Investigation of the crystal field in rare-earth doped scheelites

Abstract

8 2 for 2. 4 and 6, 8. The azimuthal angles are <1>1 + (i-I) (,r/2) and <1>2 + (i-5) ('11/2) for i=l-4 and 5-8 ligands.

Investigations of the EPR g Factors for Er3+ in CaMoO4

“…(iii) For simplicity, the D 2d approach instead of S 4 symmetry is adopted to describe the crystal-field interaction of (4) in this work. In fact, even though one takes the exact S 4 symmetry, the magnitudes of the imaginary parts of the rank-4 and rank-6 crystal-field parameters are very small, as shown in [21,32,33], and so their contributions to the coefficient C( 4 I 15/2 ;Γ γ (γ ) M J1 ) or C( 4 I 13/2 ;Γ γ (γ ) M J2 ) in Γ γ and the g factors are expected to be no more than 4%. (iv) Even in the approach of D 2d symmetry, the angular distortions for the polar angles θ j due to the size and charge mismatching substitution of Ca 2+ by Er 3+ are not considered in the calculations.…”

“…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-…”

“…So, they are also adopted for the Er 3+ center in this work, except that we takeĀ 4 (R 0 ) ≈ 50.2 cm −1 and A 6 (R 0 ) ≈ 21.1 cm −1 here for CaMoO 4 in consideration of the small difference between the structural data for CaMoO 4 and CaWO 4 [21]. The free-ion parameters of the Coulombic repulsion (F 2 ≈ 97504 cm −1 , F 4 ≈ 70746 cm −1 and F 6 ≈ 48042 cm −1 ), the twobody interaction parameters (α ≈ 20.95 cm −1 , β ≈ −689 cm −1 and γ ≈ 1839 cm −1 ) and the spin-orbit coupling coefficient (ζ 4f ≈ 2339 cm −1 ) in the energy matrix were obtained for Er 3+ -doped CaWO 4 [27].…”

Theoretical Investigations of the Electron Paramagnetic Resonance g Factors for the Trivalent Cerium Ion in LiYF4 Crystal

“…The Y 3+ ion is surrounded by eight nearest-neighbour F − ligands: four of them at a distance R 1 ≈ 2.246Å, and the other four at a slightly different distance (R 2 ≈ 2.293Å) [9,10]. The local symmetry of the Y 3+ site is S 4 .…”