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# # SW19 - Different magnetic ions | ||
# | ||
# This is a Sunny port of [SpinW Tutorial | ||
# 19](https://spinw.org/tutorials/19tutorial), originally authored by Bjorn Fak | ||
# and Sandor Toth. This tutorial illustrates how to eliminate magnetic | ||
# contributions from a subset of ions via the special value `zero(FormFactor)`. | ||
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using Sunny, GLMakie | ||
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# Build a crystal with Cu²⁺ and Fe²⁺ ions | ||
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) | ||
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# Set interactions | ||
J_Cu_Cu = 1.0 | ||
J_Fe_Fe = 1.0 | ||
J_Cu_Fe = -0.1 | ||
sys = System(cryst, (2,1,1), [SpinInfo(1,S=1/2,g=2), SpinInfo(2,S=2,g=2)], :dipole; 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])) | ||
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# Find and plot a minimum energy configuration | ||
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randomize_spins!(sys) | ||
minimize_energy!(sys) | ||
plot_spins(sys) | ||
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# Plot dispersions colored by total summed intensity for each degenerate band | ||
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swt = SpinWaveTheory(sys) | ||
q_points = [[0,0,0], [1,0,0]] | ||
path, xticks = reciprocal_space_path(cryst, q_points, 200) | ||
formula = intensity_formula(swt, :perp; kernel=delta_function_kernel) | ||
disp, intensity = intensities_bands(swt, path, formula) | ||
fig = Figure() | ||
ax = Axis(fig[1,1]; xlabel="Momentum (RLU)", ylabel="Energy (meV)", title="Spin wave dispersion", xticks) | ||
ylims!(ax, 0.0, 4.5) | ||
xlims!(ax, 1, size(disp, 1)) | ||
lines!(ax, disp[:, 1]; color=vec(sum(intensity[:, 1:2]; dims=2)), colorrange=(0,2)) | ||
lines!(ax, disp[:, 3]; color=vec(sum(intensity[:, 3:4]; dims=2)), colorrange=(0,2)) | ||
fig | ||
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# Functions to plot broadened intensities | ||
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function plot_intensities(formfactors, title) | ||
formula = intensity_formula(swt, :trace; kernel=gaussian(fwhm=0.2), formfactors) | ||
energies = collect(0:0.02:140) | ||
is = intensities_broadened(swt, path, energies, formula) | ||
fig = Figure() | ||
ax = Axis(fig[1,1]; xlabel="Momentum (RLU)", ylabel="Energy (meV)", title, xticks) | ||
ylims!(ax, 0.0, 4.5) | ||
heatmap!(ax, 1:size(is, 1), energies, is; colorrange=(0.1,50), colormap=Reverse(:thermal), lowclip=:white) | ||
for d in eachcol(disp) | ||
lines!(ax, d; color=:pink) | ||
end | ||
fig | ||
end | ||
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# Plot full intensity spectrum | ||
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plot_intensities([FormFactor("Cu2"), FormFactor("Fe2")], "Full structure factor, tr S(𝐪, ω)") | ||
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# Plot Cu-Cu correlations only | ||
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plot_intensities([FormFactor("Cu2"), zero(FormFactor)], "Only Cu-Cu correlations, tr S(𝐪, ω)") | ||
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# Fe-Fe correlations only | ||
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plot_intensities([zero(FormFactor), FormFactor("Fe2")], "Only Fe-Fe correlations, tr S(𝐪, ω)") |