Determination of charge-compensated C_3v (II) centers for Er ³⁺ ions in CdF₂ and CaF₂ crystals

A unified theoretical method is established to determine the charge-compensated C_3v (II) centers of Er³⁺ ions in CdF₂ and CaF₂ crystals by simulating the electron paramagnetic resonance (EPR) parameters and Stark energy levels. The potential (Er³⁺-F^--\mathrmO_\mathrm4^\mathrm2-) and (Er³⁺-\mathrmF_\mathrm7^\mathrm--O^2-) structures for the C_3v (II) centers of Er³⁺ ions in CdF₂ and CaF₂ crystals are checked by diagonalizing 364×364 complete energy matrices in the scheme of superposition model. Our studies indicate that the C_3v (II) centers of Er³⁺ ions in CdF₂ and CaF₂ may be ascribed to the local (Er³⁺-F^--\mathrmO_\mathrm4^\mathrm2-) structure, where the upper ligand ion F^- undergoes an off-center displacement by ∆ Z≈ 0.3 Å for CdF₂ and ∆ Z≈ 0.29 Å for the CaF₂ along the C₃ axis. Meanwhile, a local compressed distortion of the (ErFO₄)^6- cluster is expected to be ∆ R≈ 0.07 Å for CdF₂:Er³⁺ and ∆ R≈ 0.079 Å for CaF₂:Er³⁺. The considerable g-factor anisotropy for Er³⁺ ions in each of both crystals is explained reasonably by the obtained local parameters. Furthermore, our studies show that a stronger covalent effect exists in the C_3v (II) center for Er³⁺ in CaF₂ or CaF₂, which may be due to the stronger electrostatic interaction and closer distance between the central Er³⁺ ion and ligand O^2- with the (Er³⁺-F^--\mathrmO_\mathrm4^\mathrm2-) structure.