Magnetostatic surface modes in nonuniform thin films with in-plane bias fields

Abstract

We here develop an integral equation approach to the boundary value problem governing three-dimensional magnetostatic modes or waves in a thin film with either circular or rectangular geometry that applies when the dc magnetization M̄ is entirely in the plane of the film and the bias field and/or material parameters of the ferrite vary along M̄. Exchange effects, magnetic anisotropy, and dual dissipation are all neglected. The electromagnetic boundary conditions required at the film surfaces are built directly into these equations. For circular geometries the radial conditions enter through the components of the Polder susceptibility tensor. Nontrivial solutions occur when ω coincides with an eigenfrequency and we discuss a numerical method for solution of the spectra that correspond to one or more concentric rings. We also develop the analogous integral equations based upon cartesian coordinates for film configurations that involve one or more rectangular strips. For a single strip with uniform bias an approximate analytical treatment is presented. The equations govern a very wide range of physical situations. For example, coupling between modes circulating on two or more concentric annular rings spaced by an air gap can be handled as can the analogous problem involving ferrite strips.