Generalized vibronic methods and applications to the lanthanide type systems

This review is intended to study from both, experimental and theoretical viewpoints, the advantages and disadvantages of the current vibronic models widely employed, in the literature, to deal with the spectral intensities of lanthanide type crystals. For illustrative purposes, we have chosen systems such as: Cs₂NaErCl₆,Cs₂NaDyCl₆. and Cs₂NaHoCl₆. For these systems, a high quality and well resolved experimental data from linear and non linear optics at low temperatures are available. Although, the quality of the experimental data is extremely good, it is either scarce or incomplete or both. Though, these limitations, new strategies and model calculations should be elaborated to rationalize the observed spectral intensities for these and more complicated crystals. We believe that these models should be based upon a full lattice dynamic model whereby the long, the medium and the short range interaction terms must be included. It has been shown, in a variety of research articles, over the last decades that the seven atoms system model has shown a fair degree of flexibility and utility to deal with the observed spectral intensities for a number of stoichiometric chloride and bromide lanthanide crystals. Nevertheless, this seven atoms systems model should be modified and many approximations lifted to account for the most prominent features in the vibronic spectra of a variety number of lanthanide type crystals and in particular for systems such as CS ₂NaLnF₆ where the dispersion between the LO-TO, τ_iu modes is significant. Thus, we may anticipate that the coupling between the internal and external modes of vibrations, say for these fluoride crystals may become too important and therefore cannot be neglected. A new physical model should be developed, based upon new convergence tests to work out a more appropriate and realistic set of normal modes of vibrations to get a better description of the vibrational factor which together with the electronic factor determine the dipole strengths and related quantities. A preliminary version of this lattice dynamic vibronic model (LDVM) is in progress in our laboratory. The constraints employed in current calculation model are analyzed and discussed in some detail.