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

Understanding Pressure Effects on Structural, Optical, and Magnetic Properties of CsMnF4 and Other 3dn Compounds

The pressure dependence of structural, optical, and magnetic properties of the layered compound CsMnF4 are explored through first-principles calculations. The structure at ambient pressure does not arise from a Jahn-Teller effect but from an orthorhombic instability on MnF63- units in the tetragonal parent phase, while there is a P4/n → P4 structural phase transition at P = 40 GPa discarding a spin crossover transition from S = 2 to S = 1. The present results reasonably explain the evolution of spin-allowed d-d transitions under pressure, showing that the first transition undergoes a red-shift under pressure following the orthorhombic distortion in the layer plane. The energy of such a transition at zero pressure is nearly twice that observed in Na3MnF6 due to the internal electric field and the orthorhombic distortion also involved in K2CuF4. The reasons for the lack of orthorhombic distortion in K2MF4 (M = Ni, Mn) or CsFeF4 are also discussed in detail. The present calculations confirm the ferromagnetic ordering of layers in CsMnF4 at zero pressure and predict a shift to an antiferromagnetic phase for pressures above 15 GPa consistent with the reduction of the orthorhombicity of the MnF63- units. This study underlines the usefulness of first-principles calculations for a right interpretation of experimental findings.

Strain-Phonon Cooperation as a Necessary Ingredient to Understand the Jahn-Teller Effect in Solids

Spatial degeneracy is the cause of the complex electronic, geometrical, and magnetic structures found in a number of materials whose more representative example is KCuF3. In the literature the properties of this lattice are usually explained through the Kugel--Khomskii model, based on superexchange interactions. Here we provide rigorous theoretical and computational arguments against this view proving that structural and magnetic properties essentially arise from electron-vibration (vibronic) interactions. Moreover, based on the work of Öpik and Pryce, we show that the coupling between lattice (homogeneous strain) and motif (phonons) distortions is essential to understand the main stable configurations of the lattice. Using this information, we predict a new low-energy phase in KCuF3 that could strongly alter its properties and provide guidance on how to stabilize it through strain engineering.

Red Shift in Optical Excitations on Layered Copper Perovskites under Pressure: Role of the Orthorhombic Instability

The red shift under pressure in optical transitions of layered compounds with CuCl₆ ^4- units is explored through first-principles calculations and the analysis of available experimental data. The results on Cu²⁺ -doped (C₂ H₅ NH₃ )₂ CdCl₄ , that is taken as a guide, show the existence of a highly anisotropic response to pressure related to a structural instability, driven by a negative force constant, that leads to an orthorhombic geometry of CuCl₆ ^4- units but with a hole displaying a dominant 3z² -r² character (z being the direction perpendicular to the layer plane). As a result of such an instability, a pressure of only 3 GPa reduces by 0.21 Å the longest Cu²⁺ -Cl^- distance, lying in the layer plane, while leaving unmodified the two other metal-ligand distances. Owing to this fact, it is shown that the lowest d-d transition would experience a red shift of 0.34 eV while the first allowed charge transfer transition is also found to be red shifted but only by 0.11 eV that reasonably concurs with the experimental value. The parallel study on Jahn-Teller systems CdCl₂ :Cu²⁺ and NaCl:Cu²⁺ involving tetragonal elongated CuCl₆ ^4- units shows that the reduction of the long axis by a pressure of 3 GPa is three times smaller than that for the layered (C₂ H₅ NH₃ )₂ CdCl₄ :Cu²⁺ compound. Accordingly, the optical transitions of such systems, which involve a positive force constant, are much less sensitive to pressure than in layered compounds. The origin of the red shift under pressure undergone by the lowest d-d and charge transfer transitions of (C₂ H₅ NH₃ )₂ CdCl₄ :Cu²⁺ is discussed in detail.

Pressure Effects on 3d n (n=4, 9) Insulating Compounds: Long Axis Switch in Na 3 MnF 6 not Due to the Jahn‐Teller Effect

The pressure‐induced switch of the long axis of MnF₆³⁻ units in the monoclinic Na₃MnF₆ compound and Mn³⁺‐doped Na₃FeF₆ is explored with the help of first principles calculations. Although the switch phenomenon is usually related to the Jahn‐Teller effect, we show that, due to symmetry reasons, it cannot take place in 3dⁿ (n=4, 9) systems displaying a static Jahn‐Teller effect. By contrast, we prove that in Na₃MnF₆ the switch arises from the anisotropic response of the low symmetry lattice to hydrostatic pressure. Indeed, while the long axis of a MnF₆³⁻ unit at ambient pressure corresponds to the Mn³⁺−F₃⁻ direction, close to the crystal c axis, at 2.79 GPa the c axis is reduced by 0.29 Å while b is unmodified. This fact is shown to force a change of the HOMO wavefunction favoring that the long axis becomes the Mn³⁺−F₂⁻ direction, not far from crystal b axis, after the subsequent relaxation process. The origin of the different d‐d transitions observed for Na₃MnF₆ and CrF₂ at ambient pressure is also discussed together with changes induced by pressure in Na₃MnF₆. The present work opens a window for understanding the pressure effects upon low symmetry insulating compounds containing d⁴ or d⁹ ions.

New Ideas for Understanding the Structure and Magnetism in AgF2 : Prediction of Ferroelasticity

In the search for new high-temperature superconductors, it has been proposed that there are strong similarities between the fluoroargentate AgF2 and the cuprate La2 CuO4 . We explored the origin of the possible layered structure of AgF2 by studying its parent high-symmetry phase and comparing these results with those of a seemingly analogous cuprate, CuF2 . Our findings first stress the large differences between CuF2 and AgF2 . Indeed, the parent structure of AgF2 is found to be cubic, naturally devoid of any layering, even though Ag2+ ions occupy trigonal sites that, nevertheless, allow the existence of a Jahn-Teller effect. The observed Pbca orthorhombic phase is found when the system is cooperatively distorted by a local E⊗e trigonal Jahn-Teller effect around the silver sites that creates both geometrical and magnetic layering. While the distortion implies that two Ag2+ -F- bonds increase their distance by 15 % and become softer, our simulations indicate that covalent bonding and interlayer electron hopping is strong, unlike the situation in cuprate superconductors, and that, in fact, exfoliation of individual planes might be a harder task than previously suggested. As a salient feature, these results prove that the actual magnetic structure in AgF2 is a direct consequence of vibronic contributions involved in the Jahn-Teller effect. Finally, our findings show that, due to the multiple minima intrinsic to the Jahn-Teller energy surface, the system is ferroelastic, a property that is strongly coupled to magnetism in this argentate.

Key Role of Deep Orbitals in the dx2-y2-d3z2-r2 Gap in Tetragonal Complexes and 10Dq

Using first-principles calculations, we show that the origin of the intrinsic a_1g(∼3z² – r²)–b_1g(∼x² – y²) splitting, Δ_int, in tetragonal transition-metal complexes and the variations of the cubic field splitting, 10Dq, with the metal–ligand distance, R, are much more subtle than commonly thought. As a main novelty, the key role played by covalent bonding with deep valence ligand levels and thus the inadequacy of too simple models often used for the present goal is stressed. Taking as a guide the isolated D_4h CuF₆^4– complex, it is proved that Δ_int essentially arises from bonding with deep 2s(F) orbitals despite them lying ∼23 eV below 2p(F) orbitals. This conclusion, although surprising, is also supported by results on octahedral fluoride complexes where the contribution to 10Dq splitting from bonding with 2s(F) orbitals is behind its strong R dependence, stressing that explanations based on the crystal-field approach are simply meaningless.

Ground State and Optical Excitations in Compounds with Tetragonal CuF64- Units: Insight into KAlCuF6 and CuFAsF6

It has been argued that AAlCuF₆ (A = K, Cs) and CuFAsF₆ are the only known crystals that exhibit compressed CuF₆^4- units due to the Jahn-Teller effect. However, no grounds for this singular behavior have yet been reported. By means of first-principles calculations on such compounds and the isomorphous compounds involving Zn²⁺ ions instead of Cu²⁺, we prove that neither the ground state nor the equilibrium geometry of CuF₆^4- complexes in KAlCuF₆ and CuFAsF₆ is the result of a Jahn-Teller effect. In contrast, it is shown that the internal electric field, E_R(r), created by the rest of the lattice ions upon the localized electrons in the complex, plays an important role in understanding this matter as well as the d-d transitions of these two compounds. The energy of an optical transition is shown to involve two contributions: the intrinsic contribution derived for the isolated CuF₆^4- unit at equilibrium and the extrinsic contribution coming from the E_R(r) field. Aside from reproduction of the experimental d-d transitions observed for KAlCuF₆, it is found that in CuFAsF₆ the b_1g(x² - y²) → a_1g(3z² - r²) transition is not the lowest one due to the stronger effects from the internal field. Interestingly, the intrinsic contribution corresponding to that transition can simply be written as β(R_eq - R_ax) where R_eq and R_ax are the equatorial and axial Cu²⁺-F^- distances and β = 2.7 eV/Å is the same for all systems involving tetragonal CuF₆^4- units and an average metal-ligand distance close to 2.03 Å. This shows the existence of a common point shared by the Jahn-Teller system KZnF₃:Cu²⁺ and other non-Jahn-Teller systems such as KAlCuF₆, CuFAsF₆, K₂ZnF₄:Cu²⁺, and Ba₂ZnF₆:Cu²⁺. Although most Jahn-Teller systems display an elongated geometry, there are however many Cu²⁺ compounds with a compressed geometry but hidden by an additional orthorhombic instability. The lack of that instability in KAlCuF₆ and CuFAsF₆ is also discussed.

Local structure and excitations in systems with CuF64− units: lack of Jahn–Teller effect in the low symmetry compound Na2CuF4

The lack of a Jahn–Teller effect in Na₂CuF₄ is illustrated by the anisotropy of the Na₂ZnF₄ parent lattice.

Explaining the optical spectrum of CrF2 and CuF2 model materials: role of the tetragonal to monoclinic instability

The properties of MF2 (M = Cr, Cu) model compounds are usually interpreted assuming a Jahn-Teller effect leading to elongated MF64- units. By means of the analysis of experimental data and first-principles calculations on both the monoclinic P21/c structure and the parent rutile structure (tetragonal P42/mnm space group), we prove that such an assumption is not correct. It is shown that in MF2 compounds, the MF64- complexes are actually compressed in the parent phase but along a different direction, a situation that is however hidden by an additional orthorhombic instability due to a negative force constant of b2g and b3g modes of the cell. This distortion plays a key role in understanding the high experimental value of the lowest d-d transition energy, E1 = 1.23 and 0.93 eV for CrF2 and CuF2, respectively, when compared to the value E1 = 0.40 eV derived for the Jahn-Teller system of KZnF3:Cu2+. Aside from reproducing reasonably the experimental values of spin allowed d-d transitions of both compounds, our first-principles calculations show the existence of an accidental degeneracy involving the yz and xy levels in the final P21/c structure. Moreover, the internal electric field of CrF2 and CuF2 is found to be much less anisotropic than in layered compounds like K2CuF4 and thus it has little influence on the d-d transition energy. The influence of the (3z2 - r2) - (x2 - y2) hybridization, caused by the orthorhombic distortion, on the electronic density and the magnetic coupling between layers is also briefly discussed. The present results stress that the interpretation of experimental data using simple parameterized models can lead to wrong conclusions.

Understanding the Structure and Ground State of the Prototype CuF2 Compound Not Due to the Jahn-Teller Effect

Insulating CuF₂ is considered a prototype compound displaying a Jahn-Teller effect (JTE) which gives rise to elongated CuF₆^4- units. By means of first-principles calculations together with an analysis of experimental data of both CuF₂ and Cu²⁺-doped ZnF₂, we demonstrate that such an idea is not correct. For ZnF₂:Cu²⁺, we find that CuF₆^4- units are compressed always along the Z local axis with a hole essentially in a 3 z²- r² antibonding orbital, in agreement with experimental EPR data that already underline the absence of a JTE. The structure of the monoclinic CuF₂ crystal also comes from compressed CuF₆^4- complexes, although hidden by an additional orthorhombic instability due to a negative force constant of b_2g and b_3g local modes. The associated distortion, similar to that involved in K₂CuF₄ and other layered Cu²⁺ compounds, is also shown to be developed for ZnF₂:Cu²⁺ upon increasing the copper concentration. The origin of this cooperative effect is discussed together with the differences between non-Jahn-Teller systems like ZnF₂:Cu²⁺ and CuF₂ and true Jahn-Teller systems like KZnF₃:Cu²⁺. From present results and those on layered compounds, the usual assumption of a JTE for explaining the properties of d⁹ ions in low-symmetry lattices can hardly be right.

Crystal, electronic, and magnetic structures of M2AgF4 (M = Na–Cs) phases as viewed from the DFT+U method

Theoretical analysis of various polymorphic forms of a series of four alkali metal fluoroargentates(ii), M₂AgF₄ (M = Na–Cs), helped to establish clear trends of crystal structures and magnetic properties across the alkali metal series.