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

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.