  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.
