build based on 4c3b25b

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-08-30T22:33:06","documenter_version":"1.6.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-08-30T22:42:16","documenter_version":"1.6.0"}}

dev/assets/notebooks/07_Dipole_Dipole.ipynb

@@ -7,7 +7,7 @@
     "\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 real-space space with a distance cutoff. The study follows [Del Maestro and\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)."
    ],
@@ -25,7 +25,7 @@
   {
    "cell_type": "markdown",
    "source": [
-    "Create a Pyrochlore crystal from spacegroup 227."
+    "Create a pyrochlore crystal from spacegroup 227."
    ],
    "metadata": {}
   },
@@ -37,9 +37,22 @@
     "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)\n",
-    "\n",
-    "\n",
+    "view_crystal(cryst)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Create a system with antiferromagnetic nearest neighbor exchange."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
     "sys = System(cryst, [1 => Moment(s=7/2, g=2)], :dipole)\n",
     "J1 = 0.304 # (K)\n",
     "set_exchange!(sys, J1, Bond(1, 2, [0,0,0]))"
@@ -50,9 +63,9 @@
   {
    "cell_type": "markdown",
    "source": [
-    "Reshape to the primitive cell with four atoms. To facilitate indexing, the\n",
-    "function `position_to_site` accepts positions with respect to the\n",
-    "original (cubic) cell."
+    "Reshape to the primitive cell, which contains four atoms. To facilitate\n",
+    "indexing, the function `position_to_site` accepts positions with\n",
+    "respect to the original (cubic) cell."
    ],
    "metadata": {}
   },
@@ -112,7 +125,7 @@
    "source": [
     "Create a panel that qualitatively reproduces Fig. 2 of [Del Maestro and\n",
     "Gingras](https://arxiv.org/abs/cond-mat/0403494). That previous work had two\n",
-    "errors: The energy scales are too small by a factor of 2 and, in addition,\n",
+    "errors: Its energy scale is too small by a factor of 2 and, in addition,\n",
     "slight corrections are needed for the third dispersion band."
    ],
    "metadata": {}

dev/assets/scripts/07_Dipole_Dipole.jl

@@ -6,7 +6,6 @@ positions = [[1/8, 1/8, 1/8]]
 cryst = Crystal(latvecs, positions, 227, setting="1")
 view_crystal(cryst)
 
-
 sys = System(cryst, [1 => Moment(s=7/2, g=2)], :dipole)
 J1 = 0.304 # (K)
 set_exchange!(sys, J1, Bond(1, 2, [0,0,0]))

dev/examples/01_LSWT_CoRh2O4.html

@@ -24,11 +24,11 @@
 set_exchange!(sys, J, Bond(1, 3, [0, 0, 0]))
 view_crystal(sys)</code></pre><img src="01_LSWT_CoRh2O4-f235b95e.png" alt="Example block output"/><h3 id="Optimizing-spins"><a class="docs-heading-anchor" href="#Optimizing-spins">Optimizing spins</a><a id="Optimizing-spins-1"></a><a class="docs-heading-anchor-permalink" href="#Optimizing-spins" title="Permalink"></a></h3><p>To search for the ground state, call <a href="../library.html#Sunny.randomize_spins!-Union{Tuple{System{N}}, Tuple{N}} where N"><code>randomize_spins!</code></a> and <a href="../library.html#Sunny.minimize_energy!-Union{Tuple{System{N}}, Tuple{N}} where N"><code>minimize_energy!</code></a> in sequence. For this problem, optimization converges rapidly to the expected Néel order. See this with <a href="../library.html#Sunny.plot_spins"><code>plot_spins</code></a>, where spins are colored according to their global <span>$z$</span>-component.</p><pre><code class="language-julia hljs">randomize_spins!(sys)
 minimize_energy!(sys)
-plot_spins(sys; color=[S[3] for S in sys.dipoles])</code></pre><img src="01_LSWT_CoRh2O4-566ac3d0.png" alt="Example block output"/><p>The diamond lattice is bipartite, allowing each spin to perfectly anti-align with its 4 nearest-neighbors. Each of these 4 bonds contribute <span>$-J s^2$</span> to the total energy. Two sites participate in each bond, so the energy per site is <span>$-2 J s^2$</span>. Check this by calling <a href="../library.html#Sunny.energy_per_site-Union{Tuple{System{N}}, Tuple{N}} where N"><code>energy_per_site</code></a>.</p><pre><code class="language-julia hljs">@assert energy_per_site(sys) ≈ -2J*(3/2)^2</code></pre><h3 id="Reshaping-the-magnetic-cell"><a class="docs-heading-anchor" href="#Reshaping-the-magnetic-cell">Reshaping the magnetic cell</a><a id="Reshaping-the-magnetic-cell-1"></a><a class="docs-heading-anchor-permalink" href="#Reshaping-the-magnetic-cell" title="Permalink"></a></h3><p>The most compact magnetic cell for this Néel order is a primitive unit cell. Reduce the magnetic cell size using <a href="../library.html#Sunny.reshape_supercell-Tuple{System, Any}"><code>reshape_supercell</code></a>, where columns of the <code>shape</code> matrix are primitive lattice vectors as multiples of the conventional cubic lattice vectors <span>$(𝐚_1, 𝐚_2, 𝐚_3)$</span>. One could alternatively use <code>shape = cryst.latvecs \ cryst.prim_latvecs</code>. Verify that the energy per site is unchanged after the reshaping the supercell.</p><pre><code class="language-julia hljs">shape = [0 1 1;
+plot_spins(sys; color=[S[3] for S in sys.dipoles])</code></pre><img src="01_LSWT_CoRh2O4-0816aea3.png" alt="Example block output"/><p>The diamond lattice is bipartite, allowing each spin to perfectly anti-align with its 4 nearest-neighbors. Each of these 4 bonds contribute <span>$-J s^2$</span> to the total energy. Two sites participate in each bond, so the energy per site is <span>$-2 J s^2$</span>. Check this by calling <a href="../library.html#Sunny.energy_per_site-Union{Tuple{System{N}}, Tuple{N}} where N"><code>energy_per_site</code></a>.</p><pre><code class="language-julia hljs">@assert energy_per_site(sys) ≈ -2J*(3/2)^2</code></pre><h3 id="Reshaping-the-magnetic-cell"><a class="docs-heading-anchor" href="#Reshaping-the-magnetic-cell">Reshaping the magnetic cell</a><a id="Reshaping-the-magnetic-cell-1"></a><a class="docs-heading-anchor-permalink" href="#Reshaping-the-magnetic-cell" title="Permalink"></a></h3><p>The most compact magnetic cell for this Néel order is a primitive unit cell. Reduce the magnetic cell size using <a href="../library.html#Sunny.reshape_supercell-Tuple{System, Any}"><code>reshape_supercell</code></a>, where columns of the <code>shape</code> matrix are primitive lattice vectors as multiples of the conventional cubic lattice vectors <span>$(𝐚_1, 𝐚_2, 𝐚_3)$</span>. One could alternatively use <code>shape = cryst.latvecs \ cryst.prim_latvecs</code>. Verify that the energy per site is unchanged after the reshaping the supercell.</p><pre><code class="language-julia hljs">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</code></pre><p>Plotting <code>sys_prim</code> shows the two spins within the primitive cell, as well as the larger conventional cubic cell for context.</p><pre><code class="language-julia hljs">plot_spins(sys_prim; color=[S[3] for S in sys_prim.dipoles])</code></pre><img src="01_LSWT_CoRh2O4-ad2c6958.png" alt="Example block output"/><h3 id="Spin-wave-theory"><a class="docs-heading-anchor" href="#Spin-wave-theory">Spin wave theory</a><a id="Spin-wave-theory-1"></a><a class="docs-heading-anchor-permalink" href="#Spin-wave-theory" title="Permalink"></a></h3><p>With this primitive cell, we will perform a <a href="../library.html#Sunny.SpinWaveTheory"><code>SpinWaveTheory</code></a> calculation of the structure factor <span>$\mathcal{S}(𝐪,ω)$</span>. The measurement <a href="../library.html#Sunny.ssf_perp-Tuple{System}"><code>ssf_perp</code></a> indicates projection of the spin structure factor <span>$\mathcal{S}(𝐪,ω)$</span> perpendicular to the direction of momentum transfer, as appropriate for unpolarized neutron scattering. The isotropic <a href="../library.html#Sunny.FormFactor-Tuple{String}"><code>FormFactor</code></a> for Co²⁺ dampens intensities at large <span>$𝐪$</span>.</p><pre><code class="language-julia hljs">formfactors = [1 =&gt; FormFactor(&quot;Co2&quot;)]
+@assert energy_per_site(sys_prim) ≈ -2J*(3/2)^2</code></pre><p>Plotting <code>sys_prim</code> shows the two spins within the primitive cell, as well as the larger conventional cubic cell for context.</p><pre><code class="language-julia hljs">plot_spins(sys_prim; color=[S[3] for S in sys_prim.dipoles])</code></pre><img src="01_LSWT_CoRh2O4-e3d1c783.png" alt="Example block output"/><h3 id="Spin-wave-theory"><a class="docs-heading-anchor" href="#Spin-wave-theory">Spin wave theory</a><a id="Spin-wave-theory-1"></a><a class="docs-heading-anchor-permalink" href="#Spin-wave-theory" title="Permalink"></a></h3><p>With this primitive cell, we will perform a <a href="../library.html#Sunny.SpinWaveTheory"><code>SpinWaveTheory</code></a> calculation of the structure factor <span>$\mathcal{S}(𝐪,ω)$</span>. The measurement <a href="../library.html#Sunny.ssf_perp-Tuple{System}"><code>ssf_perp</code></a> indicates projection of the spin structure factor <span>$\mathcal{S}(𝐪,ω)$</span> perpendicular to the direction of momentum transfer, as appropriate for unpolarized neutron scattering. The isotropic <a href="../library.html#Sunny.FormFactor-Tuple{String}"><code>FormFactor</code></a> for Co²⁺ dampens intensities at large <span>$𝐪$</span>.</p><pre><code class="language-julia hljs">formfactors = [1 =&gt; FormFactor(&quot;Co2&quot;)]
 measure = ssf_perp(sys_prim; formfactors)
 swt = SpinWaveTheory(sys_prim; measure)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi"><span class="sgr4"><span class="sgr1">SpinWaveTheory [Dipole mode]</span></span>
   2 atoms
@@ -37,8 +37,8 @@
   [0, 0, 0] → [1/2, 0, 0] → [1/2, 1/2, 0] → [0, 0, 0]
 </code></pre><p>Calculate single-crystal scattering <a href="../library.html#Sunny.intensities-Tuple{Sunny.AbstractSpinWaveTheory, Any}"><code>intensities</code></a> along this path, for energies between 0 and 6 meV. Use <a href="../library.html#Sunny.plot_intensities"><code>plot_intensities</code></a> to visualize the result.</p><pre><code class="language-julia hljs">energies = range(0, 6, 300)
 res = intensities(swt, path; energies, kernel)
-plot_intensities(res; units, title=&quot;CoRh₂O₄ LSWT&quot;)</code></pre><img src="01_LSWT_CoRh2O4-b5f8c613.png" alt="Example block output"/><p>Sometimes experimental data is only available as a powder average, i.e., as an average over all possible crystal orientations. Use <a href="../library.html#Sunny.powder_average-Tuple{Any, Any, Any, Int64}"><code>powder_average</code></a> to simulate these intensities. Each <span>$𝐪$</span>-magnitude defines a spherical shell in reciprocal space. Consider 200 radii from 0 to 3 inverse angstroms, and collect <code>2000</code> 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.</p><pre><code class="language-julia hljs">radii = range(0, 3, 200) # (1/Å)
+plot_intensities(res; units, title=&quot;CoRh₂O₄ LSWT&quot;)</code></pre><img src="01_LSWT_CoRh2O4-15511db4.png" alt="Example block output"/><p>Sometimes experimental data is only available as a powder average, i.e., as an average over all possible crystal orientations. Use <a href="../library.html#Sunny.powder_average-Tuple{Any, Any, Any, Int64}"><code>powder_average</code></a> to simulate these intensities. Each <span>$𝐪$</span>-magnitude defines a spherical shell in reciprocal space. Consider 200 radii from 0 to 3 inverse angstroms, and collect <code>2000</code> 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.</p><pre><code class="language-julia hljs">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=&quot;CoRh₂O₄ Powder Average&quot;)</code></pre><img src="01_LSWT_CoRh2O4-e404dda4.png" alt="Example block output"/><p>This result can be compared to experimental neutron scattering data from Fig. 5 of <a href="https://doi.org/10.1103/PhysRevB.96.064413">Ge et al.</a></p><img width="95%" src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/CoRh2O4_intensity.jpg"><h3 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h3><ul><li>For more spin wave calculations of this type, browse the <a href="spinw/SW01_FM_Heseinberg_chain.html#SW01-FM-Heisenberg-chain">SpinW tutorials ported to Sunny</a>.</li><li>Spin wave theory neglects thermal fluctuations of the magnetic order. The <a href="02_LLD_CoRh2O4.html#2.-Landau-Lifshitz-dynamics-of-CoRhO-at-finite-*T*">next CoRh₂O₄ tutorial</a> demonstrates how to sample spins in thermal equilibrium, and measure dynamical correlations from the classical spin dynamics.</li><li>Sunny also offers features that go beyond the dipole approximation of a quantum spin via the theory of SU(<em>N</em>) coherent states. This can be especially useful for systems with strong single-ion anisotropy, as demonstrated in the <a href="03_LSWT_SU3_FeI2.html#3.-Multi-flavor-spin-wave-simulations-of-FeI">FeI₂ tutorial</a>.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="02_LLD_CoRh2O4.html">2. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 30 August 2024 22:33">Friday 30 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+plot_intensities(res; units, saturation=1.0, title=&quot;CoRh₂O₄ Powder Average&quot;)</code></pre><img src="01_LSWT_CoRh2O4-f461e50e.png" alt="Example block output"/><p>This result can be compared to experimental neutron scattering data from Fig. 5 of <a href="https://doi.org/10.1103/PhysRevB.96.064413">Ge et al.</a></p><img width="95%" src="https://raw.githubusercontent.com/SunnySuite/Sunny.jl/main/docs/src/assets/CoRh2O4_intensity.jpg"><h3 id="What&#39;s-next?"><a class="docs-heading-anchor" href="#What&#39;s-next?">What&#39;s next?</a><a id="What&#39;s-next?-1"></a><a class="docs-heading-anchor-permalink" href="#What&#39;s-next?" title="Permalink"></a></h3><ul><li>For more spin wave calculations of this type, browse the <a href="spinw/SW01_FM_Heseinberg_chain.html#SW01-FM-Heisenberg-chain">SpinW tutorials ported to Sunny</a>.</li><li>Spin wave theory neglects thermal fluctuations of the magnetic order. The <a href="02_LLD_CoRh2O4.html#2.-Landau-Lifshitz-dynamics-of-CoRhO-at-finite-*T*">next CoRh₂O₄ tutorial</a> demonstrates how to sample spins in thermal equilibrium, and measure dynamical correlations from the classical spin dynamics.</li><li>Sunny also offers features that go beyond the dipole approximation of a quantum spin via the theory of SU(<em>N</em>) coherent states. This can be especially useful for systems with strong single-ion anisotropy, as demonstrated in the <a href="03_LSWT_SU3_FeI2.html#3.-Multi-flavor-spin-wave-simulations-of-FeI">FeI₂ tutorial</a>.</li></ul></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../index.html">« Overview</a><a class="docs-footer-nextpage" href="02_LLD_CoRh2O4.html">2. Landau-Lifshitz dynamics of CoRh₂O₄ at finite <em>T</em> »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.6.0 on <span class="colophon-date" title="Friday 30 August 2024 22:42">Friday 30 August 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>