Anomalous crystal-field splittings of lanthanideS-states in metals

Compared are recent EPR, susceptibility, and neutron measurements of both $S$-state ($b_4^0$) and non-$S$-state ($A_4^0〈r^4〉$) lanthanide-ion crystal-field splittings in metals. The ratio of the $S$-state to the non-$S$-state fields $\mathcal{R}=\frac{b_4^0}{A_4^0〈r^4〉}$ in some metals is anomalously large and cannot be explained by the current insulator theory. We suggest that there must exist an extra "metallic" contribution to both $A_4^0〈r^4〉$ and the ratio $\mathcal{R}$. The non-$S$-state field $A_4^0〈r^4〉$ is divided into two: (i) all Coulombic and exchange contributions, and (ii) a covalent contribution similar to that found in insulators. We show that the latter term is more efficient in its contribution to the $S$-state field $b_4^0$. We suggest, in the anomalous metals, the $S$ state $b_4^0$ is dominated by covalent mixing but that for the non-$S$-state ions there is a partial cancellation between covalent and the coulomb-field contributions. Finally the implications for the ${\mathrm{Gd}}^{3+}$, $4f^7$ to $4f^8$ interconfigurational energy are explained.