Theory of bulk and surface magnons in Heisenberg ferromagnetic superlattices

Abstract

We present a theoretical study of the bulk and surface magnons of a semi-infinite stack of two different ferromagnetic films. Each film is modeled by a simple-cubic lattice of spins coupled via nearest-neighbor exchange (Heisenberg ferromagnet). The superlattice has a larger periodicity in the direction perpendicular to the slabs and therefore many magnon branches in the folded Brillouin zone. In the gaps exisiting between these magnon branches appear the surface-localized magnons. The simplicity of our model allows one to obtain in closed form the bulk and (001) surface Green's functions for this magnetic superlattice. The analytic knowledge of these functions enables us to study easily all the bulk and and surface magnetic properties of a ferromagnetic superlattice. We give here the analytic expression we obtained for the folded bulk magnons and also the expression that gives the surface-localized modes, which may appear within the extra gaps which exist between the folded bulk bands. One figure for a specific case illustrates these results.