Effective Gilbert damping in the stochastic Landau-Lifshitz-Gilbert equation

TL;DR

This paper investigates how effective damping in atomistic spin dynamics varies with temperature and momentum, revealing deviations from the standard Gilbert damping model due to spin interactions.

Contribution

It introduces a method to extract and analyze the effective damping in a 1D spin chain considering temperature and spin wave interactions.

Findings

Effective damping varies significantly from the Gilbert value at different temperatures.

The damping exhibits specific temperature and momentum scaling behaviors.

Interactions with the Gilbert bath and spin wave scattering influence the effective damping.

Abstract

Quasi particle based (e.g. Boltzmann equation) studies of spin wave transport often assume that their scattering rates follow the simple form $\eta=\alpha \omega$, with the Gilbert damping $\alpha$ and frequency $\omega$. In this work, we examine the effective damping $\alpha_{eff,T}=\eta/\omega$ observed in atomistic spin dynamics, when temperature and spin wave interactions are introduced for a 1D spin chain. We extract the dynamical correlation functions from spin trajectories propagated using the stochastic Landau-Lifshitz-Gilbert equation, and fit the dynamical structure factor, yielding the dispersion and scattering rates for a wide range of temperatures. The resulting effective damping can be very different from the initially constant Gilbert value. It exhibits a temperature and crystal momentum scaling which we explain based on interactions with the Gilbert bath and spin wave scattering by changes in local magnetic order.