Large splittings of the 4f shell of Ce3+ in garnets

Abstract

Ab initio embedded cluster calculations on Ce³⁺-doped Y₃Al₅O₁₂, Lu₃Al₅O₁₂, Gd₃Al₅O₁₂, Y₃Ga₅O₁₂, Lu₃Ga₅O₁₂, and Gd₃Ga₅O₁₂, which do not make use of any adjustable parameter, support recent assignments of the seventh 4f level of Ce³⁺ in garnets [Przybylińska et al., Appl. Phys. Lett., 2013, 102, 241112] and that the splitting of the 4f shell of Ce³⁺ in these materials is slightly smaller than 4000 cm⁻¹ and much larger than the 2000–2500 cm⁻¹ commonly assumed in analyses of 5d → 4f emission bands. Why this wrong assumption has been working well so far is explained by the fact that the intensity of the emission to the seventh level of the 4f¹ configuration is found to be only one hundredth of the integrated intensity of the emissions to the other six levels, which group themselves into two sets of three individual levels separated by 2000–2500 cm⁻¹. The effective field splitting and the spin–orbit coupling splitting are found to be of the same size. From a strong field coupling point of view, the first six levels result from the interactions between ²T_2u and ²T_1u cubic levels and the higher, isolated seventh level comes directly from the cubic ²A_2u. From a weak field coupling point of view, the first three levels result from the splitting of ²F_5/2, the second three levels from the splitting of ²F_7/2 and the seventh level from a strong, cubic field driven interaction between ²F_7/2 and ²F_5/2 components [Herrmann et al., J. Appl. Phys., 1966, 37, 1312].