Spin mode calculations in nanometric magnetic rings: Localization effects in the vortex and saturated states

We study how a varying applied magnetic field influences the localization of the spin excitations in a Permalloy nanoring. The eigenfrequencies and eigenvectors of the excitations are calculated directly in the frequency domain with the dynamical matrix method, which recently proven to be successful in explaining the spin mode spectrum measured by the Brillouin scattering in rings (G.Gubbiotti et al., Phys. Rev. Lett. 97, 247203 (2006)).When the ring is in the vortex equilibrium state at a field different from zero, we found that the localization of the (m,0) azimuthal modes may take place either where the internal field has a minimum or a maximum, depending on the mode frequency and index m. The saturated phase is characterized by a variety of modes, which may localize in the lateral arms of the ring, in the upper/lower sectors in the direction of the applied field, and at the inner or outer borders.