Local magnon modes and the dynamics of a small-radius two-dimensional magnetic soliton in an easy-axis ferromagnet

The internal dynamics of a small-radius precession magnetic soliton is considered. A variational formulation of the problem on the soliton-magnon interaction is proposed and used to calculate the frequency of a truly local mode. It is shown that this mode, as well as the conventional translational mode, remains localized in the small soliton radius limit. The presence of the local mode is confirmed by the numerical solution of the scattering problem.