Zero-field splitting of the $4f^7$ state: A systematic investigation of ${\mathrm{Gd}}^{3+}$-$M^{+}$ complexes in Ca${\mathrm{F}}_2$

In this paper we present an analysis of the results of various experiments [electron paramagnetic resonance (EPR), electric field effect (EFE) in EPR, and electron-nuclear double resonance (ENDOR)] on orthorhomic ${\mathrm{Gd}}^{3+}$-$M^{+}$ complexes in Ca${\mathrm{F}}_2$. From the detailed and systematic study of the series of complexes ($M^{+}=\mathrm{L}\mathrm{i},\mathrm{N}\mathrm{a},\mathrm{K},\mathrm{R}\mathrm{b},\mathrm{a}\mathrm{n}\mathrm{d}\mathrm{C}\mathrm{s}$), we obtain a consistent picture of the mechanisms giving rise to the zero-field splitting of ${\mathrm{Gd}}^{3+}$ in ionic materials, a problem that has puzzled scientists for a number of years. It appears that the zero-field splittings for the systems investigated can be explained in terms of a self-consistent polarizable-point-charge model using coupling mechanisms published in the literature. This conclusion is in contrast with those drawn by several authors in the literature and leads to a reconsideration of the merits of the polarizable-point-charge model.