Theory of Phase Transitions in Rare-Earth Vanadates

The crystallographic and magnetic phase transitions in the rare-earth vanadates TmVO₄, DyVO₄, and TbVO₄ are studied. Symmetry-adapted spin Hamiltonians, involving quadrupolar and dipolar interactions, are constructed and treated in the molecular-field approximation. The competition between Jahn-Teller distortion and magnetic ordering is illustrated by the comparison of TmVO₄ and TbPO₄. The two phase transitions found in DyVO₄ are reproduced and it is shown that a dipolar phase transition might appear in TbVO₄ at a very low temperature. We also determine the influence of a magnetic field applied along the various symmetry axes.