Effects of second-nearest-neighbor displacements on the Raman scattering ofTl+-doped potassium halides

The frequency dependence of the first-order Raman scattering from $E_g$ modes in ${\mathrm{Tl}}^{+}$ -doped KI, KBr, and KCl is calculated for the case when the electron-phonon interaction is a linear function of the displacements of the defect's second-nearest as well as nearest neighbors. It is shown that the inclusion of second-neighbor terms, together with the use of weakly perturbed phonons, allows one to obtain very good agreement between theory and experiment over the entire spectra, thereby removing discrepancies that occurred in the optical portions of the spectra previously calculated from the same phonons, but for the nearest-neighbor case. As an alternative explanation of the discrepancies, a model involving just nearest-neighbor electron-phonon coupling but extended force-constant perturbations is considered. For KI:${\mathrm{Tl}}^{+}$ and KBr:${\mathrm{Tl}}^{+}$ this model is found to be unsatisfactory, while for KCl:${\mathrm{Tl}}^{+}$ it is found that the inclusion of small distortion-induced force-constant perturbations can lead to agreement with experiment comparable to that found with the second-neighbor electron-phonon coupling model. The results for all three systems support the earlier conclusion of Harley, Page, and Walker that ${\mathrm{Tl}}^{+}$ acts essentially as an isotopic defect for the Raman-active modes.