The Role of Next-Nearest Neighbours for the Existence Conditions of Subsurface Spin Waves in Magnetic Films

Abstract

Spin‐wave energies and respective band structures throughout the two‐dimensional Brillouin zone are investigated in magnetic (cubic) thin films for the surface orientations sc(110), bcc(110) and fcc(110). 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 surface (SSW) and subsurface spin waves (SSSW). The necessary condition for the emergence of SSSW is found to require the NNN bonds to be cut at the surface obliquely thereto.

Spin-Wave Dynamics in the Presence of Magnetic Vortices

“…The physical properties of magnetic nanodots are related mostly to the concurrence of two types of magnetic interactions, namely exchange and dipolar ones. Usually, the coexistence of long-and short-distance interactions leads to new phenomena, such as surface and subsurface localization of the spin waves in layered magnetic systems [2,3], opening of the band gaps in magnonic crystals [4,5], or splitting the spin-wave spectrum into subbands in patterned multilayers [6,7]. In the case of exchange and dipolar interactions, the situation is even more interesting due to competitive effects of these two schematically shown in Figure 1.…”

Effects of spin-wave energy degeneracy induced by in-plane wave propagation in ferromagnetic thin films

“…In-plane wave propagation involves very interesting phenomena, such as localization of surface waves in thin films with free surfaces (studied, for example, in our previous works [1,2] for spin waves and by Gazis et al [3] for phonons) or the spin-wave spectrum collapse discovered in semi-infinite ferromagnets by Lé vy et al [4]. On the other hand, the effect of interactions between next-nearest neighbors (NNN) is also intensively studied in a variety of fields (see [2,[5][6][7] and references therein).…”

“…On the other hand, the effect of interactions between next-nearest neighbors (NNN) is also intensively studied in a variety of fields (see [2,[5][6][7] and references therein). Unfortunately, studies of surfaces or thin films most commonly deal with the simple cubic (sc) crystal structure with (0 0 1) surface(s) only.…”

“…In our previous papers, focused on the conditions of surface state emergence [1,2,13,14], we showed that in the sc(0 0 1) surface cut NNN interactions are necessary for surface modes to occur, but in other surface cuts interactions between nearest neighbors (NN) suffice to cause surface localization of spin waves. An analysis of the spatial distribution of the nearest and nextnearest neighbors led us to the conclusion that surface spin waves occur as a result of the exchange coupling oblique with respect to the surface, regardless of the range of the coupling.…”