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This work is aimed at a numerical investigation of the spin-wave energies and respective band structures throughout the two-dimensional Brillouin zone in magnetic (cubic) thin films for the surface orientations sc(001), bcc(001) and fcc(001). We apply the Heisenberg localized spin model assuming exchange nearest (NN) and next-nearest (NNN) neighbour interactions and elucidate the role of the geometrical disposition of the NN and NNN neighbourhoods for the emergence of the surface spin-waves. The necessary condition for the emergence of the surface spin-waves is turned out to require the bonds to be cut at the surface obliquely thereto irrespective of whether these "oblique" interactions are of the NN or NNN type.

The Role of Oblique-to-Surface Disposition of Neighbours in the Emergence of Surface Spin Waves in Magnetic Films