Magnetic excitations in layered media: Spin waves and the light-scattering spectrum

Abstract

We present an analysis of the spin-wave spectrum of a semi-infinite stack of ferromagnetic films, each of which is separated by a gap filled by a nonmagnetic medium. This is done within a formalism which includes the Zeeman and dipolar contributions to the spin-wave energy, with exchange omitted. We then calculate the spin-wave contribution to the Brillouin spectrum of such a system, in the backscattering geometry. The aim is to compare the spectrum for scattering from a sample with this geometry, with that from an isolated film. Two features unique to the stack appear in the spectrum. Each film, in isolation, possesses surface spin waves on its boundaries (Damon-Eshbach waves). In the layered geometry these interact to form a band of excitations of the array, which has nonvanishing component of wave vector normal to the stack. We find a feature in the spectrum associated with scattering from this band of modes; the position of the peak is controlled by dispersion introduced by interfilm interactions. Under certain conditions, the semi-infinite stack possesses a surface spin wave, whose eigenfunction is a linear superposition of individual film states, with amplitude that decays to zero as one moves down into the stack interior. This mode also produces a distinct feature in the light-scattering spectrum. These points are illustrated with a series of calculations of the spectrum, for parameters characteristic of layered ultrathin coherent structures.