An investigation of the spin excitation spectrum of charge ordered (CO) α’-NaV2O5 is presented. We discuss several different exchange models which may be relevant for this compound, namely in- line and zig-zag chain models with weak as well as strong inter- chain coupling and also a ladder model and a CO/MV (mixed valent) model. We put special emphasis on the importance of large additional exchange across the diagonals of V- ladders and the presence of exchange anisotropies on the excitation spectrum. It is shown that the observed splitting of transverse dispersion branches may both be interpreted as anisotropy effect as well as acoustic- optic mode splitting in the weakly coupled chain models. In addition we calculate the field dependence of excitation modes in these models. Furthermore we show that for strong inter- chain coupling, as suggested by recent LDA+U results, an additional high energy optical excitation appears and the spin gap is determined by anisotropies. The most promising CO/MV model predicts a spin wave dispersion perpendicular to the chains which agrees very well with recent results obtained by inelastic neutron scattering
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