fwhm=0.05) +res = powder_average(cryst, radii, 200) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units, colorrange=(0,20)) diff --git a/previews/PR319/assets/scripts/SW09_k0_kagome_AFM_DM.jl b/previews/PR319/assets/scripts/SW09_k0_kagome_AFM_DM.jl new file mode 100644 index 000000000..972d56c6e --- /dev/null +++ b/previews/PR319/assets/scripts/SW09_k0_kagome_AFM_DM.jl @@ -0,0 +1,28 @@ +using Sunny, GLMakie, LinearAlgebra + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(6, 6, 8, 90, 90, 120) +cryst = Crystal(latvecs, [[1/2, 0, 0]], 147) +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole) +J = 1.0*I + dmvec([0, 0, -0.08]) + +set_exchange!(sys, J, Bond(2, 3, [0, 0, 0])) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[-1/2,0,0], [0,0,0], [1/2,1/2,0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) + +radii = range(0, 2.5, 200) +energies = range(0, 2.5, 200) +kernel = gaussian(fwhm=0.02) +res = powder_average(cryst, radii, 1000) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units, colorrange=(0,20)) diff --git a/previews/PR319/assets/scripts/SW10_Energy_cut.jl b/previews/PR319/assets/scripts/SW10_Energy_cut.jl new file mode 100644 index 000000000..bd69ee673 --- /dev/null +++ b/previews/PR319/assets/scripts/SW10_Energy_cut.jl @@ -0,0 +1,20 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(1.0, 1.0, 3.0, 90, 90, 90) +cryst = Crystal(latvecs, [[0, 0, 0]]) + +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole; dims=(2, 2, 1)) +set_exchange!(sys, 1.0, Bond(1, 1, [1, 0, 0])) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2) + +grid = q_space_grid(cryst, [1, 0, 0], range(0, 2, 201), [0, 1, 0], range(0, 2, 201)) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +res = intensities(swt, grid; energies=[3.75], kernel=gaussian(fwhm=0.2)) +plot_intensities(res; units) + +res = intensities_static(swt, grid; bounds=(3.5, 4.01)) +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW11_La2CuO4.jl b/previews/PR319/assets/scripts/SW11_La2CuO4.jl new file mode 100644 index 000000000..27a435533 --- /dev/null +++ b/previews/PR319/assets/scripts/SW11_La2CuO4.jl @@ -0,0 +1,33 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(1, 1, 10, 90, 90, 90) +positions = [[0, 0, 0]] +types = ["Cu"] +cryst = Crystal(latvecs, positions; types) +view_crystal(cryst; ndims=2) + +sys = System(cryst, [1 => Moment(s=1/2, g=2)], :dipole; dims=(2, 2, 1)) +J = 138.3 +Jp = 2 +Jpp = 2 +Jc = 38 +set_exchange!(sys, J-Jc/2, Bond(1, 1, [1, 0, 0])) +set_exchange!(sys, Jp-Jc/4, Bond(1, 1, [1, 1, 0])) +set_exchange!(sys, Jpp, Bond(1, 1, [2, 0, 0])) + +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2) + +qs = [[3/4,1/4,0], [1/2, 1/2, 0], [1/2, 0, 0], [3/4, 1/4, 0], [1,0,0], [1/2 0 0]] +labels = ["P", "M", "X", "P", "Γ", "X"] +path = q_space_path(cryst, qs, 400; labels) +energies = range(0, 320, 400) +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +res = intensities(swt, path; energies, kernel=gaussian(fwhm=35)) +res.energies .*= 1.18 +plot_intensities(res; units) + +res = intensities_static(swt, path) +plot_intensities(res; colorrange=(0,20), units) diff --git a/previews/PR319/assets/scripts/SW12_Triangular_easy_plane.jl b/previews/PR319/assets/scripts/SW12_Triangular_easy_plane.jl new file mode 100644 index 000000000..05e4990d2 --- /dev/null +++ b/previews/PR319/assets/scripts/SW12_Triangular_easy_plane.jl @@ -0,0 +1,34 @@ +using Sunny, GLMakie + +latvecs = lattice_vectors(3, 3, 4, 90, 90, 120) +cryst = Crystal(latvecs, [[0, 0, 0]]) + +s = 3/2 +J1 = +1.0 +sys = System(cryst, [1 => Moment(; s, g=2)], :dipole; dims=(3, 3, 1)) +set_exchange!(sys, J1, Bond(1, 1, [1, 0, 0])) + +undo_classical_to_quantum_rescaling = 1 / (1 - 1/2s) +D = 0.2 * undo_classical_to_quantum_rescaling +set_onsite_coupling!(sys, S -> D*S[3]^2, 1) +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; ndims=2) + +qs = [[0, 0, 0], [1, 1, 0]] +path = q_space_path(cryst, qs, 400) +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +res = intensities_bands(swt, path) +plot_intensities(res) + +measure = ssf_custom(sys) do q, ssf + return real(ssf[3, 3]) +end +swt = SpinWaveTheory(sys; measure) +res = intensities_bands(swt, path) +plot_intensities(res) + +measure = ssf_custom((q, ssf) -> ssf, sys) +swt = SpinWaveTheory(sys; measure) +res = intensities_bands(swt, path) +res.data[7, 10] diff --git a/previews/PR319/assets/scripts/SW13_LiNiPO4.jl b/previews/PR319/assets/scripts/SW13_LiNiPO4.jl new file mode 100644 index 000000000..83c6a14bd --- /dev/null +++ b/previews/PR319/assets/scripts/SW13_LiNiPO4.jl @@ -0,0 +1,62 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = 10.02 +b = 5.86 +c = 4.68 +latvecs = lattice_vectors(a, b, c, 90, 90, 90) +positions = [[1/4, 1/4, 0]] +types = ["Ni"] +cryst = Crystal(latvecs, positions, 62, setting=""; types) +view_crystal(cryst) + +S = 3/2 +sys = System(cryst, [1 => Moment(s=1, g=2)], :dipole_large_s) +Jbc = 1.036 +Jb = 0.6701 +Jc = -0.0469 +Jac = -0.1121 +Jab = 0.2977 +Da = 0.1969 +Db = 0.9097 +set_exchange!(sys, Jbc, Bond(2, 3, [0, 0, 0])) +set_exchange!(sys, Jc, Bond(1, 1, [0, 0, -1])) +set_exchange!(sys, Jb, Bond(1, 1, [0, 1, 0])) +set_exchange!(sys, Jab, Bond(1, 2, [0, 0, 0])) +set_exchange!(sys, Jab, Bond(3, 4, [0, 0, 0])) +set_exchange!(sys, Jac, Bond(3, 1, [0, 0, 0])) +set_exchange!(sys, Jac, Bond(4, 2, [0, 0, 0])) +set_onsite_coupling!(sys, S -> Da*S[1]^2 + Db*S[2]^2, 1) + +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys; color=[S[3] for S in sys.dipoles]) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[0, 1, 0], [2, 1, 0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +fig = Figure(size=(768, 300)) +plot_intensities!(fig[1, 1], res; units); + +data_sorted = sort(res.data; dims=1, by= >(1e-12)) +ax = Axis(fig[1, 2], xlabel="Momentum (r.l.u.)", ylabel="Intensity", + xticks=res.qpts.xticks, xticklabelrotation=π/6) +lines!(ax, data_sorted[end, :]; label="Lower band") +lines!(ax, data_sorted[end-1, :]; label="Upper band") +axislegend(ax) +fig + +qs = [[0, 1, 0], [0, 1, 2]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +fig = Figure(size=(768, 300)) +plot_intensities!(fig[1, 1], res; units) + +data_sorted = sort(res.data; dims=1, by=x->abs(x)>1e-12) +ax = Axis(fig[1, 2], xlabel="Momentum (r.l.u.)", ylabel="Intensity", + xticks=res.qpts.xticks, xticklabelrotation=π/6) +lines!(ax, data_sorted[end, :]; label="Lower band") +lines!(ax, data_sorted[end-1, :]; label="Upper band") +axislegend(ax) +fig diff --git a/previews/PR319/assets/scripts/SW14_YVO3.jl b/previews/PR319/assets/scripts/SW14_YVO3.jl new file mode 100644 index 000000000..a7ca3656a --- /dev/null +++ b/previews/PR319/assets/scripts/SW14_YVO3.jl @@ -0,0 +1,40 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = 5.2821 / sqrt(2) +b = 5.6144 / sqrt(2) +c = 7.5283 +latvecs = lattice_vectors(a, b, c, 90, 90, 90) +positions = [[0, 0, 0], [0, 0, 1/2]] +types = ["V", "V"] +cryst = Crystal(latvecs, positions, 1; types) + +sys = System(cryst, [1 => Moment(s=1/2, g=2), 2 => Moment(s=1/2, g=2)], :dipole_large_s; dims=(2,2,1)) +Jab = 2.6 +Jc = 3.1 +δ = 0.35 +K1 = 0.90 +K2 = 0.97 +d = 1.15 +Jc1 = [-Jc*(1+δ)+K2 0 -d; 0 -Jc*(1+δ) 0; +d 0 -Jc*(1+δ)] +Jc2 = [-Jc*(1-δ)+K2 0 +d; 0 -Jc*(1-δ) 0; -d 0 -Jc*(1-δ)] +set_exchange!(sys, Jab, Bond(1, 1, [1, 0, 0])) +set_exchange!(sys, Jab, Bond(2, 2, [1, 0, 0])) +set_exchange!(sys, Jc1, Bond(1, 2, [0, 0, 0])) +set_exchange!(sys, Jc2, Bond(2, 1, [0, 0, 1])) +set_exchange!(sys, Jab, Bond(1, 1, [0, 1, 0])) +set_exchange!(sys, Jab, Bond(2, 2, [0, 1, 0])) +set_onsite_coupling!(sys, S -> -K1*S[1]^2, 1) +set_onsite_coupling!(sys, S -> -K1*S[1]^2, 2) + +view_crystal(sys) + +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys) + +swt = SpinWaveTheory(sys; measure=ssf_perp(sys)) +qs = [[0.75, 0.75, 0], [0.5, 0.5, 0], [0.5, 0.5, 1]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW15_Ba3NbFe3Si2O14.jl b/previews/PR319/assets/scripts/SW15_Ba3NbFe3Si2O14.jl new file mode 100644 index 000000000..6ae18b004 --- /dev/null +++ b/previews/PR319/assets/scripts/SW15_Ba3NbFe3Si2O14.jl @@ -0,0 +1,57 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = b = 8.539 # (Å) +c = 5.2414 +latvecs = lattice_vectors(a, b, c, 90, 90, 120) +types = ["Fe", "Nb", "Ba", "Si", "O", "O", "O"] +positions = [[0.24964,0,0.5], [0,0,0], [0.56598,0,0], [2/3,1/3,0.5220], + [2/3,1/3,0.2162], [0.5259,0.7024,0.3536], [0.7840,0.9002,0.7760]] +langasite = Crystal(latvecs, positions, 150; types) +cryst = subcrystal(langasite, "Fe") +view_crystal(cryst) + +sys = System(cryst, [1 => Moment(s=5/2, g=2)], :dipole; seed=0) +J₁ = 0.85 +J₂ = 0.24 +J₃ = 0.053 +J₄ = 0.017 +J₅ = 0.24 +set_exchange!(sys, J₁, Bond(3, 2, [1,1,0])) +set_exchange!(sys, J₄, Bond(1, 1, [0,0,1])) +set_exchange!(sys, J₂, Bond(1, 3, [0,0,0])) + +ϵT = -1 +if ϵT == -1 + set_exchange!(sys, J₃, Bond(2, 3, [-1,-1,1])) + set_exchange!(sys, J₅, Bond(3, 2, [1,1,1])) +elseif ϵT == 1 + set_exchange!(sys, J₅, Bond(2, 3, [-1,-1,1])) + set_exchange!(sys, J₃, Bond(3, 2, [1,1,1])) +else + error("Chirality must be ±1") +end + +axis = [0, 0, 1] +randomize_spins!(sys) +k = minimize_spiral_energy!(sys, axis) + +sys_enlarged = repeat_periodically_as_spiral(sys, (1, 1, 7); k, axis) +plot_spins(sys_enlarged; color=[S[1] for S in sys_enlarged.dipoles]) + +measure = ssf_perp(sys) +swt = SpinWaveTheorySpiral(sys; measure, k, axis) + +qs = [[0, 1, -1], [0, 1, -1+1], [0, 1, -1+2], [0, 1, -1+3]] +path = q_space_path(cryst, qs, 400) +energies = range(0, 6, 400) +res = intensities(swt, path; energies, kernel=gaussian(fwhm=0.25)) +plot_intensities(res; units, saturation=0.7, colormap=:jet, title="Scattering intensities") + +measure = ssf_custom_bm(sys; u=[0, 1, 0], v=[0, 0, 1]) do q, ssf + imag(ssf[2,3] - ssf[3,2]) +end +swt = SpinWaveTheorySpiral(sys; measure, k, axis) +res = intensities(swt, path; energies, kernel=gaussian(fwhm=0.25)) +plot_intensities(res; units, saturation=0.8, allpositive=false, + title="Im[S²³(q, ω) - S³²(q, ω)]") diff --git a/previews/PR319/assets/scripts/SW18_Distorted_kagome.jl b/previews/PR319/assets/scripts/SW18_Distorted_kagome.jl new file mode 100644 index 000000000..036ca95a9 --- /dev/null +++ b/previews/PR319/assets/scripts/SW18_Distorted_kagome.jl @@ -0,0 +1,55 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +latvecs = lattice_vectors(10.2, 5.94, 7.81, 90, 117.7, 90) +positions = [[0, 0, 0], [1/4, 1/4, 0]] +types = ["Cu1", "Cu2"] +cryst = Crystal(latvecs, positions, 12; types, setting="b1") +view_crystal(cryst) + +moments = [1 => Moment(s=1/2, g=2), 3 => Moment(s=1/2, g=2)] +sys = System(cryst, moments, :dipole, seed=0) +J = -2 +Jp = -1 +Jab = 0.75 +Ja = -J/.66 - Jab +Jip = 0.01 +set_exchange!(sys, J, Bond(1, 3, [0, 0, 0])) +set_exchange!(sys, Jp, Bond(3, 5, [0, 0, 0])) +set_exchange!(sys, Ja, Bond(3, 4, [0, 0, 0])) +set_exchange!(sys, Jab, Bond(1, 2, [0, 0, 0])) +set_exchange!(sys, Jip, Bond(3, 4, [0, 0, 1])) + +axis = [0, 0, 1] +randomize_spins!(sys) +k = minimize_spiral_energy!(sys, axis; k_guess=randn(3)) +plot_spins(sys; ndims=2) + +k_ref = [0.785902495, 0.0, 0.107048756] +k_ref_alt = [1, 0, 1] - k_ref +@assert isapprox(k, k_ref; atol=1e-6) || isapprox(k, k_ref_alt; atol=1e-6) +@assert spiral_energy_per_site(sys; k, axis) ≈ -0.78338383838 + +suggest_magnetic_supercell([k_ref]; tol=1e-3) + +new_shape = [14 0 1; 0 1 0; 0 0 2] +sys2 = reshape_supercell(sys, new_shape) +randomize_spins!(sys2) +minimize_energy!(sys2) +energy_per_site(sys2) + +measure = ssf_perp(sys; apply_g=false) +swt = SpinWaveTheorySpiral(sys; measure, k, axis) + +qs = [[0,0,0], [1,0,0]] +path = q_space_path(cryst, qs, 400) +res = intensities_bands(swt, path) +plot_intensities(res; units) + +radii = range(0, 2, 100) # (1/Å) +energies = range(0, 6, 200) +kernel = gaussian(fwhm=0.05) +res = powder_average(cryst, radii, 400) do qs + intensities(swt, qs; energies, kernel) +end +plot_intensities(res; units) diff --git a/previews/PR319/assets/scripts/SW19_Different_Ions.jl b/previews/PR319/assets/scripts/SW19_Different_Ions.jl new file mode 100644 index 000000000..efdeeac8d --- /dev/null +++ b/previews/PR319/assets/scripts/SW19_Different_Ions.jl @@ -0,0 +1,49 @@ +using Sunny, GLMakie + +units = Units(:meV, :angstrom) +a = 3.0 +b = 8.0 +c = 4.0 +latvecs = lattice_vectors(a, b, c, 90, 90, 90) +positions = [[0, 0, 0], [0, 1/2, 0]] +types = ["Cu2", "Fe2"] +cryst = Crystal(latvecs, positions, 1; types) +view_crystal(cryst) + +J_Cu_Cu = 1.0 +J_Fe_Fe = 1.0 +J_Cu_Fe = -0.1 +moments = [1 => Moment(s=1/2, g=2), 2 => Moment(s=2, g=2)] +sys = System(cryst, moments, :dipole; dims=(2, 1, 1), seed=0) +set_exchange!(sys, J_Cu_Cu, Bond(1, 1, [-1, 0, 0])) +set_exchange!(sys, J_Fe_Fe, Bond(2, 2, [-1, 0, 0])) +set_exchange!(sys, J_Cu_Fe, Bond(2, 1, [0, 1, 0])) +set_exchange!(sys, J_Cu_Fe, Bond(1, 2, [0, 0, 0])) + +randomize_spins!(sys) +minimize_energy!(sys) +plot_spins(sys) + +qs = [[0,0,0], [1,0,0]] +path = q_space_path(cryst, qs, 400) + +fig = Figure(size=(768,600)) + +formfactors = [1 => FormFactor("Cu2"), 2 => FormFactor("Fe2")] +swt = SpinWaveTheory(sys; measure=ssf_perp(sys; formfactors)) +res = intensities_bands(swt, path) +plot_intensities!(fig[1, 1], res; units, title="All correlations") + +formfactors = [1 => FormFactor("Cu2"), 2 => zero(FormFactor)] +swt = SpinWaveTheory(sys; measure=ssf_perp(sys; formfactors)) +res = intensities_bands(swt, path) +plot_intensities!(fig[1, 2], res; units, title="Cu-Cu correlations") + +formfactors = [1 => zero(FormFactor), 2 => FormFactor("Fe2")] +swt = SpinWaveTheory(sys; measure=ssf_perp(sys; formfactors)) +res = intensities_bands(swt, path) +plot_intensities!(fig[2, 2], res; units, title="Fe-Fe correlations") + +fig + +Sunny.magnetization_lswt_correction_dipole(swt; atol=1e-4) diff --git a/previews/PR319/assets/themes/catppuccin-frappe.css b/previews/PR319/assets/themes/catppuccin-frappe.css new file mode 100644 index 000000000..32e3f0082 --- /dev/null +++ b/previews/PR319/assets/themes/catppuccin-frappe.css @@ -0,0 +1 @@ +html.theme--catppuccin-frappe .pagination-previous,html.theme--catppuccin-frappe .pagination-next,html.theme--catppuccin-frappe .pagination-link,html.theme--catppuccin-frappe .pagination-ellipsis,html.theme--catppuccin-frappe 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html.theme--catppuccin-frappe .content kbd.button.is-outlined{background-color:transparent;border-color:#414559;box-shadow:none;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#414559}html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-frappe .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #414559 #414559 !important}html.theme--catppuccin-frappe 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.button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-link.is-outlined{background-color:transparent;border-color:#8caaee;box-shadow:none;color:#8caaee}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe 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.button.is-link.is-light.is-hovered{background-color:#e2eafb;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-link.is-light:active,html.theme--catppuccin-frappe .button.is-link.is-light.is-active{background-color:#d7e1f9;border-color:transparent;color:#153a8e}html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:hover,html.theme--catppuccin-frappe .button.is-info.is-hovered{background-color:#78c4b9;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus,html.theme--catppuccin-frappe .button.is-info.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info:focus:not(:active),html.theme--catppuccin-frappe .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(129,200,190,0.25)}html.theme--catppuccin-frappe .button.is-info:active,html.theme--catppuccin-frappe .button.is-info.is-active{background-color:#6fc0b5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info{background-color:#81c8be;border-color:#81c8be;box-shadow:none}html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-focused{background-color:#81c8be;border-color:#81c8be;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-outlined{background-color:transparent;border-color:#81c8be;box-shadow:none;color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#81c8be}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #81c8be #81c8be !important}html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-info.is-light{background-color:#f1f9f8;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:hover,html.theme--catppuccin-frappe .button.is-info.is-light.is-hovered{background-color:#e8f5f3;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe .button.is-info.is-light:active,html.theme--catppuccin-frappe .button.is-info.is-light.is-active{background-color:#dff1ef;border-color:transparent;color:#2d675f}html.theme--catppuccin-frappe 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.button.is-success{background-color:#a6d189;border-color:#a6d189;box-shadow:none}html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-focused{background-color:#a6d189;border-color:#a6d189;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-outlined{background-color:transparent;border-color:#a6d189;box-shadow:none;color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6d189}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6d189 #a6d189 !important}html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-success.is-light{background-color:#f4f9f0;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:hover,html.theme--catppuccin-frappe .button.is-success.is-light.is-hovered{background-color:#edf6e7;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-success.is-light:active,html.theme--catppuccin-frappe .button.is-success.is-light.is-active{background-color:#e6f2de;border-color:transparent;color:#446a29}html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:hover,html.theme--catppuccin-frappe .button.is-warning.is-hovered{background-color:#e3c386;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus,html.theme--catppuccin-frappe .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning:focus:not(:active),html.theme--catppuccin-frappe .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(229,200,144,0.25)}html.theme--catppuccin-frappe .button.is-warning:active,html.theme--catppuccin-frappe .button.is-warning.is-active{background-color:#e0be7b;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning{background-color:#e5c890;border-color:#e5c890;box-shadow:none}html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-frappe .button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-outlined:hover,html.theme--catppuccin-frappe 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.button.is-warning.is-outlined{background-color:transparent;border-color:#e5c890;box-shadow:none;color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#e5c890}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e5c890 #e5c890 !important}html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-frappe .button.is-warning.is-light{background-color:#fbf7ee;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:hover,html.theme--catppuccin-frappe .button.is-warning.is-light.is-hovered{background-color:#f9f2e4;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe .button.is-warning.is-light:active,html.theme--catppuccin-frappe .button.is-warning.is-light.is-active{background-color:#f6edda;border-color:transparent;color:#78591c}html.theme--catppuccin-frappe 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.button.is-danger.is-outlined.is-focused{background-color:#e78284;border-color:#e78284;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-frappe .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-outlined{background-color:transparent;border-color:#e78284;box-shadow:none;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#e78284}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #e78284 #e78284 !important}html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-frappe .button.is-danger.is-light{background-color:#fceeee;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:hover,html.theme--catppuccin-frappe .button.is-danger.is-light.is-hovered{background-color:#fae3e4;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-danger.is-light:active,html.theme--catppuccin-frappe .button.is-danger.is-light.is-active{background-color:#f8d8d9;border-color:transparent;color:#9a1e20}html.theme--catppuccin-frappe .button.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-frappe .button.is-small:not(.is-rounded),html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .button.is-normal{font-size:1rem}html.theme--catppuccin-frappe .button.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .button.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .button[disabled],fieldset[disabled] html.theme--catppuccin-frappe .button{background-color:#737994;border-color:#626880;box-shadow:none;opacity:.5}html.theme--catppuccin-frappe .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-frappe .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-frappe .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-frappe .button.is-static{background-color:#292c3c;border-color:#626880;color:#838ba7;box-shadow:none;pointer-events:none}html.theme--catppuccin-frappe .button.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-frappe .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-frappe .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-frappe .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-frappe .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-frappe .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-frappe .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-frappe .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-frappe .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-frappe .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-frappe .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-frappe .buttons.has-addons .button:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-frappe .buttons.has-addons .button:focus,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused,html.theme--catppuccin-frappe .buttons.has-addons .button:active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-frappe .buttons.has-addons .button:focus:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-frappe .buttons.has-addons .button:active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-frappe .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-frappe .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-frappe .buttons.is-centered{justify-content:center}html.theme--catppuccin-frappe .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-frappe .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-frappe .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-frappe .button.is-responsive.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-frappe .button.is-responsive,html.theme--catppuccin-frappe .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-frappe .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-frappe .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-frappe .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-frappe .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-frappe .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-frappe .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-frappe .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-frappe .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-frappe .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-frappe .content li+li{margin-top:0.25em}html.theme--catppuccin-frappe .content p:not(:last-child),html.theme--catppuccin-frappe .content dl:not(:last-child),html.theme--catppuccin-frappe .content ol:not(:last-child),html.theme--catppuccin-frappe .content ul:not(:last-child),html.theme--catppuccin-frappe .content blockquote:not(:last-child),html.theme--catppuccin-frappe .content pre:not(:last-child),html.theme--catppuccin-frappe .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-frappe .content h1,html.theme--catppuccin-frappe .content h2,html.theme--catppuccin-frappe .content h3,html.theme--catppuccin-frappe .content h4,html.theme--catppuccin-frappe .content h5,html.theme--catppuccin-frappe .content h6{color:#c6d0f5;font-weight:600;line-height:1.125}html.theme--catppuccin-frappe .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-frappe .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-frappe .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-frappe .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-frappe .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-frappe .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-frappe .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-frappe .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-frappe .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-frappe .content blockquote{background-color:#292c3c;border-left:5px solid #626880;padding:1.25em 1.5em}html.theme--catppuccin-frappe .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-frappe .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-frappe .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-frappe .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-frappe .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-frappe .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-frappe .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-frappe .content ul ul ul{list-style-type:square}html.theme--catppuccin-frappe .content dd{margin-left:2em}html.theme--catppuccin-frappe .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-frappe .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-frappe .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-frappe .content figure img{display:inline-block}html.theme--catppuccin-frappe .content figure figcaption{font-style:italic}html.theme--catppuccin-frappe .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-frappe .content sup,html.theme--catppuccin-frappe .content sub{font-size:75%}html.theme--catppuccin-frappe .content table{width:100%}html.theme--catppuccin-frappe .content table td,html.theme--catppuccin-frappe .content table th{border:1px solid #626880;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-frappe .content table th{color:#b0bef1}html.theme--catppuccin-frappe .content table th:not([align]){text-align:inherit}html.theme--catppuccin-frappe .content table thead td,html.theme--catppuccin-frappe .content table thead th{border-width:0 0 2px;color:#b0bef1}html.theme--catppuccin-frappe .content table tfoot td,html.theme--catppuccin-frappe .content table tfoot th{border-width:2px 0 0;color:#b0bef1}html.theme--catppuccin-frappe .content table tbody tr:last-child td,html.theme--catppuccin-frappe .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-frappe .content .tabs li+li{margin-top:0}html.theme--catppuccin-frappe .content.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-frappe .content.is-normal{font-size:1rem}html.theme--catppuccin-frappe .content.is-medium{font-size:1.25rem}html.theme--catppuccin-frappe .content.is-large{font-size:1.5rem}html.theme--catppuccin-frappe .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-frappe .icon.is-small,html.theme--catppuccin-frappe #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-frappe .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-frappe .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-frappe .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-frappe .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-frappe .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-frappe .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-frappe div.icon-text{display:flex}html.theme--catppuccin-frappe .image,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-frappe .image img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-frappe .image img.is-rounded,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-frappe .image.is-fullwidth,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-frappe .image.is-square img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-frappe .image.is-square .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-frappe .image.is-1by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-frappe .image.is-1by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-frappe .image.is-5by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-frappe .image.is-5by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-frappe .image.is-4by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-frappe .image.is-4by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-frappe .image.is-3by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-frappe .image.is-5by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-frappe .image.is-5by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-frappe .image.is-16by9 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-frappe .image.is-16by9 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-frappe .image.is-2by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-frappe .image.is-2by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-frappe .image.is-3by1 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-frappe .image.is-3by1 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1 .has-ratio,html.theme--catppuccin-frappe .image.is-4by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 img,html.theme--catppuccin-frappe .image.is-4by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5 .has-ratio,html.theme--catppuccin-frappe .image.is-3by4 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 img,html.theme--catppuccin-frappe .image.is-3by4 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by4 .has-ratio,html.theme--catppuccin-frappe .image.is-2by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 img,html.theme--catppuccin-frappe .image.is-2by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by3 .has-ratio,html.theme--catppuccin-frappe .image.is-3by5 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-frappe .image.is-3by5 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-frappe .image.is-9by16 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-frappe .image.is-9by16 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-frappe .image.is-1by2 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-frappe .image.is-1by2 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-frappe .image.is-1by3 img,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-frappe .image.is-1by3 .has-ratio,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by3 .has-ratio{height:100%;width:100%}html.theme--catppuccin-frappe .image.is-square,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-square,html.theme--catppuccin-frappe .image.is-1by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-1by1{padding-top:100%}html.theme--catppuccin-frappe .image.is-5by4,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by4{padding-top:80%}html.theme--catppuccin-frappe .image.is-4by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by3{padding-top:75%}html.theme--catppuccin-frappe .image.is-3by2,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by2{padding-top:66.6666%}html.theme--catppuccin-frappe .image.is-5by3,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-5by3{padding-top:60%}html.theme--catppuccin-frappe .image.is-16by9,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-16by9{padding-top:56.25%}html.theme--catppuccin-frappe .image.is-2by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-2by1{padding-top:50%}html.theme--catppuccin-frappe .image.is-3by1,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--catppuccin-frappe .image.is-4by5,html.theme--catppuccin-frappe #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--catppuccin-frappe .image.is-3by4,html.theme--catppuccin-frappe #documenter .docs-sidebar 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.button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-light.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-light.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-latte 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!important}html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-latte .button.is-dark.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-outlined{background-color:transparent;border-color:#ccd0da;box-shadow:none;color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#ccd0da}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ccd0da #ccd0da !important}html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-latte .button.is-primary,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-primary:hover,html.theme--catppuccin-latte .docstring>section>a.button.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte 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.docstring>section>a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after,html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined[disabled],html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-primary.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-latte .docstring>section>a.button.is-inverted.is-outlined.docs-sourcelink{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-primary.is-light,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:hover,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:hover,html.theme--catppuccin-latte .button.is-primary.is-light.is-hovered,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-hovered.docs-sourcelink{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-primary.is-light:active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.docs-sourcelink:active,html.theme--catppuccin-latte .button.is-primary.is-light.is-active,html.theme--catppuccin-latte .docstring>section>a.button.is-light.is-active.docs-sourcelink{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:hover,html.theme--catppuccin-latte .button.is-link.is-hovered{background-color:#125ef4;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:focus,html.theme--catppuccin-latte .button.is-link.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link:focus:not(:active),html.theme--catppuccin-latte .button.is-link.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(30,102,245,0.25)}html.theme--catppuccin-latte .button.is-link:active,html.theme--catppuccin-latte .button.is-link.is-active{background-color:#0b57ef;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-link[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link{background-color:#1e66f5;border-color:#1e66f5;box-shadow:none}html.theme--catppuccin-latte .button.is-link.is-inverted{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted:hover,html.theme--catppuccin-latte .button.is-link.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-link.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-link.is-outlined{background-color:transparent;border-color:#1e66f5;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-outlined:hover,html.theme--catppuccin-latte .button.is-link.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-link.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-outlined.is-focused{background-color:#1e66f5;border-color:#1e66f5;color:#fff}html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-outlined{background-color:transparent;border-color:#1e66f5;box-shadow:none;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1e66f5}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1e66f5 #1e66f5 !important}html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-link.is-light{background-color:#ebf2fe;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:hover,html.theme--catppuccin-latte .button.is-link.is-light.is-hovered{background-color:#dfe9fe;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-link.is-light:active,html.theme--catppuccin-latte .button.is-link.is-light.is-active{background-color:#d3e1fd;border-color:transparent;color:#0a52e1}html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:hover,html.theme--catppuccin-latte .button.is-info.is-hovered{background-color:#15878e;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus,html.theme--catppuccin-latte .button.is-info.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info:focus:not(:active),html.theme--catppuccin-latte .button.is-info.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(23,146,153,0.25)}html.theme--catppuccin-latte .button.is-info:active,html.theme--catppuccin-latte .button.is-info.is-active{background-color:#147d83;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-info[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info{background-color:#179299;border-color:#179299;box-shadow:none}html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-info.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;color:#179299}html.theme--catppuccin-latte .button.is-info.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-outlined.is-focused{background-color:#179299;border-color:#179299;color:#fff}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-outlined{background-color:transparent;border-color:#179299;box-shadow:none;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#179299}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #179299 #179299 !important}html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-info.is-light{background-color:#edfcfc;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:hover,html.theme--catppuccin-latte .button.is-info.is-light.is-hovered{background-color:#e2f9fb;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-info.is-light:active,html.theme--catppuccin-latte .button.is-info.is-light.is-active{background-color:#d7f7f9;border-color:transparent;color:#1cb2ba}html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:hover,html.theme--catppuccin-latte .button.is-success.is-hovered{background-color:#3c9628;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus,html.theme--catppuccin-latte .button.is-success.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success:focus:not(:active),html.theme--catppuccin-latte .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(64,160,43,0.25)}html.theme--catppuccin-latte .button.is-success:active,html.theme--catppuccin-latte .button.is-success.is-active{background-color:#388c26;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success{background-color:#40a02b;border-color:#40a02b;box-shadow:none}html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-outlined.is-focused{background-color:#40a02b;border-color:#40a02b;color:#fff}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-outlined{background-color:transparent;border-color:#40a02b;box-shadow:none;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#40a02b}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #40a02b #40a02b !important}html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-success.is-light{background-color:#f1fbef;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:hover,html.theme--catppuccin-latte .button.is-success.is-light.is-hovered{background-color:#e8f8e5;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-success.is-light:active,html.theme--catppuccin-latte .button.is-success.is-light.is-active{background-color:#e0f5db;border-color:transparent;color:#40a12b}html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:hover,html.theme--catppuccin-latte .button.is-warning.is-hovered{background-color:#d4871c;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus,html.theme--catppuccin-latte .button.is-warning.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning:focus:not(:active),html.theme--catppuccin-latte .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(223,142,29,0.25)}html.theme--catppuccin-latte .button.is-warning:active,html.theme--catppuccin-latte .button.is-warning.is-active{background-color:#c8801a;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning{background-color:#df8e1d;border-color:#df8e1d;box-shadow:none}html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-focused{background-color:#df8e1d;border-color:#df8e1d;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-outlined{background-color:transparent;border-color:#df8e1d;box-shadow:none;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-focused{background-color:#fff;color:#df8e1d}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #df8e1d #df8e1d !important}html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-warning.is-light{background-color:#fdf6ed;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:hover,html.theme--catppuccin-latte .button.is-warning.is-light.is-hovered{background-color:#fbf1e2;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-warning.is-light:active,html.theme--catppuccin-latte .button.is-warning.is-light.is-active{background-color:#faebd6;border-color:transparent;color:#9e6515}html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:hover,html.theme--catppuccin-latte .button.is-danger.is-hovered{background-color:#c60e36;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus,html.theme--catppuccin-latte .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger:focus:not(:active),html.theme--catppuccin-latte .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(210,15,57,0.25)}html.theme--catppuccin-latte .button.is-danger:active,html.theme--catppuccin-latte .button.is-danger.is-active{background-color:#ba0d33;border-color:transparent;color:#fff}html.theme--catppuccin-latte .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger{background-color:#d20f39;border-color:#d20f39;box-shadow:none}html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-latte .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-focused{background-color:#d20f39;border-color:#d20f39;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-latte .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-outlined{background-color:transparent;border-color:#d20f39;box-shadow:none;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#d20f39}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #d20f39 #d20f39 !important}html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-latte .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-latte .button.is-danger.is-light{background-color:#feecf0;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:hover,html.theme--catppuccin-latte .button.is-danger.is-light.is-hovered{background-color:#fde0e6;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-danger.is-light:active,html.theme--catppuccin-latte .button.is-danger.is-light.is-active{background-color:#fcd4dd;border-color:transparent;color:#e9113f}html.theme--catppuccin-latte .button.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-latte .button.is-small:not(.is-rounded),html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .button.is-normal{font-size:1rem}html.theme--catppuccin-latte .button.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .button.is-large{font-size:1.5rem}html.theme--catppuccin-latte .button[disabled],fieldset[disabled] html.theme--catppuccin-latte .button{background-color:#9ca0b0;border-color:#acb0be;box-shadow:none;opacity:.5}html.theme--catppuccin-latte .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-latte .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-latte .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-latte .button.is-static{background-color:#e6e9ef;border-color:#acb0be;color:#8c8fa1;box-shadow:none;pointer-events:none}html.theme--catppuccin-latte .button.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-latte .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-latte .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-latte .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-latte .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-latte .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-latte .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-latte .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-latte .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-latte .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-latte .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-latte .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-latte .buttons.has-addons .button:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-latte .buttons.has-addons .button:focus,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused,html.theme--catppuccin-latte .buttons.has-addons .button:active,html.theme--catppuccin-latte .buttons.has-addons .button.is-active,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-latte .buttons.has-addons .button:focus:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-latte .buttons.has-addons .button:active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-latte .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-latte .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-latte .buttons.is-centered{justify-content:center}html.theme--catppuccin-latte .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-latte .buttons.is-right{justify-content:flex-end}html.theme--catppuccin-latte .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--catppuccin-latte .button.is-responsive.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--catppuccin-latte .button.is-responsive,html.theme--catppuccin-latte .button.is-responsive.is-normal{font-size:.75rem}html.theme--catppuccin-latte .button.is-responsive.is-medium{font-size:1rem}html.theme--catppuccin-latte .button.is-responsive.is-large{font-size:1.25rem}}html.theme--catppuccin-latte .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--catppuccin-latte .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--catppuccin-latte .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--catppuccin-latte .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--catppuccin-latte .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--catppuccin-latte .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--catppuccin-latte .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--catppuccin-latte .content li+li{margin-top:0.25em}html.theme--catppuccin-latte .content p:not(:last-child),html.theme--catppuccin-latte .content dl:not(:last-child),html.theme--catppuccin-latte .content ol:not(:last-child),html.theme--catppuccin-latte .content ul:not(:last-child),html.theme--catppuccin-latte .content blockquote:not(:last-child),html.theme--catppuccin-latte .content pre:not(:last-child),html.theme--catppuccin-latte .content table:not(:last-child){margin-bottom:1em}html.theme--catppuccin-latte .content h1,html.theme--catppuccin-latte .content h2,html.theme--catppuccin-latte .content h3,html.theme--catppuccin-latte .content h4,html.theme--catppuccin-latte .content h5,html.theme--catppuccin-latte .content h6{color:#4c4f69;font-weight:600;line-height:1.125}html.theme--catppuccin-latte .content h1{font-size:2em;margin-bottom:0.5em}html.theme--catppuccin-latte .content h1:not(:first-child){margin-top:1em}html.theme--catppuccin-latte .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--catppuccin-latte .content h2:not(:first-child){margin-top:1.1428em}html.theme--catppuccin-latte .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--catppuccin-latte .content h3:not(:first-child){margin-top:1.3333em}html.theme--catppuccin-latte .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--catppuccin-latte .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--catppuccin-latte .content h6{font-size:1em;margin-bottom:1em}html.theme--catppuccin-latte .content blockquote{background-color:#e6e9ef;border-left:5px solid #acb0be;padding:1.25em 1.5em}html.theme--catppuccin-latte .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ol:not([type]){list-style-type:decimal}html.theme--catppuccin-latte .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--catppuccin-latte .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--catppuccin-latte .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--catppuccin-latte .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--catppuccin-latte .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--catppuccin-latte .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--catppuccin-latte .content ul ul ul{list-style-type:square}html.theme--catppuccin-latte .content dd{margin-left:2em}html.theme--catppuccin-latte .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--catppuccin-latte .content figure:not(:first-child){margin-top:2em}html.theme--catppuccin-latte .content figure:not(:last-child){margin-bottom:2em}html.theme--catppuccin-latte .content figure img{display:inline-block}html.theme--catppuccin-latte .content figure figcaption{font-style:italic}html.theme--catppuccin-latte .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--catppuccin-latte .content sup,html.theme--catppuccin-latte .content sub{font-size:75%}html.theme--catppuccin-latte .content table{width:100%}html.theme--catppuccin-latte .content table td,html.theme--catppuccin-latte .content table th{border:1px solid #acb0be;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--catppuccin-latte .content table th{color:#41445a}html.theme--catppuccin-latte .content table th:not([align]){text-align:inherit}html.theme--catppuccin-latte .content table thead td,html.theme--catppuccin-latte .content table thead th{border-width:0 0 2px;color:#41445a}html.theme--catppuccin-latte .content table tfoot td,html.theme--catppuccin-latte .content table tfoot th{border-width:2px 0 0;color:#41445a}html.theme--catppuccin-latte .content table tbody tr:last-child td,html.theme--catppuccin-latte .content table tbody tr:last-child th{border-bottom-width:0}html.theme--catppuccin-latte .content .tabs li+li{margin-top:0}html.theme--catppuccin-latte .content.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--catppuccin-latte .content.is-normal{font-size:1rem}html.theme--catppuccin-latte .content.is-medium{font-size:1.25rem}html.theme--catppuccin-latte .content.is-large{font-size:1.5rem}html.theme--catppuccin-latte .icon{align-items:center;display:inline-flex;justify-content:center;height:1.5rem;width:1.5rem}html.theme--catppuccin-latte .icon.is-small,html.theme--catppuccin-latte #documenter .docs-sidebar form.docs-search>input.icon{height:1rem;width:1rem}html.theme--catppuccin-latte .icon.is-medium{height:2rem;width:2rem}html.theme--catppuccin-latte .icon.is-large{height:3rem;width:3rem}html.theme--catppuccin-latte .icon-text{align-items:flex-start;color:inherit;display:inline-flex;flex-wrap:wrap;line-height:1.5rem;vertical-align:top}html.theme--catppuccin-latte .icon-text .icon{flex-grow:0;flex-shrink:0}html.theme--catppuccin-latte .icon-text .icon:not(:last-child){margin-right:.25em}html.theme--catppuccin-latte .icon-text .icon:not(:first-child){margin-left:.25em}html.theme--catppuccin-latte div.icon-text{display:flex}html.theme--catppuccin-latte .image,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img{display:block;position:relative}html.theme--catppuccin-latte .image img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--catppuccin-latte .image img.is-rounded,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--catppuccin-latte .image.is-fullwidth,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--catppuccin-latte .image.is-square img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--catppuccin-latte .image.is-square .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--catppuccin-latte .image.is-1by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--catppuccin-latte .image.is-1by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--catppuccin-latte .image.is-5by4 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 img,html.theme--catppuccin-latte .image.is-5by4 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by4 .has-ratio,html.theme--catppuccin-latte .image.is-4by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 img,html.theme--catppuccin-latte .image.is-4by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-4by3 .has-ratio,html.theme--catppuccin-latte .image.is-3by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 img,html.theme--catppuccin-latte .image.is-3by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by2 .has-ratio,html.theme--catppuccin-latte .image.is-5by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 img,html.theme--catppuccin-latte .image.is-5by3 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-5by3 .has-ratio,html.theme--catppuccin-latte .image.is-16by9 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 img,html.theme--catppuccin-latte .image.is-16by9 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-16by9 .has-ratio,html.theme--catppuccin-latte .image.is-2by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 img,html.theme--catppuccin-latte .image.is-2by1 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-2by1 .has-ratio,html.theme--catppuccin-latte .image.is-3by1 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by1 img,html.theme--catppuccin-latte 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img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 img,html.theme--catppuccin-latte .image.is-3by5 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-3by5 .has-ratio,html.theme--catppuccin-latte .image.is-9by16 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 img,html.theme--catppuccin-latte .image.is-9by16 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-9by16 .has-ratio,html.theme--catppuccin-latte .image.is-1by2 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 img,html.theme--catppuccin-latte .image.is-1by2 .has-ratio,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by2 .has-ratio,html.theme--catppuccin-latte .image.is-1by3 img,html.theme--catppuccin-latte #documenter .docs-sidebar .docs-logo>img.is-1by3 img,html.theme--catppuccin-latte .image.is-1by3 .has-ratio,html.theme--catppuccin-latte 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.button.is-white.is-inverted.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:hover,html.theme--catppuccin-macchiato .button.is-black.is-hovered{background-color:#040404;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:focus,html.theme--catppuccin-macchiato .button.is-black.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black:focus:not(:active),html.theme--catppuccin-macchiato .button.is-black.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(10,10,10,0.25)}html.theme--catppuccin-macchiato .button.is-black:active,html.theme--catppuccin-macchiato .button.is-black.is-active{background-color:#000;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-black[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black{background-color:#0a0a0a;border-color:#0a0a0a;box-shadow:none}html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-black.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-focused{background-color:#0a0a0a;border-color:#0a0a0a;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-black.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-outlined{background-color:transparent;border-color:#0a0a0a;box-shadow:none;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-focused{background-color:#fff;color:#0a0a0a}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #0a0a0a #0a0a0a !important}html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-black.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:hover,html.theme--catppuccin-macchiato .button.is-light.is-hovered{background-color:#eee;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus,html.theme--catppuccin-macchiato .button.is-light.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light:focus:not(:active),html.theme--catppuccin-macchiato .button.is-light.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(245,245,245,0.25)}html.theme--catppuccin-macchiato .button.is-light:active,html.theme--catppuccin-macchiato .button.is-light.is-active{background-color:#e8e8e8;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light{background-color:#f5f5f5;border-color:#f5f5f5;box-shadow:none}html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-light.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-light.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-light.is-outlined{background-color:transparent;border-color:#f5f5f5;color:#f5f5f5}html.theme--catppuccin-macchiato .button.is-light.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-light.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-focused{background-color:#f5f5f5;border-color:#f5f5f5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-light.is-outlined.is-loading::after{border-color:transparent transparent #f5f5f5 #f5f5f5 !important}html.theme--catppuccin-macchiato 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.content kbd.button{background-color:#363a4f;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:hover,html.theme--catppuccin-macchiato .content kbd.button:hover,html.theme--catppuccin-macchiato .button.is-dark.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-hovered{background-color:#313447;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus,html.theme--catppuccin-macchiato .content kbd.button:focus,html.theme--catppuccin-macchiato .button.is-dark.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark:focus:not(:active),html.theme--catppuccin-macchiato .content kbd.button:focus:not(:active),html.theme--catppuccin-macchiato .button.is-dark.is-focused:not(:active),html.theme--catppuccin-macchiato .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(54,58,79,0.25)}html.theme--catppuccin-macchiato .button.is-dark:active,html.theme--catppuccin-macchiato .content kbd.button:active,html.theme--catppuccin-macchiato .button.is-dark.is-active,html.theme--catppuccin-macchiato .content kbd.button.is-active{background-color:#2c2f40;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-dark[disabled],html.theme--catppuccin-macchiato .content kbd.button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button{background-color:#363a4f;border-color:#363a4f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-dark.is-inverted,html.theme--catppuccin-macchiato .content kbd.button.is-inverted{background-color:#fff;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted:hover,html.theme--catppuccin-macchiato 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.button.is-dark.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-focused,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-focused{background-color:#363a4f;border-color:#363a4f;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading::after{border-color:transparent transparent #363a4f #363a4f !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-dark.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-macchiato .content kbd.button.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-dark.is-outlined[disabled],html.theme--catppuccin-macchiato .content kbd.button.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-dark.is-outlined,fieldset[disabled] html.theme--catppuccin-macchiato .content kbd.button.is-outlined{background-color:transparent;border-color:#363a4f;box-shadow:none;color:#363a4f}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-macchiato .content 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.button.is-info.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-focused{background-color:#8bd5ca;border-color:#8bd5ca;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-outlined{background-color:transparent;border-color:#8bd5ca;box-shadow:none;color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#8bd5ca}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #8bd5ca #8bd5ca !important}html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-info.is-light{background-color:#f0faf8;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:hover,html.theme--catppuccin-macchiato .button.is-info.is-light.is-hovered{background-color:#e7f6f4;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-info.is-light:active,html.theme--catppuccin-macchiato .button.is-info.is-light.is-active{background-color:#ddf3f0;border-color:transparent;color:#276d62}html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:hover,html.theme--catppuccin-macchiato .button.is-success.is-hovered{background-color:#9ed78c;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus,html.theme--catppuccin-macchiato .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success:focus:not(:active),html.theme--catppuccin-macchiato .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,218,149,0.25)}html.theme--catppuccin-macchiato .button.is-success:active,html.theme--catppuccin-macchiato .button.is-success.is-active{background-color:#96d382;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success{background-color:#a6da95;border-color:#a6da95;box-shadow:none}html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-focused{background-color:#a6da95;border-color:#a6da95;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-outlined{background-color:transparent;border-color:#a6da95;box-shadow:none;color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6da95}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6da95 #a6da95 !important}html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-success.is-light{background-color:#f2faf0;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:hover,html.theme--catppuccin-macchiato .button.is-success.is-light.is-hovered{background-color:#eaf6e6;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-success.is-light:active,html.theme--catppuccin-macchiato .button.is-success.is-light.is-active{background-color:#e2f3dd;border-color:transparent;color:#386e26}html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:hover,html.theme--catppuccin-macchiato .button.is-warning.is-hovered{background-color:#eccf94;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus,html.theme--catppuccin-macchiato .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning:focus:not(:active),html.theme--catppuccin-macchiato .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(238,212,159,0.25)}html.theme--catppuccin-macchiato .button.is-warning:active,html.theme--catppuccin-macchiato .button.is-warning.is-active{background-color:#eaca89;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning{background-color:#eed49f;border-color:#eed49f;box-shadow:none}html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-focused{background-color:#eed49f;border-color:#eed49f;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-macchiato .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-outlined{background-color:transparent;border-color:#eed49f;box-shadow:none;color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#eed49f}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #eed49f #eed49f !important}html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-macchiato .button.is-warning.is-light{background-color:#fcf7ee;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:hover,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-hovered{background-color:#faf2e3;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-warning.is-light:active,html.theme--catppuccin-macchiato .button.is-warning.is-light.is-active{background-color:#f8eed8;border-color:transparent;color:#7e5c16}html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:hover,html.theme--catppuccin-macchiato .button.is-danger.is-hovered{background-color:#eb7c8c;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus,html.theme--catppuccin-macchiato .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger:focus:not(:active),html.theme--catppuccin-macchiato .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(237,135,150,0.25)}html.theme--catppuccin-macchiato .button.is-danger:active,html.theme--catppuccin-macchiato .button.is-danger.is-active{background-color:#ea7183;border-color:transparent;color:#fff}html.theme--catppuccin-macchiato .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger{background-color:#ed8796;border-color:#ed8796;box-shadow:none}html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-macchiato .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-focused{background-color:#ed8796;border-color:#ed8796;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-macchiato .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-outlined{background-color:transparent;border-color:#ed8796;box-shadow:none;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#ed8796}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #ed8796 #ed8796 !important}html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-macchiato .button.is-danger.is-light{background-color:#fcedef;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:hover,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-hovered{background-color:#fbe2e6;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-danger.is-light:active,html.theme--catppuccin-macchiato .button.is-danger.is-light.is-active{background-color:#f9d7dc;border-color:transparent;color:#971729}html.theme--catppuccin-macchiato .button.is-small,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-macchiato .button.is-small:not(.is-rounded),html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .button.is-normal{font-size:1rem}html.theme--catppuccin-macchiato .button.is-medium{font-size:1.25rem}html.theme--catppuccin-macchiato .button.is-large{font-size:1.5rem}html.theme--catppuccin-macchiato .button[disabled],fieldset[disabled] html.theme--catppuccin-macchiato .button{background-color:#6e738d;border-color:#5b6078;box-shadow:none;opacity:.5}html.theme--catppuccin-macchiato .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-macchiato .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-macchiato .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-macchiato .button.is-static{background-color:#1e2030;border-color:#5b6078;color:#8087a2;box-shadow:none;pointer-events:none}html.theme--catppuccin-macchiato .button.is-rounded,html.theme--catppuccin-macchiato #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-macchiato .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-macchiato .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-macchiato .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-macchiato .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-macchiato .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-macchiato .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-macchiato .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-macchiato .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-macchiato .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-macchiato .buttons.has-addons .button:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused,html.theme--catppuccin-macchiato .buttons.has-addons .button:active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-macchiato .buttons.has-addons .button:focus:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-focused:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button:active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-active:hover,html.theme--catppuccin-macchiato .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--catppuccin-macchiato .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--catppuccin-macchiato .buttons.is-centered{justify-content:center}html.theme--catppuccin-macchiato .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--catppuccin-macchiato 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kbd.button.is-hovered{background-color:#2c2d3d;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus,html.theme--catppuccin-mocha .content kbd.button:focus,html.theme--catppuccin-mocha .button.is-dark.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-dark:focus:not(:active),html.theme--catppuccin-mocha .content kbd.button:focus:not(:active),html.theme--catppuccin-mocha .button.is-dark.is-focused:not(:active),html.theme--catppuccin-mocha .content kbd.button.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(49,50,68,0.25)}html.theme--catppuccin-mocha .button.is-dark:active,html.theme--catppuccin-mocha .content kbd.button:active,html.theme--catppuccin-mocha .button.is-dark.is-active,html.theme--catppuccin-mocha .content kbd.button.is-active{background-color:#262735;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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kbd.button.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-focused,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-focused{background-color:#fff;color:#313244}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after,html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #313244 #313244 !important}html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined[disabled],html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-dark.is-inverted.is-outlined,fieldset[disabled] html.theme--catppuccin-mocha .content kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-primary,html.theme--catppuccin-mocha .docstring>section>a.button.docs-sourcelink{background-color:#89b4fa;border-color:transparent;color:#fff}html.theme--catppuccin-mocha 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html.theme--catppuccin-mocha .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-link.is-light{background-color:#ebf3fe;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:hover,html.theme--catppuccin-mocha .button.is-link.is-light.is-hovered{background-color:#dfebfe;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-link.is-light:active,html.theme--catppuccin-mocha .button.is-link.is-light.is-active{background-color:#d3e3fd;border-color:transparent;color:#063c93}html.theme--catppuccin-mocha .button.is-info{background-color:#94e2d5;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:hover,html.theme--catppuccin-mocha .button.is-info.is-hovered{background-color:#8adfd1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info:focus,html.theme--catppuccin-mocha 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.button.is-info.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-focused{background-color:#94e2d5;border-color:#94e2d5;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-info.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-outlined{background-color:transparent;border-color:#94e2d5;box-shadow:none;color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#94e2d5}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #94e2d5 #94e2d5 !important}html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-info.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-info.is-light{background-color:#effbf9;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:hover,html.theme--catppuccin-mocha .button.is-info.is-light.is-hovered{background-color:#e5f8f5;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-info.is-light:active,html.theme--catppuccin-mocha .button.is-info.is-light.is-active{background-color:#dbf5f1;border-color:transparent;color:#207466}html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:hover,html.theme--catppuccin-mocha .button.is-success.is-hovered{background-color:#9de097;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus,html.theme--catppuccin-mocha .button.is-success.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success:focus:not(:active),html.theme--catppuccin-mocha .button.is-success.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(166,227,161,0.25)}html.theme--catppuccin-mocha .button.is-success:active,html.theme--catppuccin-mocha .button.is-success.is-active{background-color:#93dd8d;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success{background-color:#a6e3a1;border-color:#a6e3a1;box-shadow:none}html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-focused{background-color:#a6e3a1;border-color:#a6e3a1;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-outlined{background-color:transparent;border-color:#a6e3a1;box-shadow:none;color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#a6e3a1}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #a6e3a1 #a6e3a1 !important}html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-success.is-light{background-color:#f0faef;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:hover,html.theme--catppuccin-mocha .button.is-success.is-light.is-hovered{background-color:#e7f7e5;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-success.is-light:active,html.theme--catppuccin-mocha .button.is-success.is-light.is-active{background-color:#def4dc;border-color:transparent;color:#287222}html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:hover,html.theme--catppuccin-mocha .button.is-warning.is-hovered{background-color:#f8dea3;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus,html.theme--catppuccin-mocha .button.is-warning.is-focused{border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning:focus:not(:active),html.theme--catppuccin-mocha .button.is-warning.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(249,226,175,0.25)}html.theme--catppuccin-mocha .button.is-warning:active,html.theme--catppuccin-mocha .button.is-warning.is-active{background-color:#f7d997;border-color:transparent;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning{background-color:#f9e2af;border-color:#f9e2af;box-shadow:none}html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-hovered{background-color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted{background-color:rgba(0,0,0,0.7);border-color:transparent;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-loading::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-focused{background-color:#f9e2af;border-color:#f9e2af;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-outlined.is-loading.is-focused::after{border-color:transparent transparent rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--catppuccin-mocha .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-outlined{background-color:transparent;border-color:#f9e2af;box-shadow:none;color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f9e2af}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f9e2af #f9e2af !important}html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--catppuccin-mocha .button.is-warning.is-light{background-color:#fef8ec;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:hover,html.theme--catppuccin-mocha .button.is-warning.is-light.is-hovered{background-color:#fdf4e0;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-warning.is-light:active,html.theme--catppuccin-mocha .button.is-warning.is-light.is-active{background-color:#fcf0d4;border-color:transparent;color:#8a620a}html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:hover,html.theme--catppuccin-mocha .button.is-danger.is-hovered{background-color:#f27f9f;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus,html.theme--catppuccin-mocha .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger:focus:not(:active),html.theme--catppuccin-mocha .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(243,139,168,0.25)}html.theme--catppuccin-mocha .button.is-danger:active,html.theme--catppuccin-mocha .button.is-danger.is-active{background-color:#f17497;border-color:transparent;color:#fff}html.theme--catppuccin-mocha .button.is-danger[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger{background-color:#f38ba8;border-color:#f38ba8;box-shadow:none}html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--catppuccin-mocha .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-focused{background-color:#f38ba8;border-color:#f38ba8;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--catppuccin-mocha .button.is-danger.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-outlined{background-color:transparent;border-color:#f38ba8;box-shadow:none;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:hover,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-hovered,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined:focus,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-focused{background-color:#fff;color:#f38ba8}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:hover::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading:focus::after,html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f38ba8 #f38ba8 !important}html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--catppuccin-mocha .button.is-danger.is-light{background-color:#fdedf1;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:hover,html.theme--catppuccin-mocha .button.is-danger.is-light.is-hovered{background-color:#fce1e8;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-danger.is-light:active,html.theme--catppuccin-mocha .button.is-danger.is-light.is-active{background-color:#fbd5e0;border-color:transparent;color:#991036}html.theme--catppuccin-mocha .button.is-small,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--catppuccin-mocha .button.is-small:not(.is-rounded),html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .button.is-normal{font-size:1rem}html.theme--catppuccin-mocha .button.is-medium{font-size:1.25rem}html.theme--catppuccin-mocha .button.is-large{font-size:1.5rem}html.theme--catppuccin-mocha .button[disabled],fieldset[disabled] html.theme--catppuccin-mocha .button{background-color:#6c7086;border-color:#585b70;box-shadow:none;opacity:.5}html.theme--catppuccin-mocha .button.is-fullwidth{display:flex;width:100%}html.theme--catppuccin-mocha .button.is-loading{color:transparent !important;pointer-events:none}html.theme--catppuccin-mocha .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--catppuccin-mocha .button.is-static{background-color:#181825;border-color:#585b70;color:#7f849c;box-shadow:none;pointer-events:none}html.theme--catppuccin-mocha .button.is-rounded,html.theme--catppuccin-mocha #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}html.theme--catppuccin-mocha .buttons{align-items:center;display:flex;flex-wrap:wrap;justify-content:flex-start}html.theme--catppuccin-mocha .buttons .button{margin-bottom:0.5rem}html.theme--catppuccin-mocha .buttons .button:not(:last-child):not(.is-fullwidth){margin-right:.5rem}html.theme--catppuccin-mocha .buttons:last-child{margin-bottom:-0.5rem}html.theme--catppuccin-mocha .buttons:not(:last-child){margin-bottom:1rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large){font-size:.75rem}html.theme--catppuccin-mocha .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}html.theme--catppuccin-mocha .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large){font-size:1.25rem}html.theme--catppuccin-mocha .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium){font-size:1.5rem}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--catppuccin-mocha .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--catppuccin-mocha .buttons.has-addons .button:last-child{margin-right:0}html.theme--catppuccin-mocha .buttons.has-addons .button:hover,html.theme--catppuccin-mocha .buttons.has-addons .button.is-hovered{z-index:2}html.theme--catppuccin-mocha .buttons.has-addons .button:focus,html.theme--catppuccin-mocha .buttons.has-addons .button.is-focused,html.theme--catppuccin-mocha .buttons.has-addons .button:active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-active,html.theme--catppuccin-mocha .buttons.has-addons .button.is-selected{z-index:3}html.theme--catppuccin-mocha .buttons.has-addons 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.button.is-link.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-link.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined{background-color:transparent;border-color:#1abc9c;box-shadow:none;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused{background-color:#fff;color:#1abc9c}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #1abc9c #1abc9c !important}html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-link.is-light{background-color:#edfdf9;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:hover,html.theme--documenter-dark .button.is-link.is-light.is-hovered{background-color:#e2fbf6;border-color:transparent;color:#15987e}html.theme--documenter-dark .button.is-link.is-light:active,html.theme--documenter-dark 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.button.is-info.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused{background-color:#fff;color:#3c5dcd}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #3c5dcd #3c5dcd !important}html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark 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.button.is-success.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;color:#259a12}html.theme--documenter-dark .button.is-success.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-outlined.is-focused{background-color:#259a12;border-color:#259a12;color:#fff}html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-success.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined{background-color:transparent;border-color:#259a12;box-shadow:none;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;color:#fff}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused{background-color:#fff;color:#259a12}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #259a12 #259a12 !important}html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-success.is-light{background-color:#effded;color:#2ec016}html.theme--documenter-dark .button.is-success.is-light:hover,html.theme--documenter-dark 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rgba(0,0,0,0.7) rgba(0,0,0,0.7) !important}html.theme--documenter-dark .button.is-warning.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined{background-color:transparent;border-color:#f4c72f;box-shadow:none;color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused{background-color:rgba(0,0,0,0.7);color:#f4c72f}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after,html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after{border-color:transparent transparent #f4c72f #f4c72f !important}html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined{background-color:transparent;border-color:rgba(0,0,0,0.7);box-shadow:none;color:rgba(0,0,0,0.7)}html.theme--documenter-dark .button.is-warning.is-light{background-color:#fefaec;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:hover,html.theme--documenter-dark .button.is-warning.is-light.is-hovered{background-color:#fdf7e0;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-warning.is-light:active,html.theme--documenter-dark .button.is-warning.is-light.is-active{background-color:#fdf3d3;border-color:transparent;color:#8c6e07}html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:hover,html.theme--documenter-dark .button.is-danger.is-hovered{background-color:#c13930;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus,html.theme--documenter-dark .button.is-danger.is-focused{border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger:focus:not(:active),html.theme--documenter-dark .button.is-danger.is-focused:not(:active){box-shadow:0 0 0 0.125em rgba(203,60,51,0.25)}html.theme--documenter-dark .button.is-danger:active,html.theme--documenter-dark .button.is-danger.is-active{background-color:#b7362e;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-danger[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger{background-color:#cb3c33;border-color:#cb3c33;box-shadow:none}html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-inverted:hover,html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered{background-color:#f2f2f2}html.theme--documenter-dark .button.is-danger.is-inverted[disabled],fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted{background-color:#fff;border-color:transparent;box-shadow:none;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-loading::after{border-color:transparent transparent #fff #fff !important}html.theme--documenter-dark .button.is-danger.is-outlined{background-color:transparent;border-color:#cb3c33;color:#cb3c33}html.theme--documenter-dark .button.is-danger.is-outlined:hover,html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered,html.theme--documenter-dark 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html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-danger.is-light{background-color:#fbefef;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#f8e6e5;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#f6dcda;border-color:transparent;color:#c03930}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}html.theme--documenter-dark .button.is-medium{font-size:1.25rem}html.theme--documenter-dark .button.is-large{font-size:1.5rem}html.theme--documenter-dark .button[disabled],fieldset[disabled] html.theme--documenter-dark .button{background-color:#8c9b9d;border-color:#5e6d6f;box-shadow:none;opacity:.5}html.theme--documenter-dark .button.is-fullwidth{display:flex;width:100%}html.theme--documenter-dark .button.is-loading{color:transparent !important;pointer-events:none}html.theme--documenter-dark .button.is-loading::after{position:absolute;left:calc(50% - (1em * 0.5));top:calc(50% - (1em * 0.5));position:absolute !important}html.theme--documenter-dark .button.is-static{background-color:#282f2f;border-color:#5e6d6f;color:#dbdee0;box-shadow:none;pointer-events:none}html.theme--documenter-dark .button.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{border-radius:9999px;padding-left:calc(1em + 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.buttons.has-addons .button:not(:first-child){border-bottom-left-radius:0;border-top-left-radius:0}html.theme--documenter-dark .buttons.has-addons .button:not(:last-child){border-bottom-right-radius:0;border-top-right-radius:0;margin-right:-1px}html.theme--documenter-dark .buttons.has-addons .button:last-child{margin-right:0}html.theme--documenter-dark .buttons.has-addons .button:hover,html.theme--documenter-dark .buttons.has-addons .button.is-hovered{z-index:2}html.theme--documenter-dark .buttons.has-addons .button:focus,html.theme--documenter-dark .buttons.has-addons .button.is-focused,html.theme--documenter-dark .buttons.has-addons .button:active,html.theme--documenter-dark .buttons.has-addons .button.is-active,html.theme--documenter-dark .buttons.has-addons .button.is-selected{z-index:3}html.theme--documenter-dark .buttons.has-addons .button:focus:hover,html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover,html.theme--documenter-dark .buttons.has-addons .button:active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-active:hover,html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover{z-index:4}html.theme--documenter-dark .buttons.has-addons .button.is-expanded{flex-grow:1;flex-shrink:1}html.theme--documenter-dark .buttons.is-centered{justify-content:center}html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}html.theme--documenter-dark .buttons.is-right{justify-content:flex-end}html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth){margin-left:0.25rem;margin-right:0.25rem}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}html.theme--documenter-dark .content li+li{margin-top:0.25em}html.theme--documenter-dark .content p:not(:last-child),html.theme--documenter-dark .content dl:not(:last-child),html.theme--documenter-dark .content ol:not(:last-child),html.theme--documenter-dark .content ul:not(:last-child),html.theme--documenter-dark .content blockquote:not(:last-child),html.theme--documenter-dark .content pre:not(:last-child),html.theme--documenter-dark .content table:not(:last-child){margin-bottom:1em}html.theme--documenter-dark .content h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content blockquote{background-color:#282f2f;border-left:5px solid #5e6d6f;padding:1.25em 1.5em}html.theme--documenter-dark .content ol{list-style-position:outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ol:not([type]){list-style-type:decimal}html.theme--documenter-dark .content ol.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){list-style-type:upper-roman}html.theme--documenter-dark .content ul{list-style:disc outside;margin-left:2em;margin-top:1em}html.theme--documenter-dark .content ul ul{list-style-type:circle;margin-top:0.5em}html.theme--documenter-dark .content ul ul ul{list-style-type:square}html.theme--documenter-dark .content dd{margin-left:2em}html.theme--documenter-dark .content figure{margin-left:2em;margin-right:2em;text-align:center}html.theme--documenter-dark .content figure:not(:first-child){margin-top:2em}html.theme--documenter-dark .content figure:not(:last-child){margin-bottom:2em}html.theme--documenter-dark .content figure img{display:inline-block}html.theme--documenter-dark .content figure figcaption{font-style:italic}html.theme--documenter-dark .content pre{-webkit-overflow-scrolling:touch;overflow-x:auto;padding:0;white-space:pre;word-wrap:normal}html.theme--documenter-dark .content sup,html.theme--documenter-dark .content sub{font-size:75%}html.theme--documenter-dark .content table{width:100%}html.theme--documenter-dark .content table td,html.theme--documenter-dark .content table th{border:1px solid #5e6d6f;border-width:0 0 1px;padding:0.5em 0.75em;vertical-align:top}html.theme--documenter-dark .content table th{color:#f2f2f2}html.theme--documenter-dark .content table th:not([align]){text-align:inherit}html.theme--documenter-dark .content table thead td,html.theme--documenter-dark .content table thead th{border-width:0 0 2px;color:#f2f2f2}html.theme--documenter-dark .content table tfoot td,html.theme--documenter-dark .content table tfoot th{border-width:2px 0 0;color:#f2f2f2}html.theme--documenter-dark .content table tbody tr:last-child td,html.theme--documenter-dark .content table tbody tr:last-child th{border-bottom-width:0}html.theme--documenter-dark .content .tabs li+li{margin-top:0}html.theme--documenter-dark .content.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.content{font-size:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}html.theme--documenter-dark .content.is-medium{font-size:1.25rem}html.theme--documenter-dark .content.is-large{font-size:1.5rem}html.theme--documenter-dark 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img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img{display:block;height:auto;width:100%}html.theme--documenter-dark .image img.is-rounded,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}html.theme--documenter-dark .image.is-square img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square img,html.theme--documenter-dark .image.is-square .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-square .has-ratio,html.theme--documenter-dark .image.is-1by1 img,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 img,html.theme--documenter-dark .image.is-1by1 .has-ratio,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by1 .has-ratio,html.theme--documenter-dark .image.is-5by4 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.docs-logo>img.is-3by1{padding-top:33.3333%}html.theme--documenter-dark .image.is-4by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-4by5{padding-top:125%}html.theme--documenter-dark .image.is-3by4,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by4{padding-top:133.3333%}html.theme--documenter-dark .image.is-2by3,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-2by3{padding-top:150%}html.theme--documenter-dark .image.is-3by5,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-3by5{padding-top:166.6666%}html.theme--documenter-dark .image.is-9by16,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-9by16{padding-top:177.7777%}html.theme--documenter-dark .image.is-1by2,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-1by2{padding-top:200%}html.theme--documenter-dark .image.is-1by3,html.theme--documenter-dark #documenter .docs-sidebar 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.hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/previews/PR319/assets/themeswap.js b/previews/PR319/assets/themeswap.js new file mode 100644 index 000000000..9f5eebe6a --- /dev/null +++ b/previews/PR319/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/previews/PR319/assets/warner.js b/previews/PR319/assets/warner.js new file mode 100644 index 000000000..3f6f5d008 --- /dev/null +++ b/previews/PR319/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
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uu`eI=MMrDCtfMcNh{{&{|ICPJMa}WYfPaQ21#Lt=*})F;bH#D*gnt9s1LODr literal 0 HcmV?d00001 diff --git a/previews/PR319/examples/01_LSWT_CoRh2O4.html b/previews/PR319/examples/01_LSWT_CoRh2O4.html new file mode 100644 index 000000000..c09569c55 --- /dev/null +++ b/previews/PR319/examples/01_LSWT_CoRh2O4.html @@ -0,0 +1,44 @@ + +1. Spin wave simulations of CoRh₂O₄ · Sunny documentation

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1. Spin wave simulations of CoRh₂O₄

This tutorial introduces Sunny through its features for performing conventional spin wave theory calculations. We consider the crystal CoRh₂O₄ and reproduce the calculations of Ge et al., Phys. Rev. B 96, 064413.

Get Julia and Sunny

Sunny is implemented in Julia, which allows for interactive development (like Python or Matlab) while also providing high numerical efficiency (like C++ or Fortran). New Julia users should begin with our Getting Started guide. Sunny requires Julia 1.10 or later.

From the Julia prompt, load Sunny and also GLMakie for graphics.

using Sunny, GLMakie

If these packages are not yet installed, Julia will offer to install them. If executing this tutorial gives an error, you may need to update Sunny and GLMakie from the built-in package manager.

Units

The Units object selects reference energy and length scales, and uses these to provide physical constants. For example, units.K returns one kelvin as 0.086 meV, where the Boltzmann constant is implicit.

units = Units(:meV, :angstrom);

Crystal cell

A crystallographic cell may be loaded from a .cif file, or specified from atom positions and types.

Start by defining the shape of the conventional chemical cell. CoRh₂O₄ has cubic spacegroup 227 (Fd-3m). Its lattice constants are 8.5 Å, and the cell angles are 90°. With this information, lattice_vectors constructs a 3×3 matrix latvecs. Columns of latvecs define the lattice vectors $(𝐚_1, 𝐚_2, 𝐚_3)$ in the global Cartesian coordinate system. Conversely, columns of inv(latvecs) define the global Cartesian axes $(\hat{x}, \hat{y}, \hat{z})$ in components of the lattice vectors.

a = 8.5031 # (Å)
+latvecs = lattice_vectors(a, a, a, 90, 90, 90)
3×3 StaticArraysCore.SMatrix{3, 3, Float64, 9} with indices SOneTo(3)×SOneTo(3):
+ 8.5031  0.0     0.0
+ 0.0     8.5031  0.0
+ 0.0     0.0     8.5031

Construct the Crystal cell from the spacegroup number 227 and one representative atom of each occupied Wyckoff. In the standard setting of spacegroup 227, position [0, 0, 0] belongs to Wyckoff 8a, which is the diamond cubic crystal.

positions = [[0, 0, 0]]
+cryst = Crystal(latvecs, positions, 227; types=["Co"], setting="1")
Crystal
+Spacegroup 'F d -3 m' (227)
+Lattice params a=8.503, b=8.503, c=8.503, α=90°, β=90°, γ=90°
+Cell volume 614.8
+Type 'Co', Wyckoff 8a (point group '-43m'):
+   1. [0, 0, 0]
+   2. [1/2, 1/2, 0]
+   3. [1/4, 1/4, 1/4]
+   4. [3/4, 3/4, 1/4]
+   5. [1/2, 0, 1/2]
+   6. [0, 1/2, 1/2]
+   7. [3/4, 1/4, 3/4]
+   8. [1/4, 3/4, 3/4]
+

view_crystal launches an interface for interactive inspection and symmetry analysis.

view_crystal(cryst)
Example block output

Spin system

A System will define the spin model. Each cobalt atom carries quantum spin $s = 3/2$, with a $g$-factor of 2. Specify this Moment data for cobalt atom 1. By symmetry, the same moment data also applies to cobalt atoms 2, 3, ... 7. The option :dipole indicates a traditional model type, for which quantum spin is modeled as a dipole expectation value.

sys = System(cryst, [1 => Moment(s=3/2, g=2)], :dipole)
System [Dipole mode]
+Supercell (1×1×1)×8
+Energy per site 0
+

Ge et al. demonstrated that inelastic neutron scattering data for CoRh₂O₄ is well modeled by antiferromagnetic nearest neighbor exchange, J = 0.63 meV. Call set_exchange! with the bond that connects atom 1 to atom 3, and has zero displacement between chemical cells. Consistent with the symmetries of spacegroup 227, this interaction will be propagated to all other nearest-neighbor bonds. Calling view_crystal with sys now shows the antiferromagnetic Heisenberg interactions as blue polkadot spheres.

J = +0.63 # (meV)
+set_exchange!(sys, J, Bond(1, 3, [0, 0, 0]))
+view_crystal(sys)
Example block output

Optimizing spins

To search for the ground state, call randomize_spins! and minimize_energy! in sequence. For this problem, optimization converges rapidly to the expected Néel order. See this with plot_spins, where spins are colored according to their global $z$-component.

randomize_spins!(sys)
+minimize_energy!(sys)
+plot_spins(sys; color=[S[3] for S in sys.dipoles])
Example block output

The diamond lattice is bipartite, allowing each spin to perfectly anti-align with its 4 nearest-neighbors. Each of these 4 bonds contribute $-J s^2$ to the total energy. Two sites participate in each bond, so the energy per site is $-2 J s^2$. Check this by calling energy_per_site.

@assert energy_per_site(sys) ≈ -2J*(3/2)^2

Reshaping the magnetic cell

The most compact magnetic cell for this Néel order is a primitive unit cell. Reduce the magnetic cell size using reshape_supercell, where columns of the shape matrix are primitive lattice vectors as multiples of the conventional cubic lattice vectors $(𝐚_1, 𝐚_2, 𝐚_3)$. One could alternatively use shape = cryst.latvecs \ cryst.prim_latvecs. Verify that the energy per site is unchanged after the reshaping the supercell.

shape = [0 1 1;
+         1 0 1;
+         1 1 0] / 2
+sys_prim = reshape_supercell(sys, shape)
+@assert energy_per_site(sys_prim) ≈ -2J*(3/2)^2

Plotting sys_prim shows the two spins within the primitive cell, as well as the larger conventional cubic cell for context.

plot_spins(sys_prim; color=[S[3] for S in sys_prim.dipoles])
Example block output

Spin wave theory

With this primitive cell, we will perform a SpinWaveTheory calculation of the structure factor $\mathcal{S}(𝐪,ω)$. The measurement ssf_perp indicates projection of the spin structure factor $\mathcal{S}(𝐪,ω)$ perpendicular to the direction of momentum transfer, as appropriate for unpolarized neutron scattering. The isotropic FormFactor for Co²⁺ dampens intensities at large $𝐪$.

formfactors = [1 => FormFactor("Co2")]
+measure = ssf_perp(sys_prim; formfactors)
+swt = SpinWaveTheory(sys_prim; measure)
SpinWaveTheory [Dipole mode]
+  2 atoms
+

Select lorentzian broadening with a full-width at half-maximum (FWHM) of 0.8 meV.

kernel = lorentzian(fwhm=0.8)
Broadening

Define a q_space_path that connects high-symmetry points in reciprocal space. The $𝐪$-points are given in reciprocal lattice units (RLU) for the original cubic cell. For example, [1/2, 1/2, 0] denotes the sum of the first two reciprocal lattice vectors, $𝐛_1/2 + 𝐛_2/2$. A total of 500 $𝐪$-points will be sampled along the path.

qs = [[0, 0, 0], [1/2, 0, 0], [1/2, 1/2, 0], [0, 0, 0]]
+path = q_space_path(cryst, qs, 500)
QPath (500 samples)
+  [0, 0, 0] → [1/2, 0, 0] → [1/2, 1/2, 0] → [0, 0, 0]
+

Calculate single-crystal scattering intensities along this path, for energies between 0 and 6 meV. Use plot_intensities to visualize the result.

energies = range(0, 6, 300)
+res = intensities(swt, path; energies, kernel)
+plot_intensities(res; units, title="CoRh₂O₄ LSWT")
Example block output

Sometimes experimental data is only available as a powder average, i.e., as an average over all possible crystal orientations. Use powder_average to simulate these intensities. Each $𝐪$-magnitude defines a spherical shell in reciprocal space. Consider 200 radii from 0 to 3 inverse angstroms, and collect 2000 random samples per spherical shell. As configured, this calculation completes in about two seconds. Had we used the conventional cubic cell, the calculation would be an order of magnitude slower.

radii = range(0, 3, 200) # (1/Å)
+res = powder_average(cryst, radii, 2000) do qs
+    intensities(swt, qs; energies, kernel)
+end
+plot_intensities(res; units, saturation=1.0, title="CoRh₂O₄ Powder Average")
Example block output

This result can be compared to experimental neutron scattering data from Fig. 5 of Ge et al.

What's next?

  • For more spin wave calculations of this type, browse the SpinW tutorials ported to Sunny.
  • Spin wave theory neglects thermal fluctuations of the magnetic order. The next CoRh₂O₄ tutorial demonstrates how to sample spins in thermal equilibrium, and measure dynamical correlations from the classical spin dynamics.
  • Sunny also offers features that go beyond the dipole approximation of a quantum spin via the theory of SU(N) coherent states. This can be especially useful for systems with strong single-ion anisotropy, as demonstrated in the FeI₂ tutorial.
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