Magnetism of CaV_2O_5, CaV_3O_7, CaV_4O_9: quantum effects or orbital ordering?

The quasi 2-d spin 1/2 materials CaV_nO_2n+1 (n=2,3,4) are often treated as systems in which quantum effects play a dominant role: CaV_2O_5 has a spin gap and is thought to be a spin ladder; CaV_3O_7 has unusual long-range magnetic order which is explained by quantum fluctuations; the spin gap in CaV_4O_9 is usually attributed to the formation of plaquette RVB. We show that in all these compounds there should exist an orbital ordering which strongly modifies the exchange interaction and provides an alternative explanation of their magnetic properties, without invoking special quantum effects. The type of magnetic ordering obtained for CaV_3O_7 quite naturally explains its magnetic structure which turns out to be that of a quasi 1-d antiferromagnet. The structure of CaV_4O_9 corresponds to singlet dimers rather than to a plaquette RVB. Singlet dimers should exist also in CaV_2O_5. The chirality of the crystal structure of CaV_4O_9 is also mentioned and some possible consequences are briefly discussed.