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

Figure 2

((a), (b)) Spin-wave spectra of a 7-layer thick sc(001) thin film with NNN exchange interactions (a) ferromagnetic and (b) antiferromagnetic. 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. Below each spectrum the evolution of the off-diagonal Hamiltonian matrix element is shown as a green dotted line. Blue lines represent conditions for the surface localization of symmetric (solid lines) and antisymmetric (dashed lines) modes. Wave vectors for which the antisymmetric mode starts to localize are marked with red arrows. ((c)–(h)) Mode profiles corresponding to points in the SBZ marked with purple lines in ((a), (b)).