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SW04 - Frustrated square lattice

This is a Sunny port of SpinW Tutorial 4, originally authored by Bjorn Fak and Sandor Toth. It calculates the spin wave spectrum of the frustrated square lattice.

Load Sunny and the GLMakie plotting package

using Sunny, GLMakie

To model the 2D square lattice, create an elongated tetragonal cell with one atom.

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)

Construct a spin system with competing nearest-neighbor (AFM) and next-nearest-neighbor (FM) interactions. The Néel magnetic order requires a supercell of 2×2 chemical cells.

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)

Calculate and plot intensities for a path through $𝐪$-space.

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)