Electron-paramagnetic-resonance investigation of the dynamic Jahn-Teller effect for ${\mathrm{Sc}}^{2+}$ in Ba${\mathrm{F}}^2$, Sr${\mathrm{F}}^2$, and Ca${\mathrm{F}}^2$

The EPR spectrum of ${\mathrm{Sc}}^{2+}$ has been observed in single crystals of Ba${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ca${\mathrm{F}}_2$ at liquid-helium temperatures. At 1.2 K, the spectra were characterized by intense anisotropic hyperfine patterns with partially resolved ligand hyperfine structure. The anisotropy, line shapes, and temperature dependence of the anisotropic spectrum obtained for each host crystal were described within experimental error by second-order solutions of an effective Hamiltonian for an isolated vibronic ${}_{}{}^2{}_{}{}^{}E$ state which is split by large random internal strains. Coexisting with the anisotropic pattern was a weak nearly isotropic hyperfine pattern with "conventional" line shapes. No ligand hyperfine structure was resolved on this pattern. Intensity variations as a function of temperature imply that the nearly isotropic structure results from averaging by rapid vibronic relaxation of a portion of the anisotropic pattern. This interpretation is further strengthened by the observation of a small predicted anisotropy. Observed deviations of effective Hamiltonian parameters from the values predicted by crystal-field theory imply the existence of a weak-to-moderate vibronic interaction for these systems, i.e., a dynamic Jahn-Teller effect. For $d^1$-configuration ions in cubic symmetry, the effective Hamiltonian parameters are summarized and discussed.