Linear Electric Shifts in the Paramagnetic Resonance ofAl2O3: Cr and MgO: Cr

Abstract

It is shown that the spin Hamiltonian for ${\mathrm{Cr}}^{3+}$ ions in the ${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ lattice has to be augmented by a term $\Sigma i^{}\Sigma {j\le k}^{}\frac{1}{2}{R}_{\mathrm{ijk}}{E}_i(S_j{S}_k+S_k{S}_j)$ in the presence of an externally applied electric field E. The five independent components of the third rank $R$ tensor appropriate to the point symmetry $C_3$ of the ${\mathrm{Cr}}^{3+}$ sites have been determined experimentally. In units of Mc/sec per kV/cm the results for one site are $R_{111}=-0.020\mathrm{}$, $R_{222}=0.073\mathrm{}$, $R_{333}=0.179\mathrm{}$, $R_{123}=0.04\mathrm{}$, and $R_{113}=0.09\mathrm{}$. The ${\mathrm{Cr}}^{3+}$ site in the unit cell related by inversion symmetry has all signs reversed. The two other sites which are related to this pair by a reflection in the $y$ plane have the signs of $R_{222}$ and $R_{123}$ reversed. These results are related to the known crystal structure. Their agreement with a theoretical calculation based on a partially covalent bonding orbital in the Cr${\mathrm{O}}_6^{-9\mathrm{}}$ complex is satisfactory, whereas a point-charge model of the crystal field cannot account for the spin Hamiltonian. The electric field effect for the ${\mathrm{Cr}}^{3+}$ sites with an associated vacancy in the MgO lattice, was shown to be less than 1 Mc/sec for $E={10}^5$ V/cm, in agreement with the covalent theory. Verification of the Kramers degeneracy in the presence of the crystalline field components of odd parity resulted in setting an upper bound on the permanent electric dipole moment of the electron of 1.4×${10}^{-15\mathrm{}}$ cm times $e$.