Dynamical Jahn-Teller Effects for aV3+Ion in a MgO Crystal

A theory of the acoustic paramagnetic resonance APR for ${\mathrm{V}}^{3+}$ ions in MgO is developed to explain the results of Brabin-Smith and Rampton which shows the importance of the second-order spin-orbit interaction resulting from Jahn-Teller interactions, i.e., from the excited vibronic levels. Essentially, it is this interaction which is responsible for lifting the degeneracy of the spin-orbit ground states $E_g+T_{2g}$ of the ${\mathrm{V}}^{3+}$ ions in the cubic state. Straightforward APR experiments give the $g$ value within the excited triplet $T_{2g}$ and the magnitude of the zero-field separation ($D$) between the $T_{2g}$ and $E_g$ levels is deduced from the study of the dependence of the APR spectra on temperature. The magnitudes of the Jahn-Teller energy $E_{\mathrm{J}\mathrm{T}}$ and the frequency ${\omega }_E$ of the $E_g$ mode of vibration of the molecular cluster formed around a ${\mathrm{V}}^{3+}$ ion, which give the best fit with the experimentally observed parameters $g$ and $D$, are in good agreement with the estimate of $E_{\mathrm{J}\mathrm{T}}$ in an effective point-charge model and with the results on phonon sidebands in MgO crystals doped with different paramagnetic impurities, respectively. The strongly asymmetric nature of the line shape is explained by taking into account the presence of small random strain fields of tetragonal and orthorhombic nature about the cubic site. The experimentally determined hyperfine parameter $A$ is fitted in this theory, assuming the magnitude of the contact term $k$ to be 0.2.