Spin and Orbital Ordering in Vanadates

Vanadate compounds provide ideal systems to study the interactions between spin, lattice and orbital degrees of freedom. This talk will discuss the physics of two vanadates, CaV$_{2}$O$_{4}$ and MgV$_{2}$O$_{4}$. In both materials the Vanadium ion is in the 3+ valence state resulting in two electrons in the 3d-shell and a spin of S=1. In CaV$_{2}$O$_{4}$ the V$^{3+}$ ions form quasi-one-dimensional zig-zag chains with frustrated first and second neighbor exchange interactions, while in MgV$_{2}$O$_{4}$ they lie on a frustrated pyroclore lattice. The electronic configuration of the V$^{3+}$ ions consists of two electrons in the three t$_{2g}$ levels giving rise to orbital degrees of freedom in these compounds. The orbital and magnetic degrees of freedom are strongly coupled because the magnetic interactions occur via direct overlap of the t$_{2g}$ orbitals and as a result orbital ordering has a strong impact on the exchange pathways and magnetic behaviour. Both compounds undergo structural phase transitions which either partially or fully lift both the orbital degeneracy and magnetic frustration, long-range antiferromagnetic order then occurs at a lower temperature. Heat capacity, DC susceptibility and neutron and x-ray scattering data will be presented. The results reveal that at high temperatures CaV$_{2}$O$_{4}$ behaves as a Haldane chain, but at low temperatures, it is a spin-1 ladder, while in MgV$_{2}$O$_{4}$ three-dimensional magnetism is replaced by one-dimensional behaviour at low temperatures. The results are discussed in term of orbital ordering.