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

Figure 8

((a), (b)) Spin-wave spectra of an 11-layer thick bcc(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 (b), inset, and accompanied with the evolution of the off-diagonal Hamiltonian matrix elements and shown as a green and purple dotted line, respectively. ((c)–(f)) Mode profiles corresponding to points in the SBZ marked with red lines in ((a), (b)).