Dynamic Jahn-Teller Effect forCr2+in MgO: Hypersonic Attenuation

Abstract

The acoustic attenuation due to scattering from ${\mathrm{Cr}}^{2+}$ substitutional impurities in MgO provides information on both the symmetry and energy of the states of the impurity system. Only acoustic modes which serve as a basis for an $E$ irreducible representation are observed to be resonantly scattered by the ${\mathrm{Cr}}^{2+}$ impurity system. Assuming the states of the impurity and its nearest neighbors can be approximated to first order by a molecular cluster, the acoustic modes with $E$ irreducible representation are the ones that excite the molecular-cluster vibrational mode which interacts with the electronic configuration and splits the degenerate ground state. The resonant scattering which leads to a relaxation maximum in the attenuation as a function of temperature, is interpreted as being due to indirect transitions. Energy-level separations, determined from the relaxation absorption, suggest a Jahn-Teller tunneling splitting of approximately 14 ${\mathrm{cm}}^{-1\mathrm{}}$ (1.75 meV). A detailed comparison of the experimental energy-level separations determined from the hypersonic relaxation exhibits substantial agreement with the calculated energy levels of Fletcher and Stevens and is consistent with the thermal-conductivity measurement of Challis et al. A uniaxial stress leads to a splitting of the relaxation peak and when fitted to the stain-dependent theoretical calculations, yields a Jahn-Teller coupling energy of 8.1 × ${10}^{13}$ ${\mathrm{cm}}^{-1\mathrm{}}$/m in approximate agreement with the point-ion approximation.