The complete crystal-field spin-orbit interaction matrices of point group ${\mathit{C}}_{3\mathit{v}}$ for the ${\mathit{d}}^5$ configuration have been derived. It is shown by investigating the EPR parameter that the impurity ion ${\mathrm{Mn}}^{2+}$ replaces the ${\mathrm{Li}}^{+}$ ion in ${\mathrm{LiNbO}}_3$. The argument is presented that both the spin-orbit-coupling mechanism and the superposition model are good approaches to accurate calculations.

• Received 17 January 1990

DOI:https://doi.org/10.1103/PhysRevB.43.11374