Theoretical Studies of the EPR Parameters and the Off‐Center Displacement of Cu ²⁺ Ion in Pb ₅ Ge ₃ O ₁₁ Crystal

The off‐center displacement of the Cu 2+ ion in Pb 5 Ge 3 O 11 (PGO) crystal is theoretically investigated by analyzing the electron paramagnetic resonance (EPR) parameters, g ‐factors g i ( i = x , y , z ), and hyperfine structure constants A i based on the high‐order perturbation formulas of 3d 9 ions in orthorhombically elongated octahedral crystal‐fields. The doped Cu 2+ was assumed to substitute the host Pb(8) site in the PGO lattice, with a different local environment from the original Pb 2+ due to the Jahn–Teller (JT) effect. Based on the calculation, the off‐center displacement Δz of impurity Cu 2+ is about 0.19 Å, and the planar Cu 2+ ‐O 2− bonds are found to experience the relative bond length variation δ R (≈0.013 Å) along the x and y axes. The theoretical EPR parameters based on the above local structure parameters show good agreement with the experimental values.