Classical theory of spin-wave dispersion for ferromagnetic metals

Abstract

The properties of the four spin-wave dispersion branches for a planar ferromagnetic metal with TEM microwave excitation at normal incidence have been examined to derive physical insight into (a) their dependence on material parameters and orientation, (b) the interaction between branches, and (c) the polarization character associated with the related ecxitations. The Larmor electromagnetic and spin-wave branches are found to exhibit a peculiar crossover effect at a critical damping value (α ∼ 0·014 for permalloy). The polarizations vary from circular for the static field normal to the surface to elliptical for an in-plane static field. For the in-plane case, the major polarization axes are parallel and perpendicular to the surface for the Larmor and antilarmor branches, respectively. The well known Ament-Rado and Vittoria formulations have also been modified to include the effect of exchange in the damping term of the Landau-Liftshitz equation. The secular determinant is simplified considerably and the form of the dispersion equations is changed significantly. The only large effect on the branches themselves is to increase the attenuating component of the propagation parameterk for large ¦k¦.