Spin eigenmodes of magnetic skyrmions and the problem of the effective skyrmion mass

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.