Lattice Jahn-Teller model

Extended (lattice) generalized Jahn-Teller model 633... 

EXTENDED (LATTICE) GENERALIZED JAHN-TELLER MODEL... 

Various other interactions have been considered as the driving force for spin-state transitions such as the Jahn-Teller coupling between the d electrons and a local distortion [73], the coupling between the metal ion and an intramolecular distortion [74, 75, 76] or the coupling between the d electrons and the lattice strain [77, 78]. At present, based on the available experimental evidence, the contribution of these interactions cannot be definitely assessed. Moreover, all these models are mathematically rather ambitious and do not show the intuitively simple structure inherent in the effect of a variation of molecular volume considered here. Their discussion has to be deferred to a more specialized study. 

Kambara (1979) has proposed a microscopic model in which the coupling between the d-electrons and the lattice has been given a definitive meaning. Assuming that there is Jahn-Teller coupling between the d-electrons and the local intramolecular distortion, the Hamiltonian of the system is written as... 

The spectacular relationship between the nature of the X3 species and the promotion energy shows that the VBSCD is in fact a general model of the pseudo-Jahn-Teller effect (PJTE). A qualitative application of PJTE would predict all the X3 species to be transition-state structures that relax to the distorted X ---X-X and X-X— X entities. The VBSCD makes a distinction between strong binders, which form transition states, and weak binders that form stable intermediate clusters. Thus, the VBSCD model is in tune with the general observation that as one moves in the periodic table from strong binders to weak ones (e.g., metallic) matter changes from discrete molecules to extended delocalized clusters and/or lattices. The delocalized clusters of the strong binders are the transition states for chemical reactions. 

The cooperative Jahn-Teller type interaction is obtained by the orbital-lattice coupled model [12,13]. Let us consider the Hamiltonian with the Jahn-Teller coupling g, the kinetic energy and the lattice potential for the Jahn-Teller phonon mode, the orbital-strain interaction, and the elastic-strain energy. The Jahn-Teller distortion mode Qi around a metal site i is represented by the Jahn-Teller phonon coordinates k- By introduce the canonical transformation for k, the orbital and lattice degrees of freedom are separated. The final form of the interaction between the inter-site orbitals given by... 

For TmV04 and TmAs04 the ground state in each case is a non-Kramers doublet that can be split by the true Jahn-Teller effect. For the vanadate the cooperative transition occurs at To = 2.156 K in this region the lattice heat capacity is negligible, and the co-operative anomaly dominates, as shown by the measurements of Cooke et al. (1972) in fig. 11. The distinctive triangular shape is a typical result for a molecular field model in which the splitting J of the doublet varies with temperature as... 

---