Understanding temperature-dependent SU($3$) spin dynamics in the $S=1$ antiferromagnet Ba$_2$FeSi$_2$O$_7$

TL;DR

This study demonstrates that modeling finite temperature inelastic neutron scattering data of an S=1 antiferromagnet using SU(3) coherent states accurately captures temperature-dependent spin dynamics, surpassing traditional SU(2) approaches.

Contribution

The paper introduces a generalized SU(3) Landau-Lifshitz dynamics framework to model temperature-dependent spin dynamics in S=1 antiferromagnets, providing a new classical approximation method.

Findings

SU(3) classical spins match experimental spectra well

SU(2) models are less accurate for S=1 systems

Framework applicable to various anisotropic magnetic materials

Abstract

Quantum magnets admit more than one classical limit and $N$-level systems with strong single-ion anisotropy are expected to be described by a classical approximation based on SU($N$) coherent states. Here we test this hypothesis by modeling finite temperature inelastic neutron scattering (INS) data of the effective spin-one antiferromagnet \bfso{}. The measured dynamic structure factor is calculated with a generalized Landau-Lifshitz dynamics for SU($3$) spins. Unlike the traditional classical limit based on SU($2$) coherent states, the results obtained with classical SU($3$) spins are in good agreement with the measured temperature-dependent spectrum. The SU($3$) approach developed here provides a general framework to understand the broad class of materials comprising weakly coupled antiferromagnetic dimers, trimers, or tetramers, and magnets with strong single-ion anisotropy.