The so-called "forbidden" hyperfine transitions of the $S$-state ion ${\mathrm{Mn}}^{++}$ with selection rules $\left|\Delta M\right|=1\mathrm{}$, $\Delta m=\pm 1$ have been observed in the cubic field of MgO. These transitions are shown to be observable in cubic fields because of the mixture of the zero-field splitting parameter $a$ with the off-diagonal hyperfine terms in the spin Hamiltonian which mixes neighboring hyperfine levels. Until now the intensities of these transitions had been calculated only in crystals of axial symmetry and were due to the mixing of levels with axial-field splitting $D$. The intensity for the cubic-field case is calculated and shows an interesting ${\left(\sin 4\mathrm{}\theta \right)}^2$ dependence, as compared with ${\left(\sin 2\mathrm{}\theta \right)}^2$ in the axial field case. The splittings of the "forbidden" doublets are calculated to third-order perturbation theory and both the intensities and the splittings agree well with the experimental data.

• Received 27 September 1963

DOI:https://doi.org/10.1103/PhysRev.133.A1099