Can the d-Orbital Splitting Unveil the Local Structure of Cu$$^{2+}$$ Ions? Stu dy on the K$$_2$$ZnF$$_4$$:Cu$$^{2+}$$ Archetype

Jahn-Teller (JT) transition-metal ions like Cu\(^{2+}\) (\(d^9\)) or Mn\(^{3+}\) (\(d^4\)) in octahedral coordination exhibit larger distortions than non-JT ions like Mn\(^{2+}\) or Fe\(^{3+}\) (both \(d^5\)) in oxides and halides with perovskite type structure. Their mutual interactions eventually determine the type of distortion and the way they couple each other, being at the core of some relevant physical properties. When a JT ion is introduced as an impurity in an octahedral or nearly octahedral site, it provokes a low-symmetry lattice distortion as a consequence of the instability associated with the electronic ground state degeneracy, \(e_g (x^2 -y^2, 3z^2 -r^2 )\). The distortion degree, \(\rho \), depends mainly on the electron-ion coupling interaction related to the \(E\otimes e\) JT effect, and it is modulated by the host crystal structure. This scenario explains for example why Cu\(^{2+}\) induces a large distortion of the CuF\(_6\) octahedron, when Cu\(^{2+}\) replaces Zn\(^{2+}\) either in the perovskite KZnF\(_3\) or in the layered perovskite K\(_2\)ZnF\(_4\). However, there is a long debate about whether the splitting, \(\varDelta _e\) of the \(O_h\) \(e_g (x^2 -y^2, 3z^2 -r^2 )\) orbitals into \(a_{1g}\) and \(b_{1g}\) is proportional to \(\rho \) or \(\varDelta _e\) contains additional contributions from the rest-of-the-lattice (crystal anisotropy) aside \(\rho \). Elucidation of this controversy is important in order to establish structural correlations between \(\varDelta _e\) and \(\rho \), for an eventual local structure determination of JT impurities from optical spectroscopy. Recent studies on K\(_2\)ZnF\(_4\):Cu\(^{2+}\) report different views of this problem. Here we show that \(\varDelta _e\) scales linearly with \(\rho \). High pressure experiments and JT-ion compound series of different dimensionality give support for the proposed scenario and provide structural correlations relating \(\rho \) and \(\varDelta _e\) in Cu\(^{2+}\) and Mn\(^{3+}\) systems.