Jahn–Teller impurities in tetragonal lattices: Why is the ligand octahedron of Cu2+ in layered perovskites compressed?

Cu2+ impurities in tetragonal layered perovskites display a compressed geometry (Req>Rax) along the crystal c-axis. Searching the microscopic origin of this fact DFT calculations have been performed on clusters simulating K2MgF4:Cu2+. Results for a 37 atoms cluster indicate that the difference, δec, between the energies for elongated and compressed minima along the c-axis is around 0.2 eV while Req−Rax⩽0.10 Å. This result is shown to come mainly from the tetragonal electrostatic potential due to the rest of ions on CuF64− which provides a gap, Δ, between ∼x2−y2 and ∼3z2−r2 orbitals when Req=Rax. Although δec<Δ this gap is shown to play a key role for understanding the equilibrium geometry in tetragonal perovskites.