Thermophoresis of an antiferromagnetic soliton

Abstract

We study the 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 a, 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 similar to 10(-4).