Magnon splitting induced by charge ordering in NaV₂O₅

We consider the effects of charge ordering in NaV_2O_5 (below T_SP) on the exchange constants and on the magnon dispersion. We show that the experimentally observed splitting of the magnon branches along the a direction is induced by charge ordering. We find that one can distinguish between the proposed 'zig-zag' and 'in-line' patterns of charge ordering. Only the zig-zag ordering is consistent with the experimental results regarding (i) the unusual intensity modulation observed in magnetic neutron scattering, (ii) the reduction in the intra-ladder exchange constant below T_SP, and (iii) the magnon dispersion along a. We estimate the inter-ladder exchange constant to be 1.01meV=11.7K for T>T_SP.