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

Figure 3

(a) Spin-wave spectrum of an 11-layer thick bcc(001) thin film with no NNN exchange interactions. 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 an inset. 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 line) and antisymmetric (dashed line) modes. Wave vectors for which the antisymmetric mode starts to localize are marked with red arrows. (b) The same as in (a) but for the hypothetical situation in which NN interactions are switched off while NNN interactions are switched on. The purple dotted line represents the evolution of the off-diagonal Hamiltonian matrix element .

(a) ,

(b) ,