Phonon-Induced Corrections to the Ground-State Splitting ofS-State Ions in Cubic Crystals

The ground ${}_{}{}^6{}_{}{}^{}S$ and excited ${}_{}{}^4{}_{}{}^{}L$ states of the ${\mathrm{Mn}}^{2+}$ ion are perturbed by the cubic crystalline field and mixed by the spin-orbit coupling. A two-phonon Raman process, second order in the orbit-lattice interaction, is found to contribute to the ground-state splitting. The theory is developed within the framework of Van Vleck's small-wave-vector averaging procedure for acoustic phonons. Both the zero-point vibrational contribution and the temperature-dependent parts are calculated and compared with experimental measurements in ${\mathrm{Mn}}^{2+}$-doped MgO. Good qualitative agreement between the theory and experiment is found but quantitative agreement is not obtained.