Observation of a Quadrupole Interaction for Cubic Imperfections Exhibiting a Dynamic Jahn-Teller Effect

Observations of weak $\Delta M_I=\pm 1$ EPR transitions in several systems have established the existence of a quadrupole interaction for the ${}_{}{}^2{}_{}{}^{}E_g^{}{}_{}{}^{}$ ground vibronic state of cubic imperfections which exhibit a dynamic Jahn-Teller effect. The operator representing the quadrupole interaction, $\frac{1}{2}qQ\left\{\right[3\mathrm{}{I_z}^2-I(I+1\mathrm{})]{\mathcal{E}}_{\theta }+\sqrt{3}({I_x}^2-{I_y}^2\left){\mathcal{E}}_{\in }\right\}$, occurs as a natural consequence of the vibronic degeneracy. This operator, combined with an effective Hamiltonian representing the strain, Zeeman, and hyperfine interactions for an isolated ${}_{}{}^2{}_{}{}^{}E_g^{}{}_{}{}^{}$ state, describes within experimental error the positions and intensities of the "forbidden" $\Delta M_I=\pm 1$ EPR transitions observed for Sr${\mathrm{Cl}}_2$: ${\mathrm{La}}^{2+}$, Sr${\mathrm{Cl}}_2$: ${\mathrm{Sc}}^{2+}$, Ca${\mathrm{F}}_2$: ${\mathrm{Sc}}^{2+}$, Sr${\mathrm{F}}_2$: ${\mathrm{Sc}}^{2+}$, and Ba${\mathrm{F}}_2$: ${\mathrm{Sc}}^{2+}$. The signs and magnitudes of the quadrupole-coupling coefficients ($\mathrm{qQ}$) measured for each system are consistent with predictions of crystal field theory modified to account for a weak to moderate vibronic interaction.