Theory of spin waves in magnetic interfaces, superlattices and disordered layer structures

Abstract

A general recursion method for calculating the exact local spin-wave Green function in an arbitrary ferromagnetic interface, superlattice and disordered layer structure is developed. The method is applied to magnetic insulator structures described by a nearest-neighbour exchange Hamiltonian. It is shown that the complete response function of an arbitrary layer structure can be generated from a single matrix element of the Green function in the surface plane of a magnetic overlayer. The proposed algorithm for overlayers is very simple, computationally stable and extremely accurate. The method is used to determine the exact exchange stiffness D of a ferromagnetic superlattice and of a disordered layer structure. The range of validity of the exact result for D is discussed in the light of recent experiments on the temperature dependence of the surface magnetisation. The application of the method to ferromagnets with long-range exchange interactions and to metallic layer structures is also discussed.