The angular dependence of stress-induced shifts of the gyromagnetic factor $g$ of the ${\Gamma }_7$ doublets of ${\mathrm{Yb}}^{3+}$ and ${\mathrm{Dy}}^{3+}$ in Ca${\mathrm{F}}_2$ and ${\mathrm{Er}}^{3+}$ in Ce${\mathrm{O}}_2$ and Th${\mathrm{O}}_2$ have been measured in electron-paramagnetic-resonance experiments. The observed variation of the angular dependence of the $g$ shifts is explained in terms of a phenomenological spin-lattice Hamiltonian. A microscopic theory is used to obtain a quantitative evaluation of the observed shifts using a point-charge model for the induced crystalline field. The results indicate that covalent effects and the shielding of the electric field at the impurity site are important.

• Received 12 July 1973

DOI:https://doi.org/10.1103/PhysRevB.9.4888