Diffusion of a magnetic skyrmion in 2-dimensional space

TL;DR

This paper investigates the diffusion behavior of magnetic skyrmions in two-dimensional space, validating the constant-mass approximation and deriving a tensor form of diffusion constants using advanced stochastic equations.

Contribution

It introduces a rigorous comparison of the Thiele and LLG equations for skyrmion dynamics and derives a tensor form of diffusion constants from the Fokker-Planck equation.

Findings

Validation of the constant-mass approximation for skyrmion diffusion

Derivation of a tensor form for diffusion constants

Extension of Chandrasekhar's method to Thiele dynamics

Abstract

Two-dimensional magnetic skyrmions are particle-like magnetic domains in magnetic thin films. The kinetic property of the magnetic skyrmions at finite temperature is well described by the Thiele equation, including a stochastic field and a finite mass. In this paper, the validity of the constant-mass approximation is examined by comparing the Fourier spectrum of Brownian motions described by the Thiele equation and the Landau-Lifshitz-Gilbert equation. Then, the 4-dimensional Fokker-Planck equation is derived from the Thiele equation with a mass-term. Consequently, an expression of the diffusion flow and diffusion constant in a tensor form is derived, extending Chandrasekhar's method for Thiele dynamics.