Effect of Applied Electric Fields on the Ground State of $3d^3$, $3d^5$, and $3d^8$ Ions in $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$

The effect of applied electric fields on the ground states of $3d^3$, $3d^5$, and $3d^8$ ions in $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3$ has been studied. With the applied field E along the $c$ axis, the results can be explained by allowing the spin-Hamiltonian parameter $D$ (and $a-F$ for ${\mathrm{Fe}}^{3+}$) to be a linear function of $E$. For an applied field of ${10}^6$ V/cm, the relative change in $D$ is of the order of 5% for a typical ion of these series. It seems likely, therefore, that the odd crystal-field components may make a significant contribution to $D$ for a number of these ions. A naive crystal-field model is unable to explain the variation in $\frac{\partial D}{\partial E}$ observed for the $3d^3$ and $3d^8$ ions, but these variations appear well correlated with the corresponding $g-g_{\mathrm{free}}$ values. The correlation between the microwave and previously observed optical electric field effects is found to be quite poor, thus illustrating the complex nature of the ground-state effects.