Phonon Properties and Electron-Phonon Interaction in Thallium-Doped Potassium Halides

In this work we present a detailed and consistent description of the defect vibrational properties induced by ${\mathrm{T}1\mathrm{}}^{+}$ ions in Kcl, KBr, and KI, with the purpose of investigating the electron-phonon (EP) interaction associated with the defect. A defect-induced perturbation of the dynamical matrix extending as far as fourth neighbors (4n) is adopted; calculations of several phonon-response functions, such as infrared absorption, first-order Raman scattering, and thermal conductivity, are presented and compared with the available experimental data, as well as with the results obtained by simpler defect models, i.e., isotopic defect (ID) and nearest-neighbor (nn) perturbation models. The nn and 4n models, both with a weakening of the nn force constant, are found to give a better over-all agreement than the ID model, in line with the early Kristoffel's prediction of an outward lattice distortion around ${\mathrm{Tl}}^{+}$ in KCl. Then, response functions induced by the linear EP interaction, namely the shape of the ultraviolet absorption A band and the absolute first-order Raman cross sections are calculated on the basis of the three defect models and making use of the experimental stress coefficients of the $A$ band to evaluate the parameters of the EP interaction. Again the 4n and nn models are found to give a better agreement with the experimental data. Some residual discrepancies concerning with the KCl:${\mathrm{Tl}}^{+}$ $A$ band are referred to the large Jahn-Teller effect occuring in this system and neglected in the present work. Finally, it is shown how the nondiagonal part of the EP interaction makes the scattering processes involving tetragonal and trigonal modes dominate over those involving breathing modes.