Dynamic Jahn-Teller Interaction Withγ5phonons in the Ground State Ofcu2+

Optical absorption and emission measurements of ${\mathrm{Cu}}^{2+}$ as a substitutional impurity in cubic ZnS and ZnTe are analyzed by means of an electron-phonon coupling model. The ${}^{2}D$ term of ${\mathrm{Cu}}^{2+}$ is split by a crystal field of tetrahedral symmetry into a ${}^{2}{\ensuremath{\Gamma}}_{5}$ orbital triplet and a ${}^{2}{\ensuremath{\Gamma}}_{3}$ orbital doublet. Optical transitions have been observed between these two multiplets in $\mathrm{ZnS}:{\mathrm{Cu}}^{2+}$ and within the ${}^{2}{\ensuremath{\Gamma}}_{5}$ ground state in $\mathrm{ZnTe}:{\mathrm{Cu}}^{2+}$. The theoretical model is based on crystal-field theory and includes the spin-orbit interaction and a dynamic Jahn-Teller interaction between the electronic ${}^{2}{\ensuremath{\Gamma}}_{5}$ states and a transverse acoustic phonon of ${\ensuremath{\Gamma}}_{5}$ symmetry. Starting from the ten spin-orbit wave functions appropriate to the orbital triplet and doublet manifolds, the symmetry-adapted vibronic basis is constructed and used to diagonalize the Hamiltonian matrix. Phonon overtones up to $n=14$ are included to ensure convergence of the energy eigenvalues. The measured positions and relative intensities of the spectral lines are described with good accuracy by the theoretical model, including covalency effects. In ZnS, comparison between theory and experiment yields the following values of the physical parameters: the crystal-field splitting $\ensuremath{\Delta}=5990.6$ ${\mathrm{cm}}^{\ensuremath{-}1}$, the spin-orbit coupling constants ${\ensuremath{\lambda}}_{1}=\ensuremath{-}667$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and ${\ensuremath{\lambda}}_{2}=\ensuremath{-}830$ ${\mathrm{cm}}^{\ensuremath{-}1}$, the phonon energy $\ensuremath{\Elzxh}\ensuremath{\omega}=73.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and the Jahn-Teller stabilization energy ${E}_{\mathrm{JT}}=474.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The corresponding parameters in ZnTe are $\ensuremath{\Delta}=6000$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\lambda}}_{1}=\ensuremath{-}888$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${\ensuremath{\lambda}}_{2}=\ensuremath{-}830$ ${\mathrm{cm}}^{\ensuremath{-}1}$, $\ensuremath{\Elzxh}\ensuremath{\omega}=38.8$ ${\mathrm{cm}}^{\ensuremath{-}1}$, and ${E}_{\mathrm{JT}}=468.5$ ${\mathrm{cm}}^{\ensuremath{-}1}$.