Effective charge and spin Hamiltonian for the quarter-filled ladder compound α′-NaV2O5

An effective intra- and inter-ladder charge-spin Hamiltonian for the quarter-filled ladder compound alpha'-NaV2O5 has been derived by using the standard canonical transformation method. In the derivation, it is: clear that a finite inter-site Coulomb repulsion is needed to get a meaningful result, otherwise the perturbation becomes ill-defined. various limiting cases depending on the values of the model parameters have been analyzed in detail and the effective exchange couplings are estimated. We find that the effective intra-ladder exchange may become ferromagnetic for the case of zig-zag charge ordering in a purely electronic model. We estimate the magnitude of the effective inter-rung Coulomb repulsion in a ladder and find it to be about one-order of magnitude too small in order to stabilize charge-ordering.