Dynamic Jahn-Teller effect forCr2+in MgO: Acoustic paramagnetic resonance

An empirical evaluation of the parameters defining the dynamic Jahn-Teller effect for ${\mathrm{Cr}}^{2+}$ in MgO is made using the temperature dependence of the acoustic-paramagnetic-resonance (APR) spectra. The molecular-cluster model for the tightly bound ${\mathrm{Cr}}^{2+}$ and its nearest neighbours is applied to the experimental results to determine the tunneling splitting and spin-orbit splitting. The magnitude of the tunneling splitting ($\delta \sim 19$ ${\mathrm{cm}}^{-1\mathrm{}}$) and spin-orbit splitting ($D\sim 2.3$ ${\mathrm{cm}}^{-1\mathrm{}}$) indicates the ${\mathrm{Cr}}^{2+}$ impurity is in a more extreme dynamic limit of the Jahn-Teller effect than previously assumed ($\frac{\delta }{D}\sim 8$). The gyromagnetic ratio for the paramagnetic triplet levels of ${\mathrm{Cr}}^{2+}$ ions exhibits a significant anisotropy resulting from local distortions of the cubic site due to internal strains. The anisotropy depends on the acoustic mode used to observe the spectra. For longitudinal waves the observed anisotropy of the $g$ factor can be explained as due to induced transitions in ions in a primarily tetragonal environment. The magnitude of the internal strain is found to be approximately ${10}^{-5\mathrm{}}$. Only doublet transitions are observed for the triplet even though the strain splitting (singlet-doublet) is found to be approximately 0.2 ${\mathrm{cm}}^{-1\mathrm{}}$ which would allow $\Delta m=1\mathrm{}$ transitions for the acoustic frequencies used in this investigation. The slow transverse mode couples more strongly to the chromous ion and exhibits an APR spectrum which is more complex than the longitudinal wave under similar conditions. The anisotropy of the $g$ factor is due to the same sets of ions as the longitudinal mode but the magnitude of the APR peaks depends on the direction of the magnetic field in the crystal.