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 ∼12 GHz, decreases slightly in frequency to 11 GHz as an in-plane magnetic field is applied. The lower mode, at ∼8 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.