Structural relaxation effects on the lowest $4f{-}5d$ transition of $\hbox {Ce}^{3+}$ in garnets

Abstract

The role of structural relaxations on the energy of the lowest $4f{-}5d$ transition of $\hbox {Ce}^{3+}$ in garnets is studied by means of ab initio calculations. This study completes previous studies on the roles of the interactions of the Cerium impurity with its first neighbors and with the rest of the solid hosts, before the relaxations take place. Periodic boundary conditions density functional theory calculations (DFT) and second-order perturbation theory spin–orbit coupling embedded-cluster wave function theory calculations (WFT) have been performed in the garnets $\hbox {Y}_{3}\hbox {Al}_{5}\hbox {O}_{12}$, $\hbox {Lu}_{3}\hbox {Al}_{5}\hbox {O}_{12}$, $\hbox {Y}_{3}\hbox {Ga}_{5}\hbox {O}_{12}$, $\hbox {Lu}_{3}\hbox {Ga}_{5}\hbox {O}_{12}$, and $\hbox {Ca}_{3}\hbox {Sc}_{2}\hbox {Si}_{3}\hbox {O}_{12}$ doped with $\hbox {Ce}^{3+}$. The local relaxation effects on the $4f{-}5d$ transition are similar in the WFT and DFT calculations. They produce a blue shift in Al and Ga garnets in which Ce substitutes for smaller Y and Lu cations, which is found to be basically due to the local expansions around the impurity, with only minor contributions from angular relaxations. Atomic relaxations of more distant neighbors enhance the blue shift. Although the embedding effects of the undistorted garnets are known to make the differences between the $4f{-}5d$ transition in Al and Ga garnets, we find that the structural relaxations are responsible for the small differences between the $4f{-}5d$ transition in $\hbox {Y}_{3}\hbox {Al}_{5}\hbox {O}_{12}$:$\hbox {Ce}^{3+}$ and $\hbox {Lu}_{3}\hbox {Al}_{5}\hbox {O}_{12}$:$\hbox {Ce}^{3+}$, and in $\hbox {Y}_{3}\hbox {Ga}_{5}\hbox {O}_{12}$:$\hbox {Ce}^{3+}$ and $\hbox {Lu}_{3}\hbox {Ga}_{5}\hbox{O}_{12}$:$\hbox {Ce}^{3+}$.