Pseudo spin vibronic

It is interesting to follow the role of the IT effect in this picture. Dressed with phonons, orbital states transform into the so-called IT polaron states. The orbital pseudo spin becomes vibronic pseudo spin (a detailed discussion of this side of the story is given below in Sects. 5.2 and 5.3). Instead of free rotations of the orbital pseudo spin we come to hindered rotations of the vibronic pseudo spin. At each metal site, the equipotential continuum of different orientations of the orbital spin is transformed into alternating bumps and wells of the vibronic pseudo spin. The latter ones correspond to favorable directions of the vibronic pseudo spin along metal-ligand chemical bonds. 

Fig. 14 Vibronic energy levels in the linear E e case (in units of hco) versus dimensionless coupling constant k (after Muramatsu and Sakamoto [60]). Encircled is the domain of coupling constants where the vibronic ground state is well energy separated from excited vibronic states and the concept of vibronic pseudo spin applies...

As distinguished from the orbital pseudo spin, for the vibronic pseudo spin, the mechanism of intercell coupling is different. It is dominated by the respective terms of elastic intercell interaction. 

The Strong Coupling Case. Tunneling Splitting and Extended Vibronic Pseudo Spin... 

Correspondingly, vibronic pseudo spin space has to be extended to include all tunneling splitting components. In the case of quadratic E e coupling with three wells, it is expressed by the vibronic pseudo spin x = 1 matrices 3x3. Similar to the intermediate coupling case, the intersite vibronic exchange is dominated by the elastic intercell interaction (36). 

Fig. 15 Vibronic energy levels versus the warping factor p (both E and P are in units of 4a, where a is rotational quantum) in a JT elementary cell with quadratic coupling E (S> e [after O Brien [62]). Encircled is the domain of a very small tunneling energy gap where the concept of extended vibronic pseudo spin applies...

In the case of E e coupling, under some special conditions, including higher orders of JT coupling can result in six wells [1,2]. Correspondingly, in this case, the extended vibronic pseudo spin is expressed by spin-5/2 matrices 6 x 6. In the linear T t2 case, there are four symmetry equivalent wells [2]. Correspondingly, the matrices of extended vibronic pseudo spin are 4x4, and the respective pseudo spin value is r = 3/2. 

The OOA was not designed for and does not apply to temperature dependencies of any kind in JT crystals. In particular, one cannot expect a reasonable estimate of the temperature of phase transitions in crystal lattice (structural), electron orbital, and/or spin system. This follows from the partitioning procedure that includes averaging over vibrational degrees of freedom. One can see the same reason from another perspective. The pseudo spin of a JT site, as the basic concept used in the OOA, operates in the basis of degenerate ground state wave functions. Excited vibronic states are beyond the pseudo spin setup. Therefore, in the OOA, by its very definition, temperature population of excited states does not make sense. 

The presence of vibronic structure in the emission spectra of ions in solids does not depend on the nature of the particular ion alone, but also on the nature of its surroundings. In the case of ns2 ions the strength of the spin-orbit interaction relative to the Jahn-Teller effect determines whether the progression will be in v1 or v2. However, it is not usually possible to observe any vibronic structure at all due to deviations from high symmetry (pseudo Jahn-Teller effect in the ground state). Our present understanding is of a qualitative nature. Further progress is hampered by the fact that the presence of vibronic structure in the spectra is for these ions more exception that rule. 

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