Derivation of the Thiele equation for magnetic skyrmions using the Mori-Zwanzig formalism

Abstract

We use the Mori-Zwanzig formalism to derive an exact generalized Langevin equation governing the dynamics of magnetic skyrmions. Using standard approximations, this generalized Langevin equation is found to reduce to the usual Thiele equation. Our approach provides a general route for obtaining extensions of the Thiele equation applicable to magnetic textures and degrees of freedom not covered by the standard derivation route. It also provides some insights into the microscopic justification of the standard Thiele equation, specifically concerning contributions of fast modes to the form of the drift and diffusion terms in the Fokker-Planck equation for skyrmions.