Local magnon modes and resonances for dynamical skyrmions in Heisenberg two-dimensional ferromagnets

We investigate bound magnon states localized on dynamical topological solitons (dynamical skyrmions) in two-dimensional (2D) Heisenberg weakly uniaxial ferromagnets. The exact analytical expressions for zero modes are derived. It is shown that in addition to zero modes with ``angular momentum'' numbers $m=0,\ifmmode\pm\else\textpm\fi{}1$ truly local modes can exist in 2D ferromagnets on dynamical vortices provided that the magnon dispersion relation has a gap. We study real local modes for dynamical solitons with topological charges $\ensuremath{\nu}=1,2.$ Eigenfrequencies of these modes are calculated numerically. It may be possible to observe resonance effects on eigenfrequencies of internal oscillations of dynamical skyrmions in 2D weakly easy-axis ferromagnets.

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