Introduction

Transition metal (TM) oxides host a diversity of fascinating phenomena1,2,3,4,5,6. Several possible formal oxidation states of the TM ions coupled with the innate ability to stabilize those states by structural network of oxygens give rise to a striking change in the TM–O orbital hybridization W, electron–electron correlations U and the charge transfer energy Δ7; the subtle competition between W, U and Δ across the 3d group of the periodic table is then responsible for a vast landscape of interesting magnetic and electronic ground states1,4,8. In traversing the periodic table within groups of the 3d→4d→5d TM blocks, the additional degree of freedom, the spin–orbit (SO) interaction, λ gets activated and is predicted to foster a multitude of exotic electronic and topological phases of correlated matter9,10,11,12,13,14,15.

Although the vast majority of these compounds contain TM ions at the B-site of the ABO3 perovskite structure, it is now possible to synthesize a new family of compounds with formula unit , Fig. 1a, where the perovskite A-site is partially occupied by a TM ion, labelled A′. Among this class of materials, (ACu3)B4O12 with Cu in the A′ site have garnered considerable attention because of the presence of CuO4 planes. Structurally, this family of compounds consists of two different magnetically active sublattices of TM ions: BO6 octahedral units (forming a three-dimensional octahedral network as in the typical ABO3 perovskite lattice) and the planar CuO4 units coupled with BO6 units via an apical oxygen (see Fig. 1a). Depending on the choice of B-site ion, the materials exhibit exciting properties including giant dielectric constant (B=Ti), exotic ferromagnetism (B=Ge, Sn, Fe), valence fluctuation (B=V), Mott physics (B=Ru) and inter-site charge order (B=Fe) to name a few16,17,18,19,20,21,22. They are also of particular interest owing to the preservation of the cubic lattice symmetry , despite large variations of the B-site ion including utilizing different TM series (3d or 4d or 5d) of the periodic table34,35. To track the movement of the hole in the present series of samples, we obtained O K-edge XAS spectra shown in Fig. 2b, with the post-edge normalized to 1 (at 540 eV). As immediately seen, the decrease of the relative intensity of the pre-peak indeed scales with the reduction of the ligand hole on Cu, implying a marked change in both bandwidth, W, and the charge transfer gap, Δ. The decrease of the pre-peak intensity can be rationalized in terms of a decreasing availability of empty states as the hole concentration on O decreases in moving from Co to Rh to Ir. Although the high-energy shoulder on the Cu L3 peak disappears entirely for CCIrO, the oxygen pre-peak does not, which indicates the hybridization between the B-site and O is also significant, as Cu2+ will not contribute to the pre-peak. The results of the O K-edge spectroscopy are thus in excellent agreement with the Cu L-edge observations. Another interesting observation is that the energy separation between the pre-peak and the peak around 530 eV increases from Co to Ir. The shift towards higher energy will be discussed in detail in the theory section and is attributed to the gradually increasing separation of the B-site bands (CCCoO) and both the B-site and Cu bands (CCRhO and CCIrO) from the O 2p band.

The movement of the hole away from Cu naturally implies a change in valency of the B-site ion. To verify this proposition and to corroborate the previous findings, we performed XAS on the L- and K-edges of Ir and Rh, respectively (Co was measured previously and found to be in the ~ 3.25+ state, after subtraction of an impurity peak24). Moving to the 4d compound, Rh K-edge XAS spectra have been simultaneously collected from the CCRhO sample and a standard SrRhO3 reference sample. Although the line shape from CCRhO shares similarities with SrRhO3 (Rh4+), the difference in energy at 80% of the normalized absorption was found to be ~0.68 eV lower relative to SrRhO3, Fig. 3a (ref. 36). Based on this shift, and the shift of ~1.9 eV between Rh3+ and Rh4+ (see Supplementary Fig. 2), we conclude that the Rh valence state is indeed strongly mixed between 3+ and 4+, with a value of 3.64+ (±0.1). In conjunction with the Cu and O soft XAS, the entire Rh data set strongly supports the notion that the hole still largely resides on the O anion, but spreads to the hybridized orbital with Rh. Finally, the Ir L3 edge (2p3/2→5d transition) recorded from CCIrO and SrIr(4+)O3 is shown in Fig. 3b. As seen, the remarkably similar line shape and the energy peak position both confirm that Ir is in the 4+ state. The L3 to L2 branching ratio was found to be 3.79 (analysis shown in Supplementary Fig. 2)9,11. This value is similar to that found in several other iridate compounds and signifies a large SO coupling (SOC) as expected for a 5d compound9,11,37,38. Overall, the Ir L-edge data are in excellent agreement with the Cu L-edge data stating the d9 Cu2+ ground state, with a much smaller d8 contribution compared with the Rh and Co compounds; thus, in the CCIrO compound, the hole is now almost entirely transferred from the Cu 3d–O 2p state to the Ir 5d–O 2p hybridized orbital. The obtained valences for the B-sites are also listed in Table 1.

Figure 3: Changing valency of the B-sites by hard XAS.
figure 3

(a) Hard XAS Rh K-edge measurements on the CCRhO and SrRhO3 (4+) standard. (b) XAS on the Ir L3-edge for both CCIrO and a SrIrO3 standard evidencing the nearly identical line shape and position indicating the 4+ valency. The dashed line shows the excellent agreement of the peak positions.

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Density functional theory (DFT) results

Calculating the spin-polarized electronic structure of the three compounds, as a common feature, we find that the Cu d, B d and O p states are admixed, although the degree of admixture varies between the three compounds. Site-projected partial density of states is shown in Supplementary Fig. 3 (ref. 39). A direct inspection of the plot for CCCoO reveals that the states, which are strongly admixed with states, are empty in both spin-up and spin-down channels, thus lending strong support for the valence in CCCoO. This yields a mixed valence of 3.25+ on Co and the intermediate spin state with a magnetic moment of ~1.68 μB. Moving towards the CCRhO compound, the admixture between the state and Rh states becomes markedly reduced compared with that of CCCoO. In this compound, the calculated Cu valence is found to be mixed between 2+ and 3+ (~2.5+), with Rh valence close to 3.6+. Unlike Co, magnetically Rh is found to be in the low spin state with a spin moment of 0.21 μB and largely quenched orbital moment of 0.05 μB. Finally, we consider the CCIrO. In sharp contrast to both Co and Rh, the mixing of the p states and the Ir d states is drastically reduced. This results in an almost pure p state occupied in one spin channel and empty in another, implying a Cu2+ valence and nominal Ir4+ valence. The spin moments at Ir and Cu sites are found to be 0.45 μB and 0.65 μB, respectively, with a rather large spin moment of 0.12 μB on O, arising from strong hybridization with Ir. We note that ionic Ir4+ is in the 5d5 configuration and has extensively been discussed in view of the interplay of strong SOC and correlation physics9,10,11,12,13,14,15. The large branching ratio of close to 3.8 signifies the presence of a large SOC at the Ir site, which is found to be common among many of the compounds of Ir4+ in an octahedral environment, even when the compound is metallic as in IrO2 (ref. 38). The orbital moment at the Ir site, calculated within the generalized gradient approximation (GGA)+U+SO, turned out to be 0.12 μB, smaller than the spin moment with morbital/mspin being 0.27. This is curious when compared with the values obtained in cases like BaIrO3 (ref. 11). The structure and coupling mechanisms are, however, rather different between compounds like Sr2IrO4 or BaIrO3 and the present one. In the former examples, magnetic interactions are one- or two-dimensional Ir–Ir, whereas here they are Cu–Ir with three-dimensional connectivity. The dominance of hybridization produces an additional induced spin moment at the Ir site because of the presence of the magnetic ion Cu, a behaviour qualitatively similar to the case of La2CoIrO6, discussed in recent literature37. The presence of a significant SO interaction is found to mix up and down spins and destroys half-metallicity in CCIrO. We note here that inclusion of SOC allows for the non-collinear arrangement of spins. We have therefore carried out spin-polarized calculations assuming collinear as well as non-collinear spin arrangements. The calculated magnetic moments at various atomic sites, obtained in non-collinear calculations, turn out to be very similar to that obtained assuming simple collinear arrangement of spins. The spin magnetic moments are found to be similar to that obtained from collinear calculations within 1–2%, whereas the orbital magnetic moments are found to differ from that in collinear calculation by a maximum of 0.5%, providing confidence in the general conclusion drawn from the electronic structure calculations on the various valence and spin states, irrespective of the assumed spin arrangements.

The evolution of the nominal valence of Cu from predominant 3+ (d9L) to 2+, as one moves from 3d (Co) to 4d (Rh) to 5d (Ir) elements at the B-site, is controlled by mixing between B-site d states and p states and can be vividly visualized in the effective Wannier function plots shown in Fig. 4a (upper panel). As clearly seen, the Wannier functions centred at the Cu site have the orbital character of symmetry, and the tail is shaped according to the symmetry of the orbitals mixed with it. Specifically, moving from CCCoO to CCRhO to CCIrO, we find the weight at the tails centred at the B-site (marked by a circle) progressively diminishes.

Figure 4: Theoretical calculations and Doniach phase diagram.
figure 4

(a) Top panels: plots of effective Wannier functions for O p, orbitals for CCCoO, CCRhO and CCIrO. Plotted are the constant value surfaces with lobes of different signs coloured as cyan and magenta. The Cu, B- and O-sites are shown as green, red and blue coloued balls. Bottom panels: energy level positions of Cu d, B d and O p states for CCCoO, CCRhO and CCIrO. (b) Doniach phase diagram showing the dependency on the Cu occupation.

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Microscopically, the nature of this peculiar unmixing/dehybridization effect between Cu–O and B-site in moving from 3d to 4d to 5d element at the B-site can be further elucidated by considering the energy level positions of B d, Cu d and O p states (see Fig. 4a (bottom panel)). As mentioned above, the octahedral crystal field coupled with the trigonal distortion separates the B d states into doubly degenerate , and singly degenerate a1g ones, whereas the square planar geometry of the CuO2 plane breaks the Cu d states into and the rest, with being of the highest energy. In progressing from CCCoO to CCRhO to CCIrO, the relative position of with respect to O p states increases, driven by the pushing down of O p states because of the increased crystal field splitting ( splitting) at the B-site. This, in turn, makes the hybridization between the Cu sublattice and B sublattice weaker and weaker as those ions communicate via the intervening oxygen. This highlights a key difference between CCIrO and CaCu3Ru4O12, where for the latter it was found that the suspected Kondo-like physics was unlikely due to a strong mixing of Cu with O40,41. Similar to that of high-Tc cuprates, for CCCoO, the O p states are positioned above , placing Cu in to a negative charge transfer regime, which promotes a high-Tc cuprate-like state akin to the Zhang-Rice singlet state24,25,26,42. The progressive weakening of covalency between the B sublattice and Cu–O sublattice, as one moves from CCCoO to CCRhO to CCIrO, makes the spread of the effective Wannier function (top panel of Fig. 4a) in the case of Ir dramatically reduced compared with either Co or Rh.

Unified picture

Finally, the element-resolved spectroscopic results combined with the ab-initio calculations prompts us to build a unified framework to explain their emergent physical behaviour. Although an earlier study utilizing electron energy loss spectroscopy found small changes between 3–4–5 d A-site-ordered perovskites from different columns43,44,45,46,47,48. In this framework, the overall ground state is defined by the competition between RKKY-type magnetic exchange between magnetic holes on Cu with the Kondo screening by conduction carries from the B–O sublattices. For CCIrO, with a S=1/2 d-hole localized on Cu, the large magnetic exchange is comparable in strength with the Kondo screening, resulting in the strongly enhanced effective mass observed with transport and thermal measurements27. Thus, Cheng et al. firmly placed CCIrO into the heavy fermion regime I in Fig. 4b with the antiferromagnetic local moment short-range magnetism23,27. In moving from Ir to Rh and Co, the Kondo energy scale begins to gain because of the collective hybridization of Cu d-holes into the ZR singlets. With the strong reduction in the orbital occupation, both CCRhO and CCCoO enter the regime II of mixed valency (or Kondo liquid phase) in Fig. 4b. Unlike regime I, in the mixed valence regime quantum fluctuations between different electronic configurations are highly relevant; in this regime, the local electronic and magnetic structure of Kondo centres (Cu) is defined by the redistribution of electrons between Cu d states and electrons from the strongly hybridized d- and p-states of Rh (Co) and O, that is, |3d9, S=1/2› versus . The conjectured microscopic framework that links the electronic and magnetic ground state of the A-site perovskites with macroscopic behaviour opens a path in designing emergent-ordered phases with heavy fermion behaviour, quantum criticality and unconventional superconductivity in the magnetic Kondo lattice of cuprate-like moments.

To summarize, we performed XAS measurements and first-principles calculations on a series of A-site-ordered perovskites, chemical formula CaCu3B4O12, spanning one period of the periodic table. Surprisingly, we find that the materials fit well within the Doniach phase diagram, being controlled by the hole count on Cu, leading to the conclusion that the competition between RKKY and Kondo effects is responsible for the anomalous behaviour observed in the CCIrO compound.

Methods

Sample preparation

All samples used in the present study were prepared under high-pressure and high-temperature conditions with a Walker-type multianvil module (Rockland Research Co.). The A-site-ordered perovskites CCCoO, CCRhO and CCIrO were obtained under P=9 GPa and T=1,000–1,300 °C; the reference perovskites SrRhO3 and SrIrO3 were obtained at 8 GPa, 1,200 °C and 6 GPa, 1,000 °C, respectively. About 30 wt.% KClO4 acting as oxidizing agent were added for synthesizing the compounds containing Co and Rh. The resultant KCl was washed away with deionized water. Phase purity of the above samples was examined with powder X-ray diffraction at room temperature with a Philips Xpert diffractometer (Cu Kα radiation). All the A-site-ordered perovskites adopt a cubic structure with lattice parameter increasing progressively from a=7.1259(3) Å for M=Co to a=7.3933(1) Å for M=Rh, and to a=7.4738(1) Å for M=Ir. On the other hand, the reference perovskites crystallize into the orthorhombic Pbnm structure with unit-cell parameters a=5.5673(1) Å, b=5.5399(2) Å and c=7.8550(2) Å for SrRhO3, and a=5.5979(1) Å, b=5.5669(1) Å and c=7.8909(1) Å for SrIrO3, respectively.

X-ray measurements

XAS measurements were carried out on the polycrystalline samples in the soft X-ray branch at the 4-ID-C beamline in the bulk-sensitive TFY and total electron yield modes, with a 0.1 eV (0.3 eV) resolution at the O K-edge (Cu L-edge), at the Advanced Photon Source in Argonne National Laboratory. Measurements were taken on the Cu L-edge and O K-edge for all samples, and all measurements shown here were obtained in total electron yield mode (TFY available in Supplementary Fig. 1). To measure the 4d and 5d B-site valences, hard XAS measurements with a 1.5(3) eV resolution were taken at the 4-ID-D beamline in transmission (fluorescence) mode for Ir (Rh).

Computational details

In the first-principles DFT calculations, we have primarily used the plane wave basis set and pseudo-potentials as implemented in the Vienna Ab-initio Simulation Package49. The exchange-correlation function was chosen to be that of the GGA implemented following the parametrization of Perdew-Burke-Ernzerhof50. 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.51 For the plane wave-based calculations, we used projector augmented wave52 potentials. The wave functions were expanded in the plane wave basis with a kinetic energy cutoff of 600 eV and Brillouin zone (BZ) summations were carried out with a 6 × 6 × 6 k-mesh. A U-value of 5 eV on Cu site was used. For the U-value on the B site, a value of 4 eV was used for the 3d element Co and 1–2 eV was used for 4d and 5d elements, Rh and Ir. The obtained results were verified in terms of variation of U parameter. The Hund’s rule coupling J was fixed to 0.8 eV. The plane wave results were verified in terms of full-potential linearized augmented plane wave method as implemented53 in WIEN2k. For FLAPW calculations, we chose the augmented plane wave+lo as the basis set and the expansion in spherical harmonics for the radial wave functions was taken up to l=10. The charge densities and potentials were represented by spherical harmonics up to l=6. For BZ integration, we considered about 200 k-points in the irreducible BZ and modified tetrahedron method was applied54. The commonly used criterion for the convergence of basis sets relating the plane wave cutoff, Kmax, and the smallest atomic sphere radius, RMT, RMT*Kmax, was chosen to be 7.0. Spin–orbit coupling has been included in the calculations in scalar relativistic form as a perturbation to the original Hamiltonian.

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)55-downfolding calculations. Starting from 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 MTO56 calculations. The results were cross-checked among the calculations in three different basis sets in terms of total energy differences, density of states and band structures.

Additional information

How to cite this article: Meyers, D. et al. Competition between heavy fermion and Kondo interaction in isoelectronic A-site-ordered perovskites. Nat. Commun. 5:5818 doi: 10.1038/ncomms6818 (2014).