Brillouin light scattering investigation of dynamic spin modes confined in cylindrical permalloy dots

The quantized mode spectrum of standing spin waves and edge modes in cylindrical Permalloy dots with a radius R in the range between 100 and 500 nm, thickness L550 nm, and separation 2R, is examined from both experimental and theoretical points of view. Brillouin scattering measurements in the Damon-Eshbach geometry give evidence of a marked discretization of the spectra with respect to that of the continuous Permalloy film. The modes can be classified into two distinct families according to their frequency. The upper one consists of the usual Damon-Eshbach, dipole-exchange modes. The modes belonging to the lower family, instead, oscillate parallel to the applied field and are reminescent of the backward modes of the film. Brillouin measurements performed with the applied field parallel to the transferred spin-wave wave vector, confirm this interpretation. The frequencies of these waves have been calculated using a simple theoretical model including the exchange field. Also, a laterally confined mode belonging to this family is observed and its frequency is independent on the dot radius.