Bound magnetostatic waves controlled by field gradients in YIG single crystals and epitaxial films

By appropriately designing internal magnetic field profiles within thin crystals or films of yttrium iron garnet, one should be able to create apparent "surfaces" or "tracks" of magnetic discontinuity. Magnetostatic waves bound or guided by such gradients would follow appropriate propagation paths with controlled energy velocity. If the mode amplitudes are small at the edges and corners of the sample, surface scattering is largely prevented. Consequently, the Q of the resonance should be governed primarily by the intrinsic linewidth of the bulk crystal together with normal circuit loading considerations. We here develop a general theory applicable to the two-dimensional magnetostatic modes of a single domain thin ferrite circular disk when the dc magnetic field is normal to the plane of the disk and varies radially. We then restrict the treatment to normalized z-directed magnetic fields of the form Hz(r)/M = A+Br²ⁿwhere A and B are constants, n is a positive integer and M is the saturation magnetization of the ferrite (assumed uniform). For simplicity, magnetic anisotropy and exchange effects are ignored; dissipation is treated by means of perturbation theory. We find solid theoretical justification for the "track" concept and enumerate frequencies and mode patterns for both gradient-modified boundary modes and gradient-dominated "virtual surface" waves. The important effects from rf fringing fields at the edge of the disk are also considered.