Geometrical Optics of Magnetoelastic Wave Propagation in a Nonuniform Magnetic Field

In a number of experiments, 1 2 3 propagation of magnetoelastic waves has been observed in discs and rods of y t t r i u m iron garnet. Coupling is provided through an internal field variation along the direction of propagation, radially in a disc and axially in a rod. This permits excitation of the wave in a region of small wave vector, 4 - 5 where the magnetic field can couple to the magnetization, with subsequent tapering into the magnetoelastic crossover region. T h e demagnetizing field also varies in magnitude and in orientation across the direction of propagation. In regions where the wave vector is large it is appropriate to consider the effects of this field inhomogeneity in terms of geometrical optics, and it is to be expected t h a t refraction of the magnetoelastic waves will occur. I I . T H E SLOWNESS R E L A T I O N AND GROUP VELOCITY In a cubic crystal with a dc magnetic field applied along a [100] axis x 3 and, for simplicity, assumed elastically isotropic propagation of magnetoelastic waves is governed by the set of equations 6 495