Crystal field, phonon coupling

As discussed in Sect. 6.2, the electronic states of a paramagnetic ion are determined by the spin Hamiltonian, (6.1). At finite temperamres, the crystal field is modulated because of thermal oscillations of the ligands. This results in spin-lattice relaxation, i.e. transitions between the electronic eigenstates induced by interactions between the ionic spin and the phonons [10, 11, 31, 32]. The spin-lattice relaxation frequency increases with increasing temperature because of the temperature dependence of the population of the phonon states. For high-spin Fe ", the coupling between the spin and the lattice is weak because of the spherical symmetry of the ground state. This... 

Alexandrite, the common name for Cr-doped chrysoberyl, is a laser material capable of continuously tunable laser output in the 700-800 nm region. It was established that alexandrite is an intermediate crystal field matrix, thus the non-phonon emitting state is coupled to the 72 relaxed state and behaves as a storage level for the latter. The laser-emitted light is strongly polarized due to its biaxial structure and is characterized by a decay time of 260 ps (Fabeni et al. 1991 Schepler 1984 Suchoki et al. 2002). Two pairs of sharp i -lines are detected connected with Cr " in two different structural positions the first near 680 nm with a decay time of approximately 330 ps is connected with mirror site fluorescence and the second at 690 nm with a much longer decay of approximately 44 ms is connected with inversion symmetry sites (Powell et al. 1985). The group of narrow lines between 640 and 660 nm was connected with an anti-Stokes vibronic sideband of the mirror site fluorescence. 

In the next section the rare-earth compounds that have been studied by optical means under pressure so far will be reviewed. Then, after a brief introduction of the most commonly used high pressure device, the diamond anvil cell, sect. 4 presents a discussion of the pressure-induced changes of the crystal-field levels and their interpretation. In sects. 5 and 6 some aspects of the dynamical effects under pressure are discussed. These include lifetime and intensity measurements, the influence due to excited configurations and charge transfer bands, and the electron-phonon coupling. 

The optical studies performed on most samples of table 1 were aimed at different aspects of the f-electron properties. A considerable amount of the work was concerned with the energy level shifts under pressure. From these shifts, variations of free-ion parameters, crystal-field parameters or crystal-field strengths with pressure have been deduced. Other studies concentrated on changes in lifetimes or intensities, the efficiency of energy transfer between rare earths or rare earths and other impurities or on electron-phonon coupling effects under pressure. The various aspects investigated under high pressure will be presented within the next sections. 

Non-metallic rare-earth compounds studied under high pressure. In almost all cases the energy level shifts as a function of pressure have been determined. The second column gives details concerning the measurements and evaluations made. In particular the following abbreviations are used L Luminescence-, A Absorption-, E Excitation-, S Site-selective spectroscopy, O Other methods, EPC Electron-Phonon Coupling, Int Intensities, LT Lifetime, CFP Crystal-Field Parameters, FIP Free-Ion Parameters, IP Intrinsic Parameters, ET Energy Transfer... 

Bare crystal-field (CF) and phonon (ph) energies and the CF-phonon coupling constant V at ambient pressure and the corresponding pressure coefficients for the compounds NdBa2Cu3(>7 and Pb2Sr2NdCu3Ojj (Goncharov et al., 1994). CE and SC refer to ceramic and single-crystal samples, respectively... 

Recently, the spectral study of DMTM(TCNQ)2 phase transition was performed [60]. The salt is a quarter-filled organic semiconductor containing segregated chains of TCNQ dimers and DMTM counterions. This material undergoes an inverted Peierls transition, which has tentatively been explained in terms of a crystal-field distortion. It was shown that the experimental values of unperturbed phonon frequencies and e-mv coupling constants are nearly independent of temperature. The dimer model fails to reproduce the phonon intensities and line shapes and underestimates the coupling constants, whereas the CDW model produces better results... 

The interconversion of the two tautomer forms of dimers (Fig. 2) by a concerted two proton transfer is governed by a double-well potential. In condensed phases the two possible tautomers are identical. Skinner and Trommsdorff [21 ] treated a model of crystalline benzoic acids in which the dynamics of each proton pair is uncorrelated with other pairs. Their model was based on a single doubleminimum potential coupled to a thermal bath—that is, crystal vibrations. It was believed that in a condensed phase the crystal field breaks the symmetry of the two wells (Fig. 3). If Fig. 3 indeed represents the real situation when the proton transfer from the left well to the right one should take place at the participation of vibrations of the crystal that is, phonons of some sort should activate the proton transfer. We would like to emphasize that this is the conventional viewpoint, which is widely employed by physicists. 

Consider now the case where the energy spacing 21 is very small. Such cases are encountered in the study of relaxation between spin levels of atomic ions embedded in crystal environments, so called spin-lattice relaxation. The spin level degeneracy is lifted by the local crystal field and relaxation between the split levels, caused by coupling to crystal acoustical phonons, can be monitored. The relaxation as obtained from (12.47) and (12.48) is very slow because the density of phonon modes at the small frequency (U21 is small (recall that... 

Here p is the density of phonons, n(co) is the Planck number corresponding to the thermal distribution of phonon excitations and k(co) is the spin-phonon coupling constant written as a function of frequency (instead of the wave-vector star k and the phonon branch index, as previously). Only those phonons with energy equal to the Zeeman energy h coa are of interest in a direct relaxation process. This energy is characteristically 0.1 cm-1 and the relevant phonons are of the long-wave acoustic type. Their role is to modulate the crystal field interacting with the electron. 

The dynamic crystal-field interactions and ion-phonon coupling are also expected to be stronger for the actinides. 

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