Localised modes of elementary excitations in the system of two ferromagnetic layers separated by a nonmagnetic spacer

The elementary excitations (spin waves) in the system of two ferromagnetic films of different thicknesses exchange coupled through a nonmagnetic metal lic spacer are investigated. The Hamiltonian of the system consists of the exchange, Zeeman and both the surface and interface anisotropy terms. The o scillatory exchange coupling between two ferromagnetic layers resulting fro m the interaction via itinerant electrons is employed to investigate spin w ave profiles. In presented contribution the discussion of the influence of the anisotropies at the external surfaces and at the interface is extended to the case of ferromagnetic layers of different thicknesses and interactio n parameters. The solutions of a set of difference equations for the amplitudes and wave vector k lead to real (bulk modes) and imaginary (localised modes) solution s for k. The imaginary solutions represents, modes localised at surface or (and) interface. The conditions necessary for appearance of both types of m odes are discussed. It is shown that that the coexistence of localisation a t the surface and interface depends on the ratio of thicknesses of constitu ent layers. The results obtained as a function of the spacer thickness are illustrated by the ferromagnetic resonance (FM R) spectra. The examples of the systems in which one type of surface anisotropy decides on the character of resonan ce picture are presented. Analysis of the spectra allows one to estimate th e experimental error connected with the thicknesses of magnetic and nonmagn etic layers in FMR experiments. (C) 2001 Elsevier Science Ltd. All rights r eserved.