Jahn-Teller effects in coexisting tetragonal and trigonal systems

Abstract

The strongly coupled Jahn-Teller (JT) system is studied in which an ion in an orbital T1 triplet state is coupled to both e and t2 modes of vibrations of its neighbours. Such a system is usually considered to be either a T(X)(e+t2)JT system, in which orthorhombic minima in the five-dimensional Q-space are lowest in energy, or a T(X)d system, which has a trough of lowest energy. However, it is possible also for the tetragonal and trigonal minima, usually associated with the T(X)e and T(X)tJT effects respectively, to coexist with very similar energies to each other (and be of overall lowest energy) when the bilinear term of the vibronic interaction is present. This situation is described in this paper. A set of vibronic ground states is obtained by mixing the symmetry-adapted vibronic T1 ground states of the T1(X)e and T1(X)t2JT systems. This is different to the set of states associated with the orthorhombic minima. Analytical expressions for the first- and second-order JT reduction factors are also derived for the coexisting system. As a consequence of this analysis, an improved version of the theory of second-order reduction factors is obtained. The reduction factors are compared to those of existing numerical calculations for the T1(X)dJT system and it is shown that very good agreement is obtained between the two in the strong-coupling limit.