Zhang-Rice physics and anomalous copper states in A-site ordered perovskites

Abstract

In low dimensional cuprates several interesting phenomena, including high T_c superconductivity, are deeply connected to electron correlations on Cu and the presence of the Zhang-Rice (ZR) singlet state. Here, we report on direct spectroscopic observation of the ZR state responsible for the low-energy physical properties in two isostructural A-site ordered cuprate perovskites, CaCu₃Co₄O₁₂ and CaCu₃Cr₄O₁₂ as revealed by resonant soft x-ray absorption spectroscopy on the Cu L_3,2- and O K-edges. These measurements reveal the signature of Cu in the high-energy 3+ (3d⁸), the typical 2+ (3d⁹), as well as features of the ZR singlet state (i.e., 3d⁹L, L denotes an oxygen hole). First principles GGA + U calculations affirm that the B-site cation controls the degree of Cu-O hybridization and, thus, the Cu valency. These findings introduce another avenue for the study and manipulation of cuprates, bypassing the complexities inherent to conventional chemical do** (i.e. disorder) that hinder the relevant physics.

Introduction

The many-body ZR singlet state^{1,2,3,4,5,6,7,8,9}, a doped hole on the oxygen site coupled antiferromagnetically with a hole on the copper site, can be manipulated with conventional solid-state chemistry methods by partial removal of oxygen or by non-isovalent cation exchange (e.g. La³⁺ → Sr²⁺). Such chemical routes of manipulation make the the doped cuprates prone to chemical disorder causing strong structural distortions or even changes in crystal symmetry, which in turn may severely alter the properties associated with Cu d-electron derived electronic and magnetic structures. En route to the goal of realizing the ZR state without chemical disorder or lattice distortion, while the majority of the Cu oxide compounds have the Cu ions in the B-site of the perovskite ABO₃ structure, the A-site ordered perovskites with chemical formula (ACu₃)B₄O₁₂ are intriguing candidates for investigation due to the unique Cu A-site arrangement (see Fig. 1(a)). In this structure, a surprisingly rich set of interesting physics phenomena

Figure 1

Crystal structure of A-site ordered perovskites.

(a) The entire crystal structure of CaCu₃Cr₄O₁₂. (b) CrO₆ octahedral sub-lattice. (c) CuO₄ distorted square planar sub-lattice. (d) Cr-Cr and Cr-Cu exchange pathways and (e) a sketch of B-site electronic states coupled to the ZR singlet state on Cu.

Results

Resonant x-ray absorption spectroscopy (XAS) in the soft X-ray regime is an ideal tool, extensively used in the past, to investigate the Cu and O electronic structure and the effects of electron-electron correlations in high T_c cuprates^{2,6,7,8,25,26,27}. Results of our soft XAS measurements on the Cu L_3,2- and O K-edge are shown in Fig. 2 for the two A-site ordered perovskites CaCu₃Co₄O₁₂ (CCCoO) and CaCu₃Cr₄O₁₂ (CCCrO) along with that of the optimally doped superconducting YBa₂Cu₃O_7−δ (YBCO) and metallic LaCuO₃ (LCO) perovskite with a unique formal Cu³⁺ (3d⁸) oxidation state. From the absorption line shape in Fig. 2, it is readily apparent that in CCCoO and CCCrO a mixed valency of Cu is present; we will discuss the CCCrO compound first. The sharp peak ~ 930 eV corresponds to the transition from the d⁹ ground state, featuring a single hole in the Cu e_g band, to the cd¹⁰ (here c denotes a core hole) excited state. The shoulder seen at 931.5 eV, a signature of the ZR singlet state, is a transition from the ground state d⁹L to the cd¹⁰L excited state^2,5,7,26,27. The key difference between these two transitions being that while the Cu still maintains a nearly 2+ (or d⁹) valency, a ligand hole is distributed over the neighboring oxygens as illustrated in Fig. 1(e). The interaction between this ligand hole and the core hole created by the photon absorption raises the energy required to promote the core electron to the unoccupied state in the e_g band resulting in the observed high-energy state marked by red arrows. Furthermore, to corroborate this, we show the absorption data on LCO with the formal Cu charge state of 3+. Indeed, in-line with our previous statement, the main feature of the LCO XAS around the L₃-edge at ~ 931.5 eV is the transition from the d⁹L state, thus making the ZR state the dominant contribution to the ground state in good agreement with previous reports^28,29. The aforementioned doped ligand holes are the charge carriers essential to the physics of high T_c cuprates; for instance, in hole doped cuprates the superconducting transition temperature is strongly dependent on the amount of do** present^2,30,31. To clarify the connection between these compounds and the high-temperature superconducting cuprates, XAS data was taken for an optimally doped YBCO sample. As seen in Fig. 2, the Cu L-edge spectrum of CCCrO shows remarkable resemblance to YBCO, namely the dominant d⁹ initial states followed by the higher energy ZR state shoulder. This result highlights the capacity of the A-site ordered cuprate perovskites to mimic the effects of chemical do** without provoking unwanted lattice and stoichiometry deviations inherent to conventional chemical do**. In addition, the multiplet split peak at ~ 940 eV corresponds to a transition from the metastable 3d⁸ state to the cd⁹ excited state, indicating the presence of the ionically Cu³⁺ state entirely absent in YBCO.

Figure 2

XAS measurements on Cu L- and O K-edges.

Left panel displays the Cu L-edge for all samples with the Zhang-Rice and d⁸ ground states highlighted. LCO and YBCO are shown as references for Cu 3+ and Cu 2+ respectively, highlighting the change in valence for Cu with B-site change^36,6,7,8,25. This observation of the pre-peak intensity indicates that the ZR state is the first ionization state at the Fermi energy. This further evidences our conclusion on the presence of the ZR state inferred from the Cu L-edge analysis.

Although our prime focus is on the electronic structure of Cu and O, Co and Cr L_3,2-edge absorption can serve to independently validate the Cu oxidation state. With this goal in mind, we performed L-edge XAS measurements on Co and Cr and compared this to the previous results on reference Cr and Co compounds. As shown in Fig. 3(a), a direct comparison to the Cr³⁺ and Cr⁴⁺ absorption confirms that in CCCrO the Cr valency is 4+ or very close to it³³. This verifies the conclusion that, in this compound, if Cr is 4+ then Cu must be ~2+ (assuming O²⁻ and Ca²⁺). Any deviation of Cr valency towards 3+ must then be compensated by raising the Cu charge state, thus Cu must be 2 + or very close to it, consistent with the Cu L-edge results. The Co L-edge data shown in Fig. 3(b) bear strong similarities with previous studies of LaCoO₃, which consists of ionically bound Co³⁺³⁴. Specifically, strong, high energy multiplet shoulders on the L₃ and L₂ white lines are present in both CCCoO and LaCoO₃. In variance to this, Co⁴⁺ shows a smaller shoulder shifted to even higher energy. While the high energy side of the CCCoO Co L-edge is consistent with Co³⁺, the low energy multiplet peak does not match either 3+ or 4+, implying CCCoO is neither ionically pure 3+ or 4+. Based upon the Cu L-edge conclusion of the Cu³⁺ charge state, we can independently assess the Co valency to be ~ 3.25+. In this context, the Co L-edge data is compatible with the Cu L-edge results and implies the presence of a mixed 3+/4+ Co valency, although it cannot confirm the exact 3.25+ valence state needed to conserve charge. Lending further support to this conclusion, Co L edge data in total electron yield (TEY) mode is shown in the Supplemental Figure S1.

Figure 3

XAS measurements on the Cr and Co L-edges.

(a) The Cr L-edge along with 3+ and 4+ references from³³, the CCCrO and the 4+ reference samples show strong similarities. (b) The Co L-edge with valence references from³⁴ showing a similar, but not identical line shape. No standards were available meaning any energy shift between the samples could not be analyzed, all spectra were shifted to ~ align the white lines.

To gain further understanding of the B-site influence on the unusual electronic states on Cu, we performed first-principles spin-polarized DFT calculations within the GGA+U approximation. Fig. 4 summarizes the first-principles results for CCCoO and CCCrO, respectively. Note, although no long-range magnetic ordering is reported in these compounds, spin-polarized calculations are essential for proper assignment of both charge and spin states of various constituents¹⁵. The three panel Fig. 4(a) and (b) show an inspection of the calculated density of states (DOS) projected onto B-d (B = Co/Cr), Cu-d and O-p states respectively. A direct inspection of the states in the vicinity to the Fermi energy, E_F demonstrates the existence of strong mixing between B and Cu d-states and O p-states. This strong covalency effect makes both CCCoO and CCCrO systems metallic, in agreement with experimental observations. In addition, as shown in the inset of Fig. 4(a)–(b), the octahedral crystal field of the oxygen atoms around the B ion splits the B-t_2g states from the B-e_g states; the trigonal distortion present in the BO₆ octahedra breaks the t_2g levels further into doubly degenerate, and singly degenerate a_1g states. The distorted square planar environment of oxygen atoms surrounding the Cu ion, on the other hand, lifts the 5-fold degeneracy of Cu d-levels, with large energy separation of Cu state from the rest. Here we note that the nominal d⁸ (i.e. Cu³⁺) would imply empty Cu: states in both spin up and spin down channels and for d⁹ Cu: states would be occupied in one of the spin channels and be empty in the other spin channel. From the DOS plots shown in Fig. 4(a) and (b), we find that Cu: states are empty in the down spin channel, while in the up spin channel it is indeed close to being empty for CCCoO, but mostly occupied for CCCrO. We note that DFT calculation deals with single configuration nature of the wavefunction and therefore, delivers the state with most dominant weight. Interestingly enough, the dominance of Cu 3+ state in CCCoO and Cu 2+ state in CCCrO is evident even at the level of single configuration theory. This result lends strong theoretical support for the conclusion inferred from our XAS measurements that the Cu state is predominantly in the 3+ state for CCCoO and closer to 2+ for CCCrO.

Figure 4

The GGA + U density of states, projected onto Co d (Cr d), Cu d and O p states for the A-site ordered perovskites.

(a) CaCu₃Co₄O₁₂ ((b) CaCu₃Cr₄O₁₂) compound. The positive and negative values in y-axis correspond to density of states inup and down spin channels, respectively. The zero of the energy is set at E_F. The features due to dominant contributions of various degrees of freedom have been marked. The inset in the middle panel shows the plot of the effective Cu x² − y² Wannier function, calculated by NMTO-downfolding. Shown are the isosurface with lobes of opposite signs are colored differently. The inset in the bottom panel shows the relative positions of Co d, Cu d and O p energy levels.

Next, we discuss the calculated magnetic states in connection to Cu. First, we note that occupancy of the square planar Cu d-states according to the formal valence of d⁸ would give rise to a paired electronic configuration with zero magnetic moment at Cu sites, while that of formal valence of d⁹ would give rise to one unpaired electron with magnetic moment of 1 μ_B in the fully spin polarized limit. In comparison, the calculation yields magnetic moments on Cu site 0.07 μ_B for CCCoO and 0.50 μ_B for CCCrO, thus lending additional validation of our experimental conclusion on the exotic 3+ state for CCCoO and closer to 2+ valency in CCCrO. Moreover, from the simple ionic charge count, the nominal 3+ and 2+ valences of Cu (assuming Ca²⁺ and O²⁻), would set the formal valences of the B-site ion to 3.25+ and 4+ respectively and result in d-electron occupancies of 5.75 for Co and 2 for Cr. The computed magnetic moment at the Cr site is 2.2 μ_B, in good agreement with the nearly 2+ valence of Cu and 4+ valence of Cr in CCCrO. The d-occupancy of 5.75 on Co can lead to either low or high spin magnetic state; our computed Co magnetic moment of ~1.7 μ_B, however, is in conformity with the intermediate rather than low- or high-spin state.

By examining the energy level positions, as calculated in DFT, shown in the insets in the bottom panels of Figs. 4(a–b), we find that Cu energy level is nearly degenerate with O-p states, leading to a situation very similar to that in high T_c cuprates. This electronic configuration naturally supports strong mixing of Cu and O p_x and p_y states by forming a strong pdσ anti-bonding combination, which may further bind to d-states at the B site as shown in Fig. 1(e). The formation of such a mixed state is also evident in the Wannier function plot of an effective Cu x² − y² Wannier function obtained by kee** only Cu state active and downfolding or integrating out all the other degrees of freedom (see inset of the middle panel of Fig. 4). We notice that for the Co compound mixing of Cu-O hybridized states with B-site d-states is much stronger compared to that of Cr compound, which is driven by the strong hybridization of empty orbital of Cu 3+ state with empty Co, e_g orbitals. In CCCrO, this leads to vanishing contribution of the B-site states for the selected iso-surface value of the Wannier plot, showing the typical Cu-O antibonding wavefunction, making the situation more like high T_c cuprates with dominant Cu 2+ state. The strong mixing between and O p states, which is a prerequisite for formation of the ZR state - observed as the feature around 931 eV in Cu L-edge spectra, is further corroborated by the presence of a 0.2 μ_B fraction of the magnetic moment on the O site and 0.5 μ_B on Cu. We thus conclude that the formation of a ZR like many-body state similar to what is observed on the high T_c cuprates is indeed highly favorable in these systems with enhanced probability for the Cr compound.

Discussion

In summary, resonant soft X-ray absorption data on Cu L_3,2- and O K-edges revealed the presence of the ZR singlet state in the symmetrically invariant A-site-ordered cuprate compounds, CaCu₃Co₄O₁₂ and CaCu₃Cr₄O₁₂. Additionally, the data demonstrated the existence of a mixed valency for Cu modulated by the electronic state of the B-site cation and reflected in the d⁹, d⁹L and the metastable d⁸ states of Cu d-electrons. First principles GGA + U calculations further validate the notion that within the A-site ordered perovskite family, the choice of B-site cation is an effective tool to manipulate the degree of B-Cu-O hybridization, adjusting the Cu valency towards the unusual 3+ valence state in CCCoO and away from 3+ closer to the stable 2+ valency in CCCrO. Additionally, Wannier function calculations support this direct experimental observation that in the CCCrO compound the ZR many-body state is particularly favorable and controls the low-energy physics. These findings demonstrate that the charge and spin state of Cu, fundamental to the intriguing physical properties the cuprates display, can be effectively altered by a careful choice of the B-site cation on isomorphic lattices that circumvent the chemical disorder and lattice modulation intrinsic to other do** methods.

Methods

Experimental details

Polycrystalline CaCu₃B₄O₁₂ (B = Cr and Co) samples were prepared under high-pressure and high-temperature (HPHT) conditions with a Walker-type multianvil module (Rockland Research Co.). For B = Cr, stoichiometric amounts of CaO, CuO and CrO₂ powders were thoroughly mixed and then subjected to a HPHT treatment at 7 GPa and 900°C for 30 minutes. For B = Co, a precursor containing Ca, Cu and Co ions in the 1:3:4 molar ratio obtained via a sol-gel route was mixed with 30 wt.% KClO₄ acting as an oxidizing agent and then subjected to a HPHT treatment at 9 GPa and 1000°C for 30 minutes. The resultant KCl was washed away with deionized water. Details about the sample assembly and procedures for the HPHT experiment can be found in a previous paper³⁵. Phase purity of the above samples was examined with powder X-ray diffraction (XRD) at room temperature with a Philips Xpert diffractometer (Cu Kα radiation). The B = Co sample contains a small amount of cobalt and copper oxides. The cubic lattice parameter was calculated to be a = 7.2385(5) and 7.1259(3) Å for M = Cr and Co, respectively. Reitveld refinement for the two a-site ordered compounds is available in the Supplemental Figure S2.

LCO was synthesized under high oxygen pressure to the rhombohedral symmetry, details of which can be found elsewhere³⁶. YBCO was grown with pulsed laser deposition, the details of which can also be found elsewhere³⁷.

In order to elucidate the transformation of the Cu valency across these compounds, soft XAS measurements were carried out at the soft x-ray branch at the 4-ID-C beamline in the bulk-sensitive total fluorescence yield (TFY) mode and TEY mode in the Advanced Photon Source at Argonne National Laboratory. Measurements were taken on the Cu L-edge and O-K edge for all samples. All measurements were accompanied by a CuO standard, which allows precise alignment of the energy for oxidation state comparison. The Co and Cr L-edges were also obtained for the corresponding samples. All measurements shown were obtained in TFY mode; except, the Cr L edge data and all the Cr reference absorption data were taken in TEY mode.

Computational details

In the first-principles DFT calculations we have used the plane wave basis set and pseudo-potentials as implemented in the Vienna Ab-initio Simulation Package (VASP)³⁸. The exchange-correlation function was chosen to be that of generalized gradient approximation (GGA) implemented following the parametrization of Perdew-Burke-Ernzerhof³⁹. The electron-electron correlation beyond GGA was taken into account through improved treatment of GGA + U calculation within the +U implementation of Dudarev et al.⁴⁰. For the plane wave based calculations, we used projector augmented wave (PAW)⁴¹ potentials. The wave functions were expanded in the plane wave basis with a kinetic energy cutoff of 600 eV and Brillouin zone summations were carried out with a 6 × 6 × 6 k-mesh. The U value of 5 eV on Cu site and 4 eV on B site were used for GGA + U calculations while the Hund's rule coupling J was fixed to 0.8 eV. The obtained results were verified in terms of variation of U parameter.

In order to estimate the positions of the Cu-d, B-d and O-p energy levels as well as the plots of the effective Wannier functions for B-d states, we used muffin-tin orbital (MTO) based N-th order MTO (NMTO)⁴²-downfolding calculations. Starting from a full DFT calculations, NMTO-downfolding arrives at a few-orbital Hamiltonian by integrating out degrees which are not of interest. It does so by defining energy-selected, effective orbitals which serve as Wannier-like orbitals defining the few-orbital Hamiltonian in the downfolded representation. NMTO technique which is not yet available in its self-consistent form relies on the self-consistent potential parameters obtained out of linear muffin-tine orbital (LMTO)⁴³ calculations. The results were cross-checked among the plane wave and LMTO calculations in terms of total energy differences, density of states and band structures.