Spin waves in circular soft magnetic dots at the crossover between vortex and single domain state

We report on linear spin dynamics in the vortex state of Permalloy cylindrical dots subjected to an in-plane bias magnetic field. We demonstrate experimentally by a broadband ferromagnetic resonance technique and by simulations that breaking the cylindrical symmetry of the magnetic vortex gradually changes and suppresses the azimuthal spin eigenmodes below the vortex nucleation field and leads further to the appearance of new eigenmodes. The parallel microwave field pumping is shown to be a unique tool to observe spin excitation modes localized near the strongly shifted vortex core for the bias field between the vortex nucleation and annihilation fields. Meanwhile, the perpendicular field pumping, which excites the spin waves throughout the entire dot, reveals a crossover between two dynamic vortex regimes near the nucleation field.