Hybridization of Surface and Impurity Spin Waves Induced by their Propagation in the Plane of a Thin Ferromagnetic Film

Spin waves of a thin ferromagnetic film containing in its bulk two impurity layers, each parallel to the film surface and symmetrically disposed with regard to the film centre, are theoretically investigated within the framework of the Heisenberg model. The existence conditions for surface-localized and impurity-layer localized spin waves are established. Particular attention is given to the effect of a possible hybridization of these localized excitations; it is shown that this phenomenon does in fact occur for certain specified directions of the in-plane wave vector k$\text{}_{||}$.