Diffusion of a magnetic skyrmion in two-dimensional space

Highlights: • Validity of the constant mass approximation of the skyrmion dynamics is tested. • Explicit solution of the Skyrmion's Fokker-Planck equation is given. • Expression for the diffusion flow including the gyro-diffusion is obtained. • Diffusion constant in the tensor form is obtained. • Relation with Bohr-van Leeuwen theorem is discussed. Two-dimensional magnetic skyrmions are particle-like magnetic domains in magnetic thin films. The kinetic property of magnetic skyrmions at finite temperature is well described by the Thiele equation, including a stochastic field and a finite mass. This study examines the validity of the constant-mass approximation by comparing the Fourier spectrum of the Brownian motions described by the Thiele equation and the Landau–Lifshitz–Gilbert equation. Then, the expression of the diffusion flow is derived from the four-dimensional Fokker–Planck equation by considering Chandrasekhar's solution for the Thiele dynamics. Finally, a method to observe the gyro-diffusion is discussed.