Propagation Effects in the Spin-Wave Spectrum of the Ferromagnetic Thin Film

Exchange spin waves propagating in magnetic thin films exhibit some dynamic effects, that is, the effects caused solely by the wave propagation. In this paper we put our attention in four phenomena of such kind: the surface (and subsurface) localization, the collapse of the bulk band into a single energy level, the reversal of the mode order in the spin-wave spectrum, and the dynamic separation of the thin film into two subsystems. We link these effects to properties of Hamiltonian matrix elements inherited from the spatial distribution of neighboring spins with respect to the film surface. We also provide necessary conditions for the occurrence of these effects