Crystal field parameters for Yb3+ ions at orthorhombic centers in garnets—Revisited

Crystal-field study for the orthorhombic Yb3+ centers in Ca3Sc2Ge3O12 and Lu3Ga5O12 garnets

“…(1), the concrete form of H CF depends on the local site symmetry of central 4f n ion and the chosen axis system (AS) [31,32]. In this study, the conventional form of H CF for Yb 3+ ion located at crystal field with D 2 symmetry in CaSGG and LuGG garnets can be written, in the Wybourne notation [33], as [34] HCF…”

“…However, a concrete AS should be defined first. For CaSGG garnet, a Cartesian AS adapted for D 2 site symmetry, also adopted by other SPM studies for different garnets [34,26,19], is established and shown in Fig. 1 Table 1, can be conveniently calculated by the unit cell parameters and atomic fractional coordinates given in [16].…”

“…The SPM can reduce the free variables in fitting procedures by correlating the CFPs of the central Yb 3+ ion with its local structure. Then, the general SPM expressions for CFPs B kq can be written as [34] …”

“…in which B k ðR 0 Þ (k = 2, 4, 6) with reference distance R 0 (%0.24 nm [34]) are expressed in the Wybourne notation, whereas the coordination factors K q k ðh i ; / i Þ are expressed in the extended Stevens notation [35,36]. a k,q (q P 0) are the conversion factors [29] which give a consistent transition between the Stevens and Wybourne notations and t k are the power-law exponents.…”

“…(i) If three intrinsic CFPs B k ðR 0 Þ (k = 2, 4, 6) and spin-orbit coupling parameter f are treated as adjustable parameters and t 2 (%5), t 4 (%6) and t 6 (%10) [41,34] are taken for [YbO 8 ] 13À cluster, thus N À P is equal to two and the best results obtained by matching the calculated optical spectra to the experimental ones are given as…”