Depression of vibronic levels and transition from the dynamic to static Jahn-Teller effect in theT14multiplet: The case ofCo2+in ZnSe

Abstract

A complete comparison between experimental absorption due to the ${}_{}{}^4{}_{}{}^{}A_2^{}{}_{}{}^{}\mathrm{}\left(F\right)-{}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(F\right)\mathrm{}$ transition of substitutional ${\mathrm{Co}}^{2+}$ in ZnSe and theoretical predictions based on the Jahn-$\stackrel{\mathrm{´}}{\mathrm{T}}$eller model is presented. An exact numerical solution of the full Hamiltonian, in which spin-orbit interaction and Jahn-Teller coupling are included, is in very good agreement with the energy position and intensities of the observed absorption lines. It is shown that the predominant Jahn-Teller coupling is with the low-frequency mode of $\hslash \omega =72\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ of $E$ symmetry, which originates from the peak of the density of states of the transverse-acoustic phonons of ZnSe. The frequency of this Jahn-Teller active mode coupled to the lowest electronic level of the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(F\right)\mathrm{}$ term is drastically reduced by the second-order Jahn-Teller interaction within the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(F\right)\mathrm{}$ term. The analytic expressions and numerical calculations for the depression of vibronic levels in the case of $E$- and $T_2$-mode coupling are presented and discussed. It is shown that for the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(F\right)\mathrm{}$ state the depression of vibronic levels is almost the same in the case of $E$-mode and $T_2$-mode coupling. Finally, it is shown that the ${}_{}{}^4{}_{}{}^{}T_1^{}{}_{}{}^{}\mathrm{}\left(F\right)\mathrm{}$ state of ${\mathrm{Co}}^{2+}$ in ZnSe is suffering the Jahn-Teller effect in the region of transition between the dynamic and static effect.