Magnetic transition and orbital degrees of freedom in vanadium spinels

We propose a scenario for the two phase transitions in AV₂O₄ (A=Zn, Mg, Cd), based on an effective spin-orbital model on the pyrochlore lattice. At high temperatures, spin correlations are strongly frustrated due to the lattice structure, and the transition observed at ~50K is attributed to an orbital order, supported by Jahn-Teller lattice distortion. This orbital order introduces spatial modulation of spin-exchange couplings depending on the bond direction. This partially releases the frustration and leads to a spin order observed at ~40K. We also study the stable spin configuration by taking account of third-neighbor exchange couplings and quantum fluctuations. The result is consistent with the experimental results.