Forbidden Transitions in the Paramagnetic-Resonance Spectrum ofMn2+in Cubic MgO+

Abstract

The first order "forbidden" transitions, $M=\ensuremath{-}\frac{1}{2}\ensuremath{\rightarrow}+\frac{1}{2}$, $\ensuremath{\Delta}m=\ifmmode\pm\else\textpm\fi{}1$, in the paramagnetic-resonance spectrum of ${\mathrm{Mn}}^{2+}$ in cubic MgO have been studied both experimentally and theoretically. A powder sample was used which permitted the resolution of the "forbidden" transitions which would ordinarily have been obscured by the full fine-structure spectrum. The analysis was based on a spin Hamiltonian that included the cubic crystal field interaction with the $^{6}S_{\frac{5}{2}}$ state of ${\mathrm{Mn}}^{2+}$, magnetic hyperfine interaction with the ${\mathrm{Mn}}^{2+}$ nucleus, and electronic and nuclear Zeeman interactions. Satisfactory agreement between the calculated and observed spectrum was achieved by carrying the hyperfine-perturbation calculation to third order. It was unnecessary to include a trigonal crystal field interaction or a quadrupole interaction in order to satisfactorily explain the spacings of the "forbidden" transitions. On the other hand, the appropriate mixing of states that is required for observation of the forbidden transitions requires the presence of trigonal or lower symmetry crystal field terms. Analysis of the relative intensity of the forbidden to the allowed transitions permitted an estimate to be made of the trigonal crystal field constant $D$ on the basis of an assumed trigonal distortion to the cubic crystal field. By inserting this value of $D$ into the angular dependent terms in the Hamiltonian, an estimate of the expected linewidths was obtained which agreed well with experiment. The contributions of the estimated trigonal distortion to shifts in the spectrum were too small to be observed for those transitions that are resolved with a powder sample.