Calculations on the multi-mode Jahn-Teller effect for T⊗e in a cubic lattice

Publisher Website
Google Scholar
Abstract
The Eg modes of a simple cubic lattice are described in detail for the case when all ions have the same mass and the elastic forces are of a simple nearest-neighbour form. The density of modes is then computed. A Tg ion is assumed to be coupled to such modes via an interaction linear in the Eg displacements of its nearest neighbours. The resulting Jahn-Teller effect is studied by applying to the Hamiltonian a unitary transformation chosen so that the ion-lattice coupling is replaced by a constant. The Jahn-Teller energy EJT and a first-order reduction factor gamma can then be computed, and it is found that contributions to EJT and gamma are important over a wide range of frequencies and that the major contribution to gamma is due to the motion of the ion's nearest neighbours. The displacement of lattice points which results from the Jahn-Teller interaction is shown to vary approximately as the inverse square of the distance from the magnetic ion.