Precise probing spin wave mode frequencies in the vortex state of circular magnetic dots

We report on detailed broadband ferromagnetic resonance measurements of azimuthal and radial spin wave excitations in circular Permalloy dots in the vortex ground state. Dots with aspect ratio (beta=height over radius) varied from 0.03 to 0.1 were explored. The frequency splitting of two lowest azimuthal modes was observed. The experimentally observed dependence of the frequency splitting on beta was reasonably well described by dynamic splitting model accounting the spin waves and vortex gyrotropic mode interaction.