Dynamic, intermediate, and static Jahn-Teller effect in the EPR spectra ofE2orbital states

The intermediate Jahn-Teller effect which was observed for the specific systems CaO: ${\mathrm{Ag}}^{2+}$, MgO: ${\mathrm{Ag}}^{2+}$, CaO: ${\mathrm{Cu}}^{2+}$, and Ca${\mathrm{F}}_2$: ${\mathrm{Eu}}^{2+}$ has been successfully described previously by means of a vibronic coupling model in which the properties of the ground ${}_{}{}^2{}_{}{}^{}E$ vibronic state were modified by random-strain coupling to an excited vibronic singlet level. The present work examines, in general, the question of how coupling via random strain between a ${}_{}{}^2{}_{}{}^{}E$ vibronic level and an excited $A_1$ or $A_2$ vibronic singlet can result in the transition from the dynamic Jahn-Teller effect to the intermediate effect and finally to the limiting case of the static Jahn-Teller effect. The intermediate Jahn-Teller region is particularly important since it is possible in such cases to determine the ratio of the random-strain splitting $\overline{\delta }$ to the "tunneling" splitting $3\Gamma$ by EPR techniques. A similar determination using EPR cannot be made for systems characterized by either the limiting dynamic or static Jahn-Teller effect. The intermediate Jahn-Teller effect results in significant modifications to the EPR spectra which are characteristic of either the pure dynamic or pure static cases. These modifications include (i) changes in the angular variation, (ii) selective broadening of certain portions of the spectrum, and (iii) formation of complex line shapes for the orientation $\overrightarrow{\mathrm{H}}\parallel 〈111〉$. A systematic calculation of the EPR line shapes and angular dependences has been performed for a range of values of $\frac{\overline{\delta }}{3\Gamma }$ which spans the intermediate Jahn-Teller region, and these features, which are tabulated graphically, illustrate the various types of intermediate Jahn-Teller spectra that may be observed experimentally. Additionally, a number of characteristic features of the isotropic spectrum resulting from thermal population of the first excited vibronic singlet level have been determined for the first time, and these results affect the validity of some of the criteria previously used to distinguish the possible origins of this spectrum.