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

Figure 9

Spin-wave spectrum of an 11-layer thick fcc(110) thin film for , that is, the special case for which the bulk band collapse occurs even for NNN interactions switched on. Solid lines represent the energy of individual modes; the shaded area is the bulk band for in-plane spin waves. The spectrum is plotted along the high-symmetry path shown in (a), inset, and accompanied with the evolution of off-diagonal elements of the Hamiltonian matrix (green dotted line) and (purple dotted line).