Spin excitations of magnetic vortices in ferromagnetic nanodots

Spin excitations of the magnetic vortex state in ferromagnetic nanodots are measured using Brillouin light scattering. Arrays of permalloy dots with 800-nm diameter and 60-nm thickness were fabricated by means of electron beam lithography and lift-off procedures. Two excitation modes are observed experimentally in the vortex state. One mode, at similar to12 GHz, decreases slightly in frequency to 11 GHz as an in-plane magnetic field is applied. The lower mode, at similar to8 GHz, is almost independent of applied field strength. Numerical and analytical calculations of the dynamic magnetization based on the Landau-Lifshitz equation of motion allows us to identify the higher and lower frequency modes as corresponding to dipole-dominated spin excitations localized inside the dot and at the dot edges, respectively.