Unveiling the Local Structure of Cu²⁺ Ions from d-Orbital Splitting. Application to K₂ZnF₄:Cu²⁺ and KZnF₃:Cu²

This work investigates why Jahn-Teller (JT) transition-metal ions like Cu²⁺ (d⁹) or Mn³⁺ (d⁴) with octahedral coordination exhibit low-symmetry distortions of the CuF₆^4- (or MnF₆^3-) octahedron, when Cu²⁺ replaces Zn²⁺ either in the cubic perovskite KZnF₃ or in the layer perovskite K₂ZnF₄. The aim is to establish correlations between the splitting Δ_e of the parent O_h e_g(x² - y², 3z² - r²) d orbitals and the low-symmetry local distortion ρ, allowing us to unravel the local structure of Cu²⁺ introduced as an impurity into such perovskites. However, the question of whether tetragonal a_1g - b_1g splitting Δ_e of Cu²⁺ is proportional to ρ or Δ_e contains additional contributions from the rest of the lattice (crystal anisotropy) is controversial. Here we show that Δ_e depends linearly on ρ. High-pressure experiments and compound series involving JT ions give support for the proposed scenario and provide correlations relating ρ and Δ_e in Cu²⁺ and Mn³⁺ systems, from which the electron-vibration coupling for the E⊗e JT effect is obtained experimentally.