build based on 6c5d991

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-12T23:53:04","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-20T16:59:28","documenter_version":"1.7.0"}}

dev/assets/notebooks/01_LSWT_CoRh2O4.ipynb

@@ -50,16 +50,16 @@
   {
    "cell_type": "markdown",
    "source": [
-    "### Units"
+    "### Units system"
    ],
    "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."
+    "The `Units` object selects reference energy and length scales,\n",
+    "and uses these to provide physical constants. For example, `units.K` returns\n",
+    "one kelvin as 0.086 meV, where the Boltzmann constant is implicit."
    ],
    "metadata": {}
   },

dev/assets/notebooks/09_Disorder_KPM.ipynb

@@ -0,0 +1,261 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "source": [
+    "# 9. Disordered system with KPM\n",
+    "\n",
+    "This example uses the kernel polynomial method (KPM) to efficiently calculate\n",
+    "the neutron scattering spectrum of a disordered triangular antiferromagnet.\n",
+    "The model is inspired by YbMgGaO4, as studied in [Paddison et al, Nature\n",
+    "Phys., **13**, 117–122 (2017)](https://doi.org/10.1038/nphys3971) and [Zhu et\n",
+    "al, Phys. Rev. Lett. **119**, 157201\n",
+    "(2017)](https://doi.org/10.1103/PhysRevLett.119.157201). Disordered occupancy\n",
+    "of non-magnetic Mg/Ga sites can be modeled as a stochastic distribution of\n",
+    "exchange constants and $g$-factors. Including this disorder introduces\n",
+    "broadening of the spin wave spectrum."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "using Sunny, GLMakie"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Set up minimal triangular lattice system. Include antiferromagnetic exchange\n",
+    "interactions between nearest neighbor bonds. Energy minimization yields the\n",
+    "magnetic ground state with 120° angles between spins in triangular plaquettes."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "latvecs = lattice_vectors(1, 1, 10, 90, 90, 120)\n",
+    "cryst = Crystal(latvecs, [[0, 0, 0]])\n",
+    "sys = System(cryst, [1 => Moment(s=1/2, g=1)], :dipole; dims=(3, 3, 1))\n",
+    "set_exchange!(sys, +1.0, Bond(1, 1, [1,0,0]))\n",
+    "\n",
+    "randomize_spins!(sys)\n",
+    "minimize_energy!(sys)\n",
+    "plot_spins(sys; color=[S[3] for S in sys.dipoles], ndims=2)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Select a $𝐪$-space path for the spin wave calculations."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "qs = [[0, 0, 0], [1/3, 1/3, 0], [1/2, 0, 0], [0, 0, 0]]\n",
+    "labels = [\"Γ\", \"K\", \"M\", \"Γ\"]\n",
+    "path = q_space_path(cryst, qs, 150; labels)\n",
+    "kernel = lorentzian(fwhm=0.4);"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Perform a traditional spin wave calculation. The spectrum shows sharp modes\n",
+    "associated with coherent excitations about the K-point ordering wavevector,\n",
+    "$𝐪 = [1/3, 1/3, 0]$."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "energies = range(0.0, 3.0, 150)\n",
+    "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n",
+    "res = intensities(swt, path; energies, kernel)\n",
+    "plot_intensities(res)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Use `repeat_periodically` to enlarge the system by a factor of 10 in\n",
+    "each dimension. Use `to_inhomogeneous` to disable symmetry\n",
+    "constraints, and allow for the addition of disordered interactions."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "sys_inhom = to_inhomogeneous(repeat_periodically(sys, (10, 10, 1)))"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Use `symmetry_equivalent_bonds` to iterate over all nearest neighbor\n",
+    "bonds of the inhomogeneous system. Modify each AFM exchange with a noise term\n",
+    "that has variance of 1/3. The newly minimized energy configuration allows for\n",
+    "long wavelength modulations on top of the original 120° order."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "for (site1, site2, offset) in symmetry_equivalent_bonds(sys_inhom, Bond(1,1,[1,0,0]))\n",
+    "    noise = randn()/3\n",
+    "    set_exchange_at!(sys_inhom, 1.0 + noise, site1, site2; offset)\n",
+    "end\n",
+    "\n",
+    "minimize_energy!(sys_inhom, maxiters=5_000)\n",
+    "plot_spins(sys_inhom; color=[S[3] for S in sys_inhom.dipoles], ndims=2)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Traditional spin wave theory calculations become impractical for large system\n",
+    "sizes. Significant acceleration is possible with the [kernel polynomial\n",
+    "method](https://arxiv.org/abs/2312.08349). Enable it by selecting\n",
+    "`SpinWaveTheoryKPM` in place of the traditional\n",
+    "`SpinWaveTheory`. Using KPM, the cost of an `intensities`\n",
+    "calculation becomes linear in system size and scales inversely with the width\n",
+    "of the line broadening `kernel`. Error tolerance is controlled through the\n",
+    "dimensionless `tol` parameter. A relatively small value, `tol = 0.01`, helps\n",
+    "to resolve the large intensities near the ordering wavevector. The alternative\n",
+    "choice `tol = 0.1` would be twice faster, but would introduce significant\n",
+    "numerical artifacts.\n",
+    "\n",
+    "Observe from the KPM calculation that disorder in the nearest-neighbor\n",
+    "exchange serves to broaden the discrete excitation bands into a continuum."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "swt = SpinWaveTheoryKPM(sys_inhom; measure=ssf_perp(sys_inhom), tol=0.01)\n",
+    "res = intensities(swt, path; energies, kernel)\n",
+    "plot_intensities(res)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Now apply a magnetic field of magnitude 7.5 (energy units) along the global\n",
+    "$ẑ$ axis. This field fully polarizes the spins. Because gap opens, a larger\n",
+    "tolerance of `tol = 0.1` can be used to accelerate the KPM calculation without\n",
+    "sacrificing much accuracy. The resulting spin wave spectrum shows a sharp mode\n",
+    "at the Γ-point (zone center) that broadens into a continuum along the K and M\n",
+    "points (zone boundary)."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "set_field!(sys_inhom, [0, 0, 7.5])\n",
+    "randomize_spins!(sys_inhom)\n",
+    "minimize_energy!(sys_inhom)\n",
+    "\n",
+    "energies = range(0.0, 9.0, 150)\n",
+    "swt = SpinWaveTheoryKPM(sys_inhom; measure=ssf_perp(sys_inhom), tol=0.1)\n",
+    "res = intensities(swt, path; energies, kernel)\n",
+    "plot_intensities(res)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "Add disorder to the $z$-component of each magnetic moment $g$-tensor. This\n",
+    "further broadens intensities, now across the entire path. Some intensity\n",
+    "modulation within the continuum is also apparent. This modulation is a\n",
+    "finite-size effect, and would be mitigated by enlarging the system beyond\n",
+    "30×30 chemical cells."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "for site in eachsite(sys_inhom)\n",
+    "    noise = randn()/6\n",
+    "    sys_inhom.gs[site] = [1 0 0; 0 1 0; 0 0 1+noise]\n",
+    "end\n",
+    "\n",
+    "swt = SpinWaveTheoryKPM(sys_inhom; measure=ssf_perp(sys_inhom), tol=0.1)\n",
+    "res = intensities(swt, path; energies, kernel)\n",
+    "plot_intensities(res)"
+   ],
+   "metadata": {},
+   "execution_count": null
+  },
+  {
+   "cell_type": "markdown",
+   "source": [
+    "For reference, the equivalent non-disordered system shows a single coherent\n",
+    "mode."
+   ],
+   "metadata": {}
+  },
+  {
+   "outputs": [],
+   "cell_type": "code",
+   "source": [
+    "set_field!(sys, [0, 0, 7.5])\n",
+    "randomize_spins!(sys)\n",
+    "minimize_energy!(sys)\n",
+    "swt = SpinWaveTheory(sys; measure=ssf_perp(sys))\n",
+    "res = intensities(swt, path; energies, kernel)\n",
+    "plot_intensities(res)"
+   ],
+   "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
+}

dev/assets/notebooks/SW02_AFM_Heisenberg_chain.ipynb

@@ -101,7 +101,7 @@
    "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",
+    "path = q_space_path(cryst, qs, 401)\n",
     "res = intensities_bands(swt, path)\n",
     "plot_intensities(res; units)"
    ],

dev/assets/notebooks/SW03_Frustrated_chain.ipynb

@@ -141,7 +141,7 @@
    "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",
+    "path = q_space_path(cryst, qs, 401)\n",
     "res = intensities_bands(swt, path)\n",
     "plot_intensities(res; units)"
    ],

dev/assets/notebooks/SW04_Frustrated_square.ipynb

@@ -86,7 +86,7 @@
    "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",
+    "path = q_space_path(cryst, qs, 400)\n",
     "res = intensities_bands(swt, path)\n",
     "plot_intensities(res; units)"
    ],

dev/assets/scripts/09_Disorder_KPM.jl

@@ -0,0 +1,59 @@
+using Sunny, GLMakie
+
+latvecs = lattice_vectors(1, 1, 10, 90, 90, 120)
+cryst = Crystal(latvecs, [[0, 0, 0]])
+sys = System(cryst, [1 => Moment(s=1/2, g=1)], :dipole; dims=(3, 3, 1))
+set_exchange!(sys, +1.0, Bond(1, 1, [1,0,0]))
+
+randomize_spins!(sys)
+minimize_energy!(sys)
+plot_spins(sys; color=[S[3] for S in sys.dipoles], ndims=2)
+
+qs = [[0, 0, 0], [1/3, 1/3, 0], [1/2, 0, 0], [0, 0, 0]]
+labels = ["Γ", "K", "M", "Γ"]
+path = q_space_path(cryst, qs, 150; labels)
+kernel = lorentzian(fwhm=0.4);
+
+energies = range(0.0, 3.0, 150)
+swt = SpinWaveTheory(sys; measure=ssf_perp(sys))
+res = intensities(swt, path; energies, kernel)
+plot_intensities(res)
+
+sys_inhom = to_inhomogeneous(repeat_periodically(sys, (10, 10, 1)))
+
+for (site1, site2, offset) in symmetry_equivalent_bonds(sys_inhom, Bond(1,1,[1,0,0]))
+    noise = randn()/3
+    set_exchange_at!(sys_inhom, 1.0 + noise, site1, site2; offset)
+end
+
+minimize_energy!(sys_inhom, maxiters=5_000)
+plot_spins(sys_inhom; color=[S[3] for S in sys_inhom.dipoles], ndims=2)
+
+swt = SpinWaveTheoryKPM(sys_inhom; measure=ssf_perp(sys_inhom), tol=0.01)
+res = intensities(swt, path; energies, kernel)
+plot_intensities(res)
+
+set_field!(sys_inhom, [0, 0, 7.5])
+randomize_spins!(sys_inhom)
+minimize_energy!(sys_inhom)
+
+energies = range(0.0, 9.0, 150)
+swt = SpinWaveTheoryKPM(sys_inhom; measure=ssf_perp(sys_inhom), tol=0.1)
+res = intensities(swt, path; energies, kernel)
+plot_intensities(res)
+
+for site in eachsite(sys_inhom)
+    noise = randn()/6
+    sys_inhom.gs[site] = [1 0 0; 0 1 0; 0 0 1+noise]
+end
+
+swt = SpinWaveTheoryKPM(sys_inhom; measure=ssf_perp(sys_inhom), tol=0.1)
+res = intensities(swt, path; energies, kernel)
+plot_intensities(res)
+
+set_field!(sys, [0, 0, 7.5])
+randomize_spins!(sys)
+minimize_energy!(sys)
+swt = SpinWaveTheory(sys; measure=ssf_perp(sys))
+res = intensities(swt, path; energies, kernel)
+plot_intensities(res)

dev/assets/scripts/SW02_AFM_Heisenberg_chain.jl

@@ -15,7 +15,7 @@ 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)
+path = q_space_path(cryst, qs, 401)
 res = intensities_bands(swt, path)
 plot_intensities(res; units)
 

dev/assets/scripts/SW03_Frustrated_chain.jl

@@ -23,6 +23,6 @@ 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)
+path = q_space_path(cryst, qs, 401)
 res = intensities_bands(swt, path)
 plot_intensities(res; units)

dev/assets/scripts/SW04_Frustrated_square.jl

@@ -16,6 +16,6 @@ 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);
+path = q_space_path(cryst, qs, 400)
 res = intensities_bands(swt, path)
 plot_intensities(res; units)