Splitting of spin excitations in nanometric rings induced by a magnetic field

We present a Brillouin light scattering investigation of the eigenmode spectrum of nanometric permalloy rings as a function of the applied magnetic field. In particular, different splitting effects induced by the applied magnetic field on the radial and azimuthal excitations have been observed and explained in terms of either mode localization or symmetry. The dynamical matrix approach has been used to calculate the whole set of eigenvectors and eigenvalues of the system, in both the vortex and saturated states.