Magnetostatic spin wave focusing and defocusing in cylindrically symmetric non-laplacian magnetic fields

A simple analytic criterion is developed which determines the focusing or defocusing of near axis magnetostatic spin waves propagating in a cylindrically symmetric ferromagnet. The crystal is assumed to be magnetically saturated by an axial magnetic field which, due to nonzero volume divergence of the magnetization, is in general, non-Laplacian in character. In addition, both magnetic dipolar coupling and variation of the angle between the magnetization vector and the local propagation vector are included in the model, which thus extends the analytic work of previous authors. The asymptotic behavior of the spin wave trajectories is found to predict either focusing or defocusing. In analogy to under- and over-damped resonators, the former occurs either by the monotonic or damped oscillatory approach of a ray toward the axis; the condition for critical damping is also given. The theory is applied to the case of a magnetically saturated YIG cylinder of commonly employed dimensions (3 mm d. × 10 mm).