Electric-Field-InducedgShifts for Loose Yb Ions in Three Scheelite Lattices

Theoretical studies of the spin‐Hamiltonian parameters for Er3+ in CaWO4 and SrWO4

“…2, charge compensation ions may be far enough from the impurity centers and so influence on the local symmetry should be negligible [13]. As regards the second case, Kiel et al found that impurity ions (e.g., divalent or trivalent 3d n ions) smaller than 0.8 Å would be unstable at the Ba 2+ site in scheelite BaWO 4 (where r Ba2+ ≈ 1.34 Å [27]) and then take an off-center displacement away from the ideal cation site, based on the Born-Mayer theory of ionic bonding [18]. Thus, for the studied tetragonal center in CaWO 4 (or SrWO 4 ), the impurity Er 3+ (r i ≈ 0.881 Å [27] ) is not sufficiently small to be unstable at the regular Ca 2+ (or Sr…”

“…(2)- (5), the basis function Γγ (or γ ′, where γ and γ ′ denote the two components of the Γ irreducible repre- ) site occupied by the impurity Er 3+ has S 4 local symmetry. However, D 2d symmetry is proved to be a good approximation due to the rather small distortion from D 2d to S 4 [18], as treated for trivalent rare-earth ions in similar scheelite-type LiYF 4 by many authors [19][20][21]. So we still take D 2d approximation here for simplicity.…”

Investigations of the EPR g Factors for Er3+ in CaMoO4

“…On the one hand, charge compensation ions may be far enough from the impurity center and then influence on the local symmetry may be negligible [13]. On the other hand, Kiel and Mims [20] found that impurity ions (e. g., divalent or trivalent 3d n ions) smaller than 0.8Å would be unstable at the Ba 2+ (with the ionic radius of about 1.34Å [29]) site in scheelite-type BaWO 4 and then are off-center displaced away from the ideal cation site, based on the Born-Mayer theory of ionic bonding. However, for the studied tetragonal center in CaMoO 4 , the impurity Er 3+ (with the ionic radius of about 0.881Å [29]) is not sufficiently small to be unstable at the host Ca 2+ site.…”

“…However, the D 2d symmetry is proved to be a good approach due to the rather small distortion from D 2d to S 4 [20,21], as treated for some trivalent rare earth ions in similar scheelite-type LiYF 4 by many authors [22,23]. So we still take the D 2d approximation here for simplicity.…”

“…t k andĀ(R 0 ) are, respectively, the power-law exponents and the intrinsic parameters (with the reference distance R 0 ). The Ca 2+ ion in CaMoO 4 is coordinated to eight nearest O 2− ions, with four of them at the distance R 1 and angles θ 1 and φ 1 , and the other four at the different distance R 2 and angles θ 2 and φ 2 , where θ j and φ j ( j = 1, 2) are, respectively, the polar angles and the azimuthal angles of the metal-ligand distances R j related to the Z (or fourfold) and X axes of the crystal [20,21] [21]. According to [21,26], the power-law exponents t 2 ≈ 3.5, t 4 ≈ t 6 ≈ 6 and the intrinsic pa-…”