Anisotropic skyrmion mass induced by surrounding conduction electrons: A Schwinger-Keldysh field theory approach

The current-driven motion of magnetic skyrmions, as topologically protected winding vector fields of local magnetization, has attracted considerable attention due to both fundamental interest in the dynamics of topological solitons, and potential spintronic applications. While widely-used Thiele equation with zero skyrmion mass captures its rigid motion under the assumption of preserved skyrmion shape, experiments on realistic skyrmions find deviation due to inertial mass with numerous attempts to account for it by invoking internal skyrmion dynamics, geometry of the nanowire, and interaction with magnons or phonons. However, experimentally observed skyrmion mass is often much larger than predicted by these theories. In this Letter, we employ Schwinger-Keldysh field-theoretical approach to study conduction electrons interacting with localized magnetic moments comprising a skyrmion to obtain a stochastic differential equation of its motion. By analyzing its time-retarded damping kernel, we extract an anisotropic mass governed by conduction electrons and demonstrate its substantial effect on the current-driven skyrmion motion, even in the absence of any skyrmion deformation.