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.