Jahn-Teller effect cooperative

The elastic excitation mode (strain mode) is the soft mode in many of the second-order CJTE transitions. 

Most of the experimental results on CJTE can be explained on the basis of molecular field theory. This is because the interaction between the electron strain and elastic strain is fairly long-range. Employing simple molecular field theory, expressions have been derived for the order parameter, transverse susceptibility, vibronic states, specific heat, and elastic constants. A detailed discussion of the theory and its applications may be found in the excellent review by Gehring Gehring (1975). In Fig. 4.23 various possible situations of different degrees of complexity that can arise in JT systems are presented. 

As mentioned earlier, rare-earth zircons are ideal cases for the study of CJTE. In TmV04, at high temperatures, the lowest electronic state of Tm ion is an E doublet. A pseudo-JT effect occurs if there is accidental or near degeneracy. DyVO is such an example where two Kramers doublets are separated by 9cm another example is TbV04. The rather unusual features of the low-lying electronic states of rare-earth 

Strain by neutron scattering. The three order parameters have been compared and found to show fairly good agreement (Fig. 4.25). The order parameters also follow the (Tj — 7) behaviour within 0.2° of (Sturge et al., 1975). 

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Maaskant WJA (1995) On Helices Resulting from a Cooperative Jahn-Teller Effect in Hexagoal Perovskites. 83 55-88... 

This general feature of both class I and class II behaviour of the copper(II) ion, i.e. the ability to exist in a high symmetry environment against the prediction of both the first- and second-order Jahn-Teller effects, is the best single piece of evidence for the cooperative Jahn-Teller effect and has recently been reviewed.432 It is generally responsible for the whole range of fluxional copper(II) stereochemistries and of the temperature variable ESR spectra of... 

Orbital Ordering and the Cooperative Jahn-Teller Effect in Single Crystals of the Magnetic Perovskite La7/8Sr1/8Mn03... 

Microscopic Approach to Cooperative Jahn-Teller Effect in Crystals with Strong Intra-Site Vibronic Coupling... 

An effective Hamiltonian for a static cooperative Jahn-Teller effect acting in the space of intra-site active vibronic modes is derived on a microscopic basis, including the interaction with phonon and uniform strains. The developed approach allows for simple treatment of cooperative Jahn-Teller distortions and orbital ordering in crystals, especially with strong vibronic interaction on sites. It also allows to describe quantitatively the induced distortions of non-Jahn-Teller type. 

Effective Hamiltonian for cooperative Jahn-Teller effect 650... 

In this chapter an effective Hamiltonian for a static cooperative Jahn-Teller effect is proposed. This Hamiltonian acts in the space of local active distortions only and possesses extrema points of the potential energy equivalent to those of the full microscopic Hamiltonian, defined in the space of all phonon and uniform strain coordinates. First we present the derivation of this effective Hamiltonian for a general case and then apply the theory to the investigation of the structure of Jahn-Teller hexagonal perovskites. 

EFFECTIVE HAMILTONIAN FOR COOPERATIVE JAHN-TELLER EFFECT... 

It is generally accepted in the theory of the cooperative Jahn-Teller effect to include the interaction with uniform strains in the way proposed by Kanamori [14], i.e., as additional terms of vibronic interaction at each Jahn-Teller ion. On the other hand, within one-centre-coordinate approach used here the vibronic interaction is fully described by means of one-centre active nuclear displacements qn. Therefore the interaction with uniform strains can be included implicitfy as additional terms in the Van Vleck expansion (3). Since phonons and uniform strains are independent degrees of freedom this new expansion is written as follows ... 

Replacing in equation (5) by defined in equations (23) and (24), we obtain the general form of the effective Hamiltonian (7) for the static cooperative Jahn-Teller effect. Note that this has been obtained without any approximations. 

The proposed approach to static cooperative Jahn-Teller effect is based on the exact effective Hamiltonian (7), acting in the reduced space of active one-centre distortions only. It involves effective force constants, which are analytically related to the parameters of the full microscopic Hamiltonian. Direct electronic interactions between sites, such as orbital-dependent electrostatic and exchange interactions [28], can be added to the effective Hamiltonian without modifying it. This approach proves to be especially efficient in the case of strong Jahn-Teller distortions, when the effects of second-order Jahn-Teller coupling become important. 

The so-called cooperative Jahn-Teller effect is another occurance of the static distortions. Here, interaction, that is, cooperation between different crystal centers, make the phenomenon observable. Without interaction, the nuclear motion around each center would be independent and of a dynamic character. 

Lattice vibrations tend to destroy the correlation among Jahn-Teller centers. Thus, with increasing temperature, these centers may become independent of each other at a certain point, and their static Jahn-Teller effects convert to dynamic ones. At this point the crystal as a whole becomes more symmetric. This temperature-dependent static -O- dynamic transition is called a Jahn-Teller phase transition. Below the temperature of the phase transition, the cooperative Jahn-Teller effect governs the situation providing static distortion the overall structure of the crystal is of a lower symmetry. Above this temperature, the cooperation breaks down, the Jahn-Teller distortion becomes dynamic and the crystal itself becomes more symmetric. 

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