Dynamic Origin of Azimuthal Modes Splitting in Vortex-State Magnetic Dots

A spin-wave theory explaining experimentally observed frequency splitting of dynamical spin excitations with azimuthal symmetry of a magnetic dot in a vortex ground state is developed. It is shown that this splitting is a result of the dipolar hybridization of three spin-wave modes of a dot having azimuthal indices m=1: two high-frequency azimuthal dipolar modes of the in-plane part of the vortex with indices m=+/- 1 and a low-frequency (Goldstone-like) gyrotropic mode, describing translational motion of the vortex core and having index m=+1. The analytically calculated magnitude of the frequency splitting is proportional to the ratio of the dot thickness to its radius and quantitatively agrees with the results of time-resolved Kerr experiments.