Dynamical Jahn-Teller effects in the groundT1g4and the excitedT2g4orbital triplets ofCo2+ion in a MgO crystal

In the background of the failure of the simple crystal field theory to explain the spin-orbit splitting and the Zeeman effect of the ground (${}_{}{}^4{}_{}{}^{}T_{1g}^{}{}_{}{}^{}$) and the excited (${}_{}{}^4{}_{}{}^{}T_{2g}^{}{}_{}{}^{}$) levels of MgO:${\mathrm{Co}}^{2+}$, the dynamical Jahn-Teller effects—or, in other words, the vibronic interactions—are shown to explain consistently and satisfactorily all the experimental observables. The theory is worked out in the approximation of the cluster model. Because of the difference in the relative imporance of the Jahn-Teller energy ($E_{\mathrm{JT}}$) and the spin-orbit coupling strength for the two levels, a numerical solution of the problem is necessary for ${}_{}{}^4{}_{}{}^{}T_{1g}^{}{}_{}{}^{}$, and for ${}_{}{}^4{}_{}{}^{}T_{2g}^{}{}_{}{}^{}$ one can use Ham's theory directly. Besides showing the importance of the vibronic interactions, this analysis brings out two features: First, the effective frequency (${\omega }_E$) of the $E_g$ mode of vibration of the cluster interacting with the electron orbital is same for the ground and the excited states; second, the effect due to covalency is less important than assumed earlier. The analysis is extended to compare the results on KMg${\mathrm{F}}_3$:${\mathrm{Co}}^{2+}$. Conclusions that are arrived at regarding the values of ${\omega }_E$ and $E_{\mathrm{JT}}$ and covalency effects are physically justified for MgO as well as for KMg${\mathrm{F}}_3$.