Linear Electric Field Effects in Paramagnetic Resonance for ${\mathrm{Ce}}^{3+}$-${\mathrm{F}}^{-}$ Tetragonal Sites in Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, Ba${\mathrm{F}}_2$

We have measured the electric-field-induced $g$ shifts for tetragonal ${\mathrm{Ce}}^{3+}$ sites in Ca${\mathrm{F}}_2$, Sr${\mathrm{F}}_2$, and Ba${\mathrm{F}}_2$. These systems were chosen because they afford one of the simplest types of site in which odd-field effects can be studied. The ${\mathrm{Ce}}^{3+}$ ion substitutes at a ${\mathrm{Ca}}^{2+}$ (or ${\mathrm{Sr}}^{2+}$, ${\mathrm{Ba}}^{2+}$) lattice site. The odd field is essentially due to a charge-compensating ${\mathrm{F}}^{-}$ interstitial ion lying along one of the $〈100〉$ cubic axes. The magnitude of the electric effect has been calculated by taking into account both the odd and even harmonics in the new crystal-field potentials which are induced at the ${\mathrm{Ce}}^{3+}$ site when an electric field is applied to the sample. The basic crystal-field calculations have been made by means of a point-charge point-dipole model. The values obtained in this way are too large, but can be brought into better agreement with the experimental values by allowing for screening effects and for distortions in the lattice caused by the interstitial ${\mathrm{F}}^{-}$ ion. An attempt has been made to interpret the changes in $g$ shifts observed through the series of host lattices.