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Thermally Assisted Current-Driven Skyrmion Motion

We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele's equation and its corresponding Fokker-Planck equation. The resulting Fokker-Planck equation is recognized as the one for a high-friction Brownian particle which has been studied extensively in different physical contexts. It is shown that thermal fluctuations favor the skyrmion motion allowing a finite mobility even in presence of pinning traps. We calculate explicitly the mobility tensor of skyrmions in linear response to an electric current finding that it increases with temperature.