Compounds Containing Tetragonal Cu²⁺ Complexes: Is the d_x²–y²–d_3z²–r² Gap a Direct Reflection of the Distortion?

Abstract

It is widely assumed that the gap, Δ, between d x 2 −y 2 and d 3z 2 −r 2 orbitals in fluorides and oxides containing tetragonal Cu 2+ or Ag 2+ complexes directly reflects the tetragonal distortion in the MX 6 complex (M = d 9 ion; X = F − , O 2− ). This assumption on that relevant quantity is shown to be not correct through the study of pure K 2 CuF 4 -, KCuF 3 -, and Cu 2+ -doped KZnF 3 and K 2 ZnF 4 model compounds. Indeed, ab initio calculations prove that Δ in these insulating materials also depends on the internal electric field created by the rest of lattice ions on active electrons confined in a given CuF 6 4− complex. This internal field, especially important for layered compounds, is shown to explain all puzzling experimental facts on the d−d transitions of the studied systems and is of interest in the search of new Cu 2+ and Ag 2+ superconducting materials where a strong correlation between Δ and the transition temperature, T c , has been conjectured.

Changing the Usual Interpretation of the Structure and Ground State of Cu2+-Layered Perovskites

“…A nearly identical pattern is encountered for other members of the (CnH2n+1NH3)2CuCl4 family (Table 2) 18,19 . This situation is thus seemingly similar to that found for Cu 2+ -doped cubic lattices, like KZnF3 [20][21][22][23] or NaCl [25][26][27] , where the ligand octahedron is elongated and the local symmetry tetragonal as a result of a static Jahn-Teller effect (JTE) 28,29 . For this simple reason, it has systematically been accepted [9][10][11][12][13][14][15][16]30,31 that the JTE is behind the local distortion around the metal cation in RCuCl4 compounds.…”

A Genuine Jahn–Teller System with Compressed Geometry and Quantum Effects Originating from Zero‐Point Motion

“…ing among the three adiabatic minima not destroyed by random strains. [18,23,26] The present ideas are also useful to understandt he behavior of the barrieri no ther systemsf or which the complex is elastically coupled to the lattice.F or instance, for KZnF 3 :Cu 2 + ,w hich exhibits as tatic JTE [55,72] and for which Cu 2 + enters the Zn 2 + site, we calculated B = 8.1 meV;a lthough positive, this value is one order of magnitude smaller than the value of B for systems such as NaCl:Rh 2 + (B = 63.2 meV) [23,29] or KCl:Ag 2 + (B = 126.9 meV), [23,58] in which the complex is elastically decoupled from the lattice to ag ood extent. [18] Notably,a l-thoughR eynolds et al [25] found ad ynamic JT effect on the studied samples of CaO:Cu 2 + ,L ow and Suss [42] suggestt oh ave found in another sample at T = 1.7 Kastatic JT effect displaying ac ompressed geometry.T his situation is not necessarily inconsistent, as the occurrence of ad ynamic or as tatic JTE drastically dependso nt he magnitude of random strains present in the explored sample.…”

“…Indeed, for complexes elasticallycoupled to the host lattice the interaction of ligands with close ions of the host lattice plays ak ey role [50,71] in understanding the equilibrium geometry and, thus, the existence of ac ompressed conformation. [40,72] Notably,d 7 ions with S = 1/2 in octahedral symmetry often give rise to as tatic JT effect with an elongated equilibrium geometry and an unpaired electron in the j 3 z 2 Àr 2 i orbital. Indeed, although active electrons are confined in the complex, the electronic levels are also sensitivet ot he internal electric field created by close ions belonging to the host lattice.…”

“…[18] Notably,a l-thoughR eynolds et al [25] found ad ynamic JT effect on the studied samples of CaO:Cu 2 + ,L ow and Suss [42] suggestt oh ave found in another sample at T = 1.7 Kastatic JT effect displaying ac ompressed geometry.T his situation is not necessarily inconsistent, as the occurrence of ad ynamic or as tatic JTE drastically dependso nt he magnitude of random strains present in the explored sample. [18,23,26] The present ideas are also useful to understandt he behavior of the barrieri no ther systemsf or which the complex is elastically coupled to the lattice.F or instance, for KZnF 3 :Cu 2 + ,w hich exhibits as tatic JTE [55,72] and for which Cu 2 + enters the Zn 2 + site, we calculated B = 8.1 meV;a lthough positive, this value is one order of magnitude smaller than the value of B for systems such as NaCl:Rh 2 + (B = 63.2 meV) [23,29] or KCl:Ag 2 + (B = 126.9 meV), [23,58] in which the complex is elastically decoupled from the lattice to ag ood extent. The low value B = 8.1 meV for KZnF 3 :Cu 2 + is qualitativelyc onsistent with the expected elastic couplingo ft he CuF 6 4À complex with the lattice, as Cu 2 + and Zn 2 + have practically the same ionic radius.…”

“…Interestingly, this electric field,w hich is responsible for the different colors of ruby,e merald, and alexandrite, [20,80] plays ar elevant role even in the case of the cubic MgO lattice doped with Cr 3 + [81] and, at the same time, explainsw hy K 2 ZnF 4 :Cu 2 + is not ap roper JT system. [40,72] Notably,d 7 ions with S = 1/2 in octahedral symmetry often give rise to as tatic JT effect with an elongated equilibrium geometry and an unpaired electron in the j 3 z 2 Àr 2 i orbital. For cases such as NaCl:Rh 2 + [69,79] or AgX:M (X = Cl, Br;M = Rh 2 + , Pd 3 + ), although the experimental g k Àg 0 value is positive and lies in the region of 0.01 to 0.06, [61,79,82,83] it can hardly be ascribed to the O'Briene ffect.…”