Systematization of crystal field parameters for trivalent rare-earth (RE3+) ions at orthorhombic sites in selected laser materials—standardization approach

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

“…The second important point, systematic behavior of fitted CFPs for Yb 3+ ion in different garnets, is closely related to their reliability and can be conveniently performed by the standardization procedures that were developed and utilized by Rudowicz and coworkers (see more details in the literature [53][54][55][56][57]). According to this idea, we find that all the obtained CFPs in Eqs.…”

Tools for magnetostructural correlations for the 3d8(3A2 state) ions at orthorhombic sites: Comparative study with applications to Ni2+ ions in Y2BaNiO5 and Nd2BaNiO5

“…It turns out that that the transformation of the axis systems that yields Eq. (4) is equivalent to one of the six standardization transformations denoted S1 to S6 utilized in the orthorhombic standardization [42,43]. Importantly, the orthorhombic standardization yields six alternative orthorhombic ZFSP sets for all ranks (k ¼2, 4, 6) for transition ions, which are physically equivalent yet numerically different.…”

“…Importantly, the orthorhombic standardization yields six alternative orthorhombic ZFSP sets for all ranks (k ¼2, 4, 6) for transition ions, which are physically equivalent yet numerically different. The transformations Si enable orthorhombic standardization of H ZFS (as well as H CF ) according to the orthorhombicity ratio [42,43]:…”

“…with λ 0 , λ, or κ out of the standard range, may be transformed into its alternative standard image [39]. Importantly, the six parameter sets (S1-S6) are intrinsically incompatible [42,43] and direct comparisons are valid only for the sets expressed in the same range.…”

“…The idea of the limit of λ¼E/D has originally been introduced in EMR area based on experimental observations and has lead to two conventions [42,43]. The standard range 0 rλ r1/3 corresponds in terms of the conventional ZFS D tensor (S.D.S) to |D XX | r|D YY | r|…”