Theory of interface magnons in magnetic multilayer films

Abstract

A review is given of the properties of interface spin-waves in ferromagnetic multilayer films. We start from the general model assumptions made when dealing with this magnetic films; complete generality is ensured by assuming the spin quantization axes in each monolayer as different. The Hamiltonian diagonalization procedure is based on the Tyblikov-Bogolyubov scheme, appropriately modified for the film structure considered; the diagonalization leads to elementary magnetic excitations, i.e., spine-waves of the multilayer system. We concentrate specifically on the spine-wave spectrum of exchange-coupled bilayer films, for which the appropriate Surface-Interface Inhomogeneity Model is elaborated and the respective Heisenberg Hamiltonian is established and diagonalized. The theory is valid for Bravais lattices with arbitrary surface/interface orientation, and holds for arbitrary (with respect to the film normal z) configurations of the bilayer film magnetization, arbitrary ferro/antiferromagnetic interface exchange coupling, and arbitrary (easy-axis/easy-plane) uniaxial interface anisotropy taken as a single-ion anisotropy of the DS 2 z type. When exact Hamiltonian diagonalizationis achieved, the microscopic theory of bilayer spin-wave resonance (SWR) is developed in detail. Particular attention is given to the conditions for the occurence of interface-mode (IM) peaks in the bilayer resonance spectrum, and the use of these when determining the interface parameters (interface pinning anisotropy and interface coupling). First, the essential feastures of the bilayer SWR spectrum are discussed for the case when the external static field is applied perpendicularly to the film surface and intrinsic surface and interface anisotropies are absent. We show that the pattern of the SWR spectrum is determined by the nature of the interface exchange-coupling integral, with the firlst two (high-field side) lines exhibiting pronounce intensities if the interface coupling is antiferromagnetic, and that the highest-field line arises by excitation of the mode which is localized on the bilayer interface. When the bilayer Hamiltonian includes both surface and interface pinning anisotropies (of uniaxial type) we establish conditions for the coexistence of surface and interface modes, and moreover predict the the possibility of creation of bilocalized surface-interface hybrids of these two modes. The general bilocalization conditions involving the interfacial coupling and surface/interface anisotropies are tabulated separately for symmetrical and antisymmetrical modes. Next, in the more general case when the external field is tilted to the bilayer film surface, we predict the existence of a “critical configuration angle θ c” for IM emergence at film magnetization rotation. For antiferrogmagnetic interface coupling θ c is a function of the interface parameters. We stress the importance of a formula permitting the determination of the iterface parameters from the experimental resonace peaks intensity ratio R = I BM I IM (where I IM is the intesity of the IM mode existing in the respective configuration and T BM is that of an appropriately chosen bulk mode). A separate problem concersn the existence of Propagating interface-localized spine-waves in bilayer films. At fixed static interface conditions, an interface spine-wave can propagate only in certain permitted directions in the plane of the film. This restriction is visualized graphically by plotting the existence regions of the interface spine-waves in the two-dimensional Brillouin zone. The regions are then studied as to their form and size versus the interface parameters. Our general mathematical analysis of the bilayer spine-wave spectrum is based on the exact solution of the respective eigenvalue problem as enabled by our newly invented interface-rescaling approach. Finally, we propose an exact solution of the eigenvalue problem for triple-layer films. Therefore, our stepwise interface-rescaling procedure is shown to be well adapted for research on more highly complex multilayer magnetic films.