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

Figure 4

((a), (b)) Spin-wave spectra of an 11-layer thick fcc(110) thin film (a) without and (b) with NNN exchange interactions. Solid lines represent the energy of individual modes; the shaded area is the bulk band for in-plane spin waves. Each spectrum is plotted along the high-symmetry path shown in (a), inset, and accompanied with the evolution of off-diagonal elements (green dotted line) and (purple dotted line) of the Hamiltonian matrix. (c) Mode profiles of the four lowest modes corresponding to the point in the SBZ, marked with a red line in (b).

(a)

(b)

(c)