Determination of charge-compensated C _3υ (II) centers for Er³⁺ ions in CdF₂ and CaF₂ crystals*

Abstract

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−– O 4 2 − ) and (Er3+– F 7 − –O2–) 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−– O 4 2 − ) structure, where the upper ligand ion F− undergoes an off-center displacement by ΔZ ≈ 0.3 Å for CdF2 and ΔZ ≈ 0.29 Å for the CaF2 along the C 3 axis. Meanwhile, a local compressed distortion of the ( ErFO 4 ) 6 − cluster is expected to be ΔR ≈ 0.07 Å for CdF2:Er3+ and ΔR ≈ 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 O2– with the (Er3+–F−– O 4 2 − ) structure.