Mass and generalized Thiele equation of the magnetic skyrmion

TL;DR

This paper derives an analytical expression for the mass of a magnetic skyrmion and formulates its generalized Thiele equations, revealing the skyrmion's massless charge center and finite mass magnetization center, supported by micromagnetic simulations.

Contribution

It provides the first analytical expression for the skyrmion mass and extends the Thiele equation to include mass and external force derivatives.

Findings

The skyrmion charge center is effectively massless.

The magnetization center has a finite mass comparable to domain wall mass.

Simulation results agree with theoretical predictions.

Abstract

An analytical expression is obtained for the mass of an isolated magnetic skyrmion and its linearized equation of motion. The magnetic skyrmion is viewed as a topologically protected spin-wave soliton in the magnetic ultrathin films stabilized by the interfacial-Dzyaloshinskii-Moriya interaction. The equations of motion are derived from the Landau-Lifshitz-Gilbert equation for both the skyrmion charge and magnetization centers. They are generalized Thiele equations, including the gyro-term, dissipation term, external force, acceleration term with the tensorial mass, and time derivatives of the external forces. The equation of motion of the center of the skyrmion charge essentially shows the massless nature of the skyrmion. In contrast, the equation of motion for the magnetization center results in a finite mass that is in the same order as the Doring mass density for the linear domain wall. Furthermore, the time derivative of the external force predominantly contributes to the immediate response of the skyrmion motion, i.e., the mass-less property remains even after the skyrmion acquires its kinetic mass. A micromagnetic simulation based on the LLG equation was performed for various magnetic parameters. Obtained trajectories at 0 K are compared with the theoretical predictions.