Spin eigen-excitations of the magnetic skyrmion and problem of the effective mass

TL;DR

This paper investigates magnon modes localized on ferromagnetic skyrmions, revealing asymptotic behaviors of eigenfrequencies for large skyrmions and demonstrating that skyrmion dynamics follow a massless Thiele equation.

Contribution

It provides a detailed analysis of magnon eigenmodes on skyrmions and clarifies that their dynamics are governed by a massless Thiele equation, resolving the effective mass problem.

Findings

Eigenfrequency asymptotics for large skyrmions identified

Magnon eigenfunctions characterized in detail

Skyrmion dynamics shown to be massless Thiele type

Abstract

Properties of magnon modes localized on a ferromagnetic skyrmion are studied. Three types of possible asymptotic behavior of the modes eigenfrequencies are found for the case of large skyrmion radius $R_s$, namely $\omega_0\sim R_s^{-2}$ for the breathing mode, $\omega_{-|\mu|}\sim R_s^{-1}$ and $\omega_{|\mu|}\sim R_s^{-3}$ for modes with negative and positive azimuthal quantum numbers, respectively. A number of properties of the magnon eigenfunctions are determined. This enables us to demonstrate that the skyrmion dynamics based on the traveling wave model is described by the massless Thiele equation.