Thermophoresis of an Antiferromagnetic Soliton

TL;DR

This paper models the behavior of antiferromagnetic solitons under temperature gradients, deriving equations that predict their drift and diffusion, with potential applications in spintronics.

Contribution

It introduces a stochastic Landau-Lifshitz-Gilbert framework and derives a Langevin and Fokker-Planck equation for antiferromagnetic solitons, providing new insights into their thermally driven dynamics.

Findings

Solitons behave as massive particles in viscous media.

Drift velocity can reach tens of m/s under realistic temperature gradients.

Diffusion coefficient inversely proportional to damping constant.

Abstract

We study dynamics of an antiferromagnetic soliton under a temperature gradient. To this end, we start by phenomenologically constructing the stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid of the fluctuation-dissipation theorem. We then derive the Langevin equation for the soliton's center of mass by the collective coordinate approach. An antiferromagentic soliton behaves as a classical massive particle immersed in a viscous medium. By considering a thermodynamic ensemble of solitons, we obtain the Fokker-Planck equation, from which we extract the average drift velocity of a soliton. The diffusion coefficient is inversely proportional to a small damping constant $\alpha$, which can yield a drift velocity of tens of m/s under a temperature gradient of $1$ K/mm for a domain wall in an easy-axis antiferromagnetic wire with $\alpha \sim 10^{-4}$.