The properties of magnon modes localized on a ferromagnetic skyrmion are studied. Mode eigenfrequencies display three types of asymptotic behavior for large skyrmion radius Rₛ, namely, ω₀∝Rₛ^-2 for the breathing mode and ω_-|μ|∝Rₛ^-1 and ω_|μ|∝Rₛ^-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 for a traveling-wave ansatz obeys the massless Thiele equation.
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Kravchuk et al. (2018) studied this question.
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