Magnetostatic waves bound to a DC field gradient

We discuss the conditions necessary to cause magnetostatic waves to be bound or confined by dc magnetic field gradients both in rectangular slabs and solid or hollow cylinders when the wave propagation is parallel to the surfaces and perpendicular to the dc field direction. General equations which govern the eigenmode potential are developed, as are expressions that allow evaluation, of the group velocity and wave attenuation factor. However, we also discuss a special family of field profiles that, at special points of the dispersion diagrams, allows analytic expressions to be found for all quantities of interest. By proper choice of the gradient, the bound wave frequencies and the ratio of the wave energy inside the crystal to that outside can be controlled. As expected, the waves are nonreciprocal with respect to propagation direction. With appropriate gradients, even a single surface can support bound mode propagation in either direction. We also consider the effect of very steep gradients caused by abrupt changes in field and/or saturation magnetization within either slabs or cylinders. Finally, a brief discussion of waves bound to positive or negative curvature field wells is included.