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

Abstract

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 $c=+0.0185\ifmmode\pm\else\textpm\fi{}0.0005$ and $d=\ensuremath{-}0.0004\ifmmode\pm\else\textpm\fi{}0.0002$ ${\mathrm{cm}}^{\ensuremath{-}1}$, where the total ground-state splitting is $8c\ensuremath{-}2d$. The $g$ factor is $g=1.991\ifmmode\pm\else\textpm\fi{}0.002$. 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.