Spin dynamics simulations of the magnetic dynamics of RbMnF$_3$ and direct comparison with experiment

TL;DR

This paper uses large-scale spin-dynamics simulations to study the magnetic behavior of RbMnF$_3$, comparing results with experimental data to understand critical dynamics and spin-wave properties.

Contribution

It introduces a new simulation algorithm for the classical Heisenberg antiferromagnet and provides a direct comparison with experimental results for RbMnF$_3$.

Findings

Estimated dynamic critical exponent z=1.43

Good agreement with recent experimental dispersion curves

Observed crossover from hydrodynamic to critical behavior

Abstract

Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes $L\leq 60$. This system is widely recognized as an appropriate model for the magnetic properties of RbMnF$_3$. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm implemented by Krech {\it etal}, which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\pm 0.03)$, which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF$_3$ are presented.