Exchange interactions and magnetic properties of the layered vanadates CaV2O5, MgV2O5, CaV3O7, and CaV4O9

We have performed ab initio calculations of exchange couplings in the layered vanadates CaV2O5, MgV2O5, CaV3O7, and CaV4O9. The uniform susceptibility of the Heisenberg model with these exchange couplings is then calculated by the quantum Monte Carlo method; it agrees well with the experimental measurements. Based on our results we naturally explain the unusual magnetic properties of these materials, especially the huge difference in spin gap between CaV2O5 and MgV2O5, the unusual long range order in CaV3O7, and the "plaquette resonating valence bond" spin gap in CaV4O9.