Theory of Phase Transitions in Rare-Earth Vanadates

Abstract

The crystallographic and magnetic phase transitions in the rare-earth vanadates TmV${\mathrm{O}}_{4}$, DyV${\mathrm{O}}_{4}$, and TbV${\mathrm{O}}_{4}$ 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 TmV${\mathrm{O}}_{4}$ and TbP${\mathrm{O}}_{4}$. The two phase transitions found in DyV${\mathrm{O}}_{4}$ are reproduced and it is shown that a dipolar phase transition might appear in TbV${\mathrm{O}}_{4}$ at a very low temperature. We also determine the influence of a magnetic field applied along the various symmetry axes.