Numerical calculations of crossover effects in rare-earth zircons

Abstract

The Hamiltonian used to describe Jahn-Teller compounds like DyVO₄, TbVO₄, TmVO₄, TbAsO₄, etc., has a non-analytic term arising from the coupling of the lattice displacements to the pseudo-spins. One explicitly calculates the angular dependence of this term, for both types of distortion involved. The values of the elastic constants are used to obtain numerical values of the quantities that prove relevant for a study of the associated crossover effects. A simple approximation to the form of the interaction is used; the effective exponent gamma _eff is then evaluated as a function of the temperature, within an epsilon -expansion calculation. The corrections introduced when the exact form of the interaction is considered do not significantly change the crossover behaviour. The critical behaviour expected of compounds that suffer a B_1g distortion (DyVO₄) and the ones undergoing a B_2g distortion (TbVO₄, etc.) is discussed in terms of the differences of the respective values of h(0).