Acoustic Paramagnetic Resonance Spectrum ofCr2+in MgO

The theory of acoustic paramagnetic resonance (APR) for the ${\mathrm{Cr}}^{2+}\left(3\mathrm{}{d}^4\right)$ ion at cubic crystal sites with octahedral coordination is developed for comparison with data by Marshall and Rampton for ${\mathrm{Cr}}^{2+}$ in MgO. An analytic model that takes explicit account of random strain is obtained and shown to predict in a simple way both the angular dependence of the resonance lines and the asymmetric line shape found experimentally. Although most ${\mathrm{Cr}}^{2+}$ ions experience distortions of effectively orthorhombic symmetry, the apparent presence of a tetragonal distortion at the site of the relatively few acoustically active ions is shown to result from the conditions of the experiments, in which the random strain splitting of the ${\mathrm{Cr}}^{2+}$ levels is typically larger than the acoustic energy quantum. Using this model, we show that the data for ${\mathrm{Cr}}^{2+}$ in MgO may be accounted for quantitatively if the ${\mathrm{Cr}}^{2+}$ is subject to a dynamic Jahn-Teller effect for which the tunneling splitting $3\Gamma$ is large compared with the spin-orbit splitting of the ${}_{}{}^5{}_{}{}^{}E$ state. This interpretation differs from one proposed previously by Fletcher and Stevens, in which a much smaller value for $3\Gamma$ was obtained. It is shown that from presently available data one cannot yet determine $3\Gamma$ or other Jahn-Teller parameters of the system with any certainty. The theory of a dynamic Jahn-Teller effect for a ${}_{}{}^5{}_{}{}^{}E$ state is developed in a general way to encompass the regime of weak Jahn-Teller coupling, which would be applicable to APR experiments on ${\mathrm{Fe}}^{2+}$ in tetrahedral coordination, while also including the limit of strong coupling in which the adiabatic approximation used by Fletcher and Stevens is applicable.