Paramagnetic Resonance Spectrum of Trivalent Gadolinium in the Cubic Field of Calcium Fluoride

The paramagnetic resonance spectrum of ${\mathrm{Gd}}^{3+}$ in Ca${\mathrm{F}}_2$ has been analyzed at 3 cm wavelength at room and liquid helium temperatures. The spectrum shows that the cubic symmetry is essentially preserved around the gadolinium ion. The fourth-order and sixth-order cubic field splitting parameter have been evaluated as $c=+0.0185\mathrm{}\pm 0.0005$ and $d=-0.0004\mathrm{}\pm 0.0002$ ${\mathrm{cm}}^{-1\mathrm{}}$, where the total ground-state splitting is $8c-2d$. The $g$ factor is $g=1.991\mathrm{}\pm 0.002$. Various mechanisms causing the ground-state splitting of an $S$ state in a cubic field are discussed. The preservation of cubic symmetry and the absence of association with vacancies or interstitial ions can be explained by a stabilization of the complex by the spherical charge distribution of the $S$ ion and an effective strong crystalline field.