Analysis of crystal-field effects on the energy levels of Mn4+ ions doped in different photoluminescent host lattices, exhibiting lowering of site symmetry: Exchange charge and superposition model calculations, for potential applications

Effects of distortions in ion-host systems on optical spectra, crystal-field and spin-Hamiltonian parameters of Cr3+ ions doped pyrochlores Y2Ti2O7 and Y2Sn2O7: exchange charge model and superposition model calculations

“…To resolve this dilemma, we have employed the 3DD package 64 for standardization of triclinic CFP sets predicted in ref. 18. The 3DD package 64 enables expressing any triclinic CFP sets in the same unique axis system, The method is based on the diagonalization of triclinic CFP sets in a principal axis system, which is rotated by the Euler angles ( α , β , γ ) w.r.t.…”

“…, ref. 7, 8, 17, 18, 31, 33, 35 and references therein. For the sake of clarity, here we provide only a brief outline of key notions and notations.…”

“…Our matched value of B (see, Table 4) is smaller than the above octahedral value due to lower site symmetry of the Cr 3+ ion than the octahedral. 10,18 The variation of the two B values and that of the nephelauxetic ratio, β 1 , with x are shown in Fig. 1.…”

“…The reliability and validity of these theoretical methods are confirmed by their demonstrated success in calculating the CFPs and SHPs as well as energy levels of the transition metal and rare-earth ions in different host lattices; see, e.g., ref. 7,8,17,18,31,33,35 and references therein. For the sake of clarity, here we provide only a brief outline of key notions and notations.…”

“…Thus, the combined effects of low symmetry crystalfield (CF) and the magnetic interactions partly remove the spin degeneracy and split the 4 A 2g ground state into two Kramers spin doublets (see, for example, Fig. 1 18 ) with the effective electron spin quantum numbers, M s = AE1/2 and M s = AE3/2. This splitting is parametrized by the effective spin-Hamiltonian parameters (SHPs), i.e., for axial site symmetry: the g-factors (g 8 , g > ) and the zero-field splitting (ZFS) parameter (ZFSP), D, of the 4 A 2g state.…”