Magnetostatic (MSW) modes in a Dielectric@Ferromagnetic (Core@Shell) spherical structure

Abstract

The solutions for magnetostatic spin waves (MSW) modes in a spherical structure were studied. A spherical core@shell structure, of soft ferromagnetic (FM) shell and a dielectric core material, was the geometry used for the calculation by solving the Walker equation. The dielectric is a sphere of radius r1 covered by an FM shell of inner radius r1 and outer radius r2. The transformation of the Walker equation in the FM shell was performed based on the solution proposed by Plumier. The resultant expression of solution presented here for the MSW modes are not reported in the literature. The solution involves integrals that are solved numerically and the result are the dispersion relations curves. These curves show deviations from the solution for an empty shell with no core (vacuum@FM) previously reported. The changes in the presented curves are mainly due to the displacement currents that arise in the dielectric core. The curves were calculated for silica and for alumina core, the most commonly used to grow spherical shells. This result here is important because hollow spherical structures are usually grown on dielectric support.