Spinwellen in dünnen ferromagnetischen Schichten

Abstract

This paper is concerned with an ideal spin-l/2-HEisENBERG-model for thin ferromagnetic films. A general method is given for the calculation of the one-spinwave eigenstates and their spectrum in dependence on the lattice type and the orientation of the surfaces of the film. The function that characterises the shape of the spinwave perpendicular to the film must fulfil a linear eigenvalue-difference-equation as well as a set of boundary conditions. For next-neighbour interactions this system may be evaluated for an especially simple case. For it spinwavestates of the form of cos-sin-functions as well as surface states are found. Their momenta are given by some transcendental equations, which are discussed. For all other cases the given difference-equation cannot be solved in a closed form, but at any rate it is a starting point for numerical calculations. In a subsequent paper it will be shown that the special case mentioned above covers some important surface orientations of the cubic lattice types. For films of these orientations the dependence of the magnetization on temperature and thickness of the film will be derived from the spinwave spectra.