Angular Dependence of the Intensities of "Forbidden" Transitions ofMn2+in MgO

There have been numerous studies of the positions and intensities of $\Delta M=\pm 1$, $\Delta m=\pm 1$ ESR lines of the divalent manganese ion in a variety of hosts. However, in determining expressions governing the line intensities, it has been assumed that the microwave field ${\mathbf{H}}_1$ is perpendicular to the static field ${\mathbf{H}}_0$. Depending upon the cavity mode and the placement of the sample within a microwave cavity, one may have significant ${\mathbf{H}}_1$ components parallel to ${\mathbf{H}}_0$. This paper gives expressions for the intensities of the $\Delta M=\pm 1$, $\Delta m=\pm 1$ lines of ${\mathrm{Mn}}^{2+}$ in MgO (octahedral symmetry) as a function of orientation of the field ${\mathbf{H}}_0$ relative to crystal axes and ${\mathbf{H}}_1$. The predicted ratio of intensities of the $(\frac{1}{2},m)\leftrightarrow (-\frac{1}{2},m-1)$ and the $(\frac{1}{2},m-1)\leftrightarrow (-\frac{1}{2},m)$ lines is $\frac{{(0.87\mathrm{}cos\alpha -sin4\theta sin\alpha )}^2}{{\left(sin4\theta sin\alpha \right)}^2}$. This prediction is found to be in accord with experiment. In most of the hosts previously studied, the ${\mathrm{Mn}}^{2+}$ ion experiences a significant axial electric field component; for these the intensities of the $\Delta m\pm 1$ lines would be nearly identical.