Jahn-Teller crystal

M. Kaplan and B. Vekhter, Cooperative Phenomena in Jahn-Teller Crystals, Plenum Press, New York, 1995. 

Multicentre vibronic interactions are found in a wide number of systems such as impurity Jahn-Teller centres, molecular clusters and Jahn-Teller crystals [1], In these compounds the localized electrons in orbitally degenerate states interact directly only with active distortions of the local environment of corresponding vibronic centres. The distortions of different centres interact via the common vibrational modes of the system, which thus mediate the indirect interaction between Jahn-Teller centres [2,3]. As a result the corresponding vibronic problem becomes rather involved, with many electronic states mixed by many vibrational modes. 

The potential energy of the Jahn-Teller crystal is described by the operator... 

Thus the problem of finding extrema of the potential energy of Jahn-Teller crystal is reduced to the space of active local distortions only. Having found the equilibrium values of these distortions, q, we obtain the equilibrium values for all phonon modes ... 

The above derivation of the effective Hamiltonian is only complete when, for some reasons, the uniform strains of the crystal are not relevant. This is clearly the case for crystals with low concentration of Jahn-Teller impurities. Contrary to that, bulk deformations often arise in its low-symmetry structural phases of Jahn-Teller crystals [2,11]. The uniform strains describing the bulk deformations of the crystal cannot be reduced to a combination of phonon modes, as it was first pointed out by... 

Abstract Keeping in mind the pedagogical goal of the presentation the first third of the review is devoted to the basic definitions and to the description of the cooperative Jahn-Teller effect. Among different approaches to the intersite electron correlation in crystals the preference is with the most fundamental and systematic Hamiltonian shift transformation method. Order parameter equations and their connection to the crystal elastic properties and to the orbital ordering are considered. An especial attention is paid to the dynamics of Jahn-Teller crystals based on the coupled electronic, vibrational, and magnetic excitations which are of big interest nowadays in orbital physics. 

Fig. 5 Schematical presentation of the electron-phonon excitations in the Jahn-Teller crystals at different temperatures [7]...

The fundamental role of the dynamic electron-phonon coupling in the Jahn-Teller crystals was clearly demonstrated by the Raman light scattering experiments [18],... 

Fig. 10 Static and dynamic magnetostriction in the DyV04 (a,b), TbV04 (c), and Tbi xGdxV04 (d) Jahn-Teller crystals, (a) and (b) are the experimental restilts by V. Sokolov, Z. Kazey e.a. (c) and (d) ate the theoretical data by M. Kaplan, B. Vekhter e.a. [10]...

Fig. 11 Experimental and theoretical data demonstrating the metamagnetism and metamagnetoelasticity of the Jahn-Teller crystals with structural transitions M(B) - metamagnetism of KDy(Mo04)2 [27] M/Mo(h/2) - theory (h = l/2g/usi7) U(h/2) - metamagnetoelasticity of an antiferroelastic (theory) [29]...

Abstract A review is made on the developments in the last two decades in the held of the Jahn-Teller effect on itinerant electrons in Jahn-Teller crystals. Special attention is paid to the current status of the researches on the fullerene superconductors and the manganite perovskites exhibiting the colossal magnetoresistance. Present knowledge about the polarons and bipolarons in the typical Jahn-Teller model systems is also summarized, together with some original results of our own. 

COOPERATIVE PHENOMENA IN JAHN-TELLER CRYSTALS Michael D. Kaplan and Benjamin G. Vekhter... 

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