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

Abstract

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 fieldtheoretical 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.

Microscopic theory of current-induced skyrmion transport and its application in disordered spin textures

“…This is indicative of the presence of a finite skyrmion mass, which has been discussed in previous studies [61,62]. In particular, it was recently proposed that the magnitude of the skyrmion mass is affected by the interactions between localized moments and free electrons [37,38], consistent with the present findings.…”

“…In a different direction, the results obtained here can be used to benchmark other methods that deal with electron and localized spins. For example, one can imagine validating methods that, still in a spin-only framework, go beyond the standard LLG equation [37,38].…”

“…Based on the Thiele equation, electrons enter only via the external current density, taken from a static solution of the macroscopic Maxwell equations. A more detailed description often considered in the literature is to obtain the individual spin dynamics from the LLG equation [31] and to include the effects of electrons and external fields via a generalized force [37,38]. The LLG equation, with itinerant electrons included implicitly, has provided important insights into skyrmion behavior in a large range of materials, and its use is widespread.…”

“…The importance of explicitly accounting for itinerant electrons in the description of skyrmion dynamics was originally pointed out in [15], where a small two-dimensional spin texture containing a single skyrmion was made to interact with a nanowire carrying a timedependent current. Since then, the significance of including electronic degrees of freedom in the description of skyrmion dynamics (as well as more general spin textures) has been addressed in several contexts [16,37,38,[43][44][45]. For example, it was recently demonstrated [16] that explicitly accounting for the dynamics of itinerant electrons can be of crucial importance in capturing the interaction between skyrmions and laser light.…”