Dipole-exchange spin excitations in a thin ferromagnetic nanoshell

In this paper spin excitations in spherical ferromagnetic nanoshells are investigated. The magnetic dipoledipole interaction, the exchange interaction and the anisotropy effects are taken into consideration. For such spin excitations, an equation for the magnetic potential perturbation is obtained. For a nanoshell that is thin compared to its size, the dispersion relation for nonzero spin excitation modes and the only possible frequency for zero-mode spin excitations are found. Limitations on the mode numbers are derived.