Competition between heavy-fermion and Kondo interaction in isoelectronic A-site orderedperovskites

D. Meyers,1, ∗ S. Middey,1 J.-G. Cheng,2, 3 Swarnakamal Mukherjee,4 B. A. Gray,1 Yanwei Cao,1 J.-S. Zhou,3

J. B. Goodenough,3 Yongseong Choi,5 D. Haskel,5 J. W. Freeland,5 T. Saha-Dasgupta,4 and J. Chakhalian1

1Department of Physics, University of Arkansas, Fayetteville, AR 727012Beijing National Laboratory for Condensed Matter Physics,

and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China3Texas Materials Institute, ETC 9.102, University of Texas at Austin, Austin, Texas 78712

4Department of Condensed Matter Physics and Materials Science,S.N.Bose National Centre for Basic Sciences, Kolkata 700098, India

5Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA

Soft and hard X-ray spectroscopy are performed on a series of isostructural and isoelectronic A-site orderedperovskites with Cu in the A site and B-sites (Co, Rh, Ir) descending along the 9th group of the periodic table toelucidate the emerging electronic and magnetic properties as d-orbitals change from the partially filled 3d, 4d to5d. The experiments uncover that physical properties are modulated by effective transfer of a hole from the to theB-site controlled by the covalency between the A-, B-, and O-sites. First-principle calculations corroborate theexperimental findings, showing that the shift in relative energy positions of A-site, B-site and O, as one movesdown from 3d to 4d to 5d at B-site, drive this interesting behavior. The high degree of covalency together withfinite distortion quenches the effect of a strong spin-orbit interaction, otherwise expected in Rh and Ir compounds.These findings point towards the competing Kondo and RKKY interactions as a function of the average 3dx2-y2

orbital occupation of Cu in the framework of the Doniach phase diagram .

Transition metal (TM) oxides host a diversity of fascinat-ing phenomena[1–6]. Several possible formal oxidation statesof the TM ions coupled with the innate ability to stabilizethose states by structural network of oxygens give rise toa striking change in the TM – O orbital hybridization W ,electron-electron correlations U , and the charge transfer en-ergy ∆ across the 3d group of the periodic table[7]; the subtlecompetition between W,U and ∆ is then responsible for avast landscape of interesting magnetic and electronic groundstates[1, 4, 8]. In traversing the periodic table within groups ofthe 3d→4d→5d TM blocks, the additional degrees of freedom,the spin-orbit (SO) interaction, λ gets activated and is predictedto foster a multitude of exotic electronic and topological phasesof correlated matter [9–14].

While the vast majority of these compounds contain TMions at the B site of the ABO3 perovskite structure, it is nowpossible to synthesize a new family of compounds with a for-mula unit (AA′3)B4O12, Fig. 1(a), where the perovskite Asite is partially occupied by a TM ion, labeled A′. Amongthis class of materials, (ACu3)B4O12 with Cu in the A′ sitehave garnered considerable attention due to the presence ofCuO4 planes. Structurally this family of compounds consistsof two different and magnetically active sub-lattices of TMions: BO6 octahedral units (forming a 3D octahedral networkas in the typical ABO3 perovskite lattice) and the planar CuO4

units coupled with BO6 units via an apical oxygen. Depend-ing on the choice of B-site ion, the materials exhibit excitingproperties including giant dielectric constant (B = Ti), exoticferromagnetism (B = Ge, Sn, Fe), valence fluctuation (B =V), Mott physics (B = Ru), and inter-site charge order (B= Fe) to name a few[15–21]. They are also of particular in-terest due to the preservation of the cubic lattice symmetry(IM3) despite large variations of the B-site ion. This provides

a unique platform to investigate the emergence of the elec-tronic and magnetic states; for example, in recent work on(CaCu3)B4O12 (B = Cr, Co) it has been demonstrated that theZhang-Rice quantum state (essential for hole doped high Tcsuperconductivity) can be realized in these compounds, despitethe lack of the superconducting ground state [22–24].

Very recently, Cheng et al. showed that these class ofmaterials display a crossover between the magnetic insulat-ing and paramagnetic metallic states[25], depending on theCu-O and B-O bond lengths. It was further suggested thatthe CaCu3Ir4O12 (CCIrO) compound with the bond-lengthwithin the crossover region possess anomalous electronic andmagnetic properties arising presumably due to the interactionbetween localized Cu and itinerant Ir states. However, themechanism by which the electronic structure transforms tocreate this emergent behavior in CCIrO is not microscopicallyunderstood. In order to shed light on this specific issue, threeisostructural and isoelectronic compounds whose B-site spansthe 9th group of the periodic table, (CaCu3)B4O12 (B = Co,Rh, Ir) were synthesized. Within the proposed phase diagramof Cheng et al. the first two compounds occupy the paramag-netic metallic state while CCIrO is at the crossover region asreflected for instance in anomalous d.c. transport propertiesshown in Fig. 1(b).

In this Letter, we investigate the electronic and magneticstructure of this new class of materials by combination of res-onant soft and hard x-ray absorption spectroscopy (XAS) onthe Cu L-edge, O K-edge, and B-site L- and K-edges. Compli-mentary first-principles GGA+U calculations corroborate theexperimental findings, providing microscopic understanding,in terms of the evolution of Cu valence and magnetic momentfrom the Zhang-Rice like d9L state for Co compound to pured9 in Cu2+ for Ir compound, facilitated by the transfer of a

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hole from the magnetic Cu sublattice in to the B-site sublatticeas one traverses through the 9th column. Our results revealthat the unusual physical properties of those compounds aremicroscopically controlled by the degree of Cu 3d9x2-y2 orbitaloccupancy, strength of B-O covalency, and quenched spin-orbit interaction.

XAS measurements were carried out at the soft x-ray branchat the 4-ID-C beamline in the bulk-sensitive total fluorescenceyield (TFY) and total electron yield (TEY) modes at the Ad-vanced Photon Source in Argonne National Laboratory. Mea-surements were taken on the Cu L-edge and O-K edge for allsamples, and all measurements shown were obtained in TFYmode. To measure the 4d and 5d B-site valencies, hard XASmeasurements were taken at the 4-ID-D beamline in trans-mission and fluorescence mode. The ab-initio calculationswere carried out in terms of density functional theory (DFT)within the generalized gradient approximation (GGA+U) inplane wave as well as linear augmented plane wave basis. Forthe 4 and 5d compounds, CCRhO and CCIrO respectively,calculations were carried out with spin-orbit (SO) couplingincluded.

First we discuss the evolution of the Cu ground state. Cu L3

edge XAS are presented plotted in Fig. 2(a). In accord with thepreviously reported results [22], for CaCu3Co4O12 (CCCoO)the main absorption line at 931.4 eV arises due to absorptionfrom the d9L→ cd10L transition where L stands for a ligandhole whereas c indicates a hole in the Cu 2p core states. Thelow-energy shoulder (white line) around 930 eV arises fromthe d9 → cd10 transition; the spectral weight ratio (SPR) ofthose two transitions (d9/d9L) is only ∼ 2 %, indicating thatthere is a large Cu - O hybridization present in CCCoO. Theline shape of the Cu L3 absorption edge for CaCu3Rh4O12

(CCRhO), containing the 4d element Rh at the B-site, alsocontains a lesser and yet still dominant d9L contribution. Onthe other hand, for CCIrO, the d9L state is no longer presentand the L3 line shape is almost analogous to that recorded frompurely ionic d9 Cu2+ charge state [2, 3, 26–28]. This impliesthat the hole is no longer interacts with the Cu cd10 final state,showing a significant reduction of the hole contribution to thehybridized orbital between Cu and O. Furthermore, the smallmultiplet split peak seen around ∼ 940 eV for all Cu L3-edgespectra is due to a transition from the metastable 3d8 (Cu3+) tocd9 state; the small decrease in this 3d8 peak spectral weight ingoing from Co to Ir also indicates movement towards the ionic3d9 state of Cu [27–29]. Taken as a whole, the Cu L3-edgedata directly illustrate that in the presence of 4 or 5d orbitalsit is energetically more favorable to transfer the hole on to theB-site instead of stabilizing the energetically unfavorable Cu3+

state, suggesting a strong change in covalences occurs.In the past the electronic structure of Cu has been extensively

studied in the context of high Tc superconducting cuprates,where it was found that the reduction of ligand hole weight onCu causes a decrease of the pre-peak intensity around 528 eV inthe O K-edge XAS spectrum [30–33]. To track the movementof the hole in the present series of samples, we obtained O K-edge XAS spectra shown in Fig. 2(b). As immediately seen, the

decrease of the relative intensity of the pre-peak indeed scaleswith the reduction of the ligand hole on Cu, implying a markedchange in both bandwidth, W and the charge excitation gap,∆ . The decrease of the pre-peak intensity can be rationalizedin terms of a decreasing availability of empty states as the holeconcentration around Cu decreases in moving from Co to Ir.The results of O K edge are thus in excellent agreement withthe Cu L-edge observations. Another interesting observation isthat the energy separation between the pre-peak and the peakaround 530 eV, which is attributed to an admixture of O 2pstates in to the upper Hubbard band in cuprates, increases fromCo to Ir. The shift towards higher energy will be discussed indetail in the theory section and is attributed to the graduallyincreasing separation of the Cu and B-site bands from the O2p band.

The movement of the hole away from Cu naturally implies achange in valency of the B-site ion. To verify this propositionand to corroborate the previous findings we performed XASon L and K edges of Ir and Rh respectively (Co was measuredpreviously and found to be in the ∼ +3.25 state, after subtrac-tion of an impurity peak[22]). Moving to the 4d compound, RhK-edge XAS spectra have been simultaneously collected fromthe CCRhO sample and a standard SrRhO3 reference sample.Though the line shape from CCRhO shares similarities withSrRhO3 (Rh+4), the center of the edge jump appears at ∼ 0.6 -0.3 eV lower, Fig. 3(a). Based on this shift, whereas there is ashift of 1.6 eV between 3+ and 4+ (SFig. 1), we conclude thatthe Rh valence state is indeed strongly mixed between 3+ and4+, somewhere between 3.625+ and 3.825+. In conjunctionwith the Cu and O soft XAS, the entire Rh data set stronglysupports the notion that the hole still largely resides on the Oanion, but spreads to the hybridized orbital with Rh. Finally,the Ir L3 edge (2p3/2 → 5d transition) recorded from CCIrOand SrIr(4+)O3 at 50 K is in Fig. 3(c). As seen, the remarkablysimilar line shape and the energy peak position both confirmthat Ir is in the +4 state. Interestingly, the L3 to L2 branchingratio was found to be ∼ 2.8, which is close to the statisticalvalue of 2, as oppose to previous works where a value closerto 4 was found, indicating a much less significant contributionof the SO coupling in this compound[9]. Overall, the Ir L edgedata is in excellent agreement with the Cu L edge data statingthe d9 Cu2+ ground state, with a much smaller d8 contributioncompared to the Rh and Co compounds; thus, in the CCIrOcompound the hole is now almost entirely transferred from theCu 3d - O 2p state to the Ir 5d - O 2p hybridized orbital.

In order to provide microscopic insight, we performed elec-tronic structure calculations of the three compounds. Firstof all, as a common feature, we find that the spin-polarizedcalculation of the three compounds[34] lead to the electronicstructure in which Cu d, B d and O p states are admixed,though the degree of admixture varies between the three com-pounds. Site projected partial density of states (PDOS) isshown in the Supplemental (see SFig. 2). A direct inspectionof the plot for CCCoO, reveal that Cu dx2−y2 -O (p) statestrongly admixed with Co eg (eσg ) states are empty in both spinup- and spin down channels, thus lending strong support for

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the formal Cu3+ (d9L) valence in CCCoO. This yields mixedvalence of 3.25+ on Co and the intermediate spin state witha magnetic moment of ∼ 1.68 µB . Moving towards CCRhOcompound, the admixture between Cu dx2−y2 + O state and Rhstates becomes markedly reduced compared to that of CCCoO.In this compound, the calculated Cu valence is found to bemixed between 2+ and 3+ (∼ 2.5+), with Rh valence closeto 3.6+. Interestingly, unlike Co, magnetically Rh is found tobe in the low spin state with a spin moment of 0.21 µB andlargely quenched orbital moment of 0.05 µB .

Finally, we consider the CCIrO. In sharp contrast to bothCo and Rh, the mixing of the Cu dx2−y2 - O p states andthe Ir d states is drastically reduced. This results in almostpure Cu dx2−y2 - O p states occupied in one spin channel andempty in another, implying Cu2+ valence and nominal Ir4+

valence. The spin moments at Ir and Cu sites are found tobe 0.45 µB and 0.65 µB respectively, with a rather large spinmoment of 0.12 µB on O, arising from strong hybridizationwith Ir. We note that ionic Ir4+ is in the 5d5 configurationand has extensively been discussed in view of the interplayof strong SO coupling and correlation physics (see Ref [11]and references therein). In moving from Co where the SOinteraction is quenched to Ir where the atomic value of SOcoupling, λ reaches 0.4 eV, one can naively expect that suchlarge SO interaction would play an important role in definingelectronic and magnetic ground state. Contrary to the expecta-tion, switching on the SO coupling in our calculation, we findthe calculated orbital moment at the Ir site to be 0.12 µB - thevalue far smaller compared to the orbital moment observed inother Irridium oxide compounds with the Ir4+ configuration[9].The surprising weakening of the SO interaction in CCIrO maybe rationalized as follows. In CCIrO the strong crystal field ofthe oxygen octahedra around Ir ion, splits Ir d states into lowert2g , and upper eg orbitals which are high in energy and empty.λ further splits the spin containing t2g manifold into a higherenergy Jeff = 1/2 doublet and a lower Jeff = 3/2 quadruplet.Note that the splitting to Jeff = 1/2 and Jeff = 3/2 is strictlyvalid provided the t2g states are degenerate. However, unlikepreviously reported irridum oxides, the compounds under dis-cussion possess a finite trigonal splitting, δ. δ mixes the Jeff =3/2 and Jeff = 1/2 characters, and the higher energy doublets(i.e. Kramers doublet) evolve from a pure Jeff = 1/2 to S = 1/2as a function of δ/λ[11]. In addition, λ is known to be reducedby the 5d electron delocalization[11]. The presence of bothstrong delocalization (i.e. Cu-O-Ir hybridization) and trigonaldistortion, thereby, jointly weaken the effect of SOC and resultsin S = 1/2 like situation of Ir for the CCIrO compound. Herewe note, unlike vast majority of previously reported SO drivenMott insulators in Ir oxides compounds[9–14], CCIrO repre-sents an unusual case of a dominance of hopping, t, in selectingthe metallic ground state even in the presence of a formallylarge SO interaction. The presence of SO coupling, however,leads to a metallic solution, as opposed to half-metallic solu-tion obtained in its absence, as weak and yet significant SOImixes up and down spins and destroys half-metallicity.

The progressive change of the nominal valence of Cu from

predominant 3+ (d9L) to 2+ as one moves from 3d (Co) to4d (Rh) to 5d (Ir) elements at the B site is, therefore, entirelysupported by our theoretical calculations. This evolution iscontrolled by mixing between B site d states and Cu dx2−y2 -O p states and can be vividly visualized in the effective Wan-nier function plots shown in Fig. 4(a) (upper panel). As clearlyseen, the Wannier functions centered at the Cu site have theorbital character of d2x − y2 symmetry, and the tail is shapedaccording to the symmetry of the orbitals mixed with it. Specif-ically, moving from CCCoO to CCRhO to CCIrO, we find theweight at the tails centered at theB site (marked by a circle)progressively diminishes.

Microscopically, the nature of this peculiar unmixing / dehy-bridization effect between Cu-O and B site in moving from 3dto 4d to 5d element at the B site can be further elucidated byconsidering the energy level positions of B d, Cu d, and O pstates (see Fig. 4(a) ( bottom panel)). As mentioned above, theoctahedral crystal field coupled with the trigonal distortion, sep-arates the B d states into doubly degenerate eσg , eπg and singlydegenerate a1g ones, while the square planar geometry of theCuO2 plane breaks the Cu d states into Cu dx2−y2 and the rest,with Cu dx2−y2 being of the highest energy. In progressingfrom CCCoO to CCIrO two phenomena play an important role.First, the relative position of Cu dx2−y2 with respect to O pstates increases, driven by the pushing down of O p states dueto the increased crystal field splitting (eσg - eπg /a1g splitting) atthe B site. This, in turn, makes the hybridization between theCu sublattice and B sublattice weaker and weaker since thoseions communicate via the intervening oxygen. Unexpectedlyand similar to that of high Tc cuprates, for CCCoO the O pstates are positioned above Cu dx2−y2 , placing Cu in to a neg-ative charge transfer regime[35] which promotes a high-Tccuprate like d9L state akin to the Zhang-Rice singlet state[22–24]. The progressive weakening of covalency between the Bsublattice and Cu-O sublattice as one moves from CCCoO toCCRhO to CCIrO, makes the spread of the effective Cu dx2−y2

Wannier function in case Ir dramatically reduced compared toeither Co or Rh.

The element resolved spectroscopic results combined withthe ab-initio calculations allows us to build a unified frame-work to explain their emergent physical behavior. Specifically,our data reveal that upon ascending the column of the peri-odic table from Ir to Co, the Cu 3dx2−y2 orbital occupationchanges from practically ionic 3d9x2−y2 (S=1/2) for CCIrOto the non-magnetic cuprate Zhang-Rice like state with 3d9L(S = 0) for CCCoO. Along with it, as shown in Fig. 4(a),these localized and magnetically active Cu d-states in CuIrshift towards the Fermi surface demonstrating a rapid changein hybridization compared to both CCRhO and CCCoO. Onthe opposite end, such a drastic change in the Cu orbital occu-pation results in the mixed valence intermediate spin state ofCo3.25+, mixed valence Rh ∼ 3.7+ but ionic Ir4+ (5d5). Thesefindings allow us to place the three compounds under discus-sion in the context of the Doniach phase diagram depictedin Fig. 4(b), where the fundamental control parameter is theaverage occupation 〈n〉Cu of dx2−y2 orbital modulated by the

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hybridization between Fermi electrons from the strongly mixedB-site d- and O p-bands[36–38]. In the the modern versionof the Doniach phase diagram, Fig. 4(b), interesting physicsinvolving heavy fermions manifests itself as a competition be-tween the Kondo liquid and spin liquid behavior mediated bychemical doping, while very little attention has been given tothe mixed valency regime, particularly in d-electron systemsand in the absence of doping[36–41]. In this framework theoverall ground state is defined by the competition betweenRKKY type magnetic exchange between magnetic holes on Cuwith the Kondo screening by conduction carries from the B-Osublattices. For CCIrO, with S = 1/2 d-hole localized on Cuthe large magnetic exchange is comparable in strength with theKondo screening, resulting in the strongly enhanced effectivemass observed with transport and thermal measurements[25].This in turn places CCIrO in to the heavy fermion regime I inFig. 4(b) with the antiferromagnetic local moment short-rangemagnetism. In moving from Ir to Rh and Co, the Kondo en-ergy scale starts to gain due to the collective hybridization ofCu d-holes into the ZR singlets. With the strong reduction inthe Cu dx2−y2 orbital occupation both CCRhO and CCCoOenter the regime II of mixed valency (or Kondo liquid phase)in Fig. 4(b). Unlike regime I, in the mixed-valence regimequantum fluctuations between different electronic configura-tions are highly relevant; in this regime, the local electronicand magnetic structure of Kondo centers (Cu) is defined by theredistribution of electrons between Cu d-states and electronsfrom strongly hybridized d and p-states of Rh(Co) and O, i.e.| 3d9,S=1/2〉 vs. |3d9L, S = 0〉.The conjectured microscopicframework that links the electronic and magnetic ground stateof the A-site perovskites with macroscopic behaviour opens apath to designing emergent ordered phases with heavy fermionbehaviour, quantum critically and unconventional superconduc-tivity 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 theperiodic table. Surprisingly, we find that the materials fit wellwithin the Doniach phase diagram, being controlled by thehole count on Cu, leading to the conclusion that the competi-tion between RKKY and Kondo effects is responsible for theanomalous behavior observed in the CCIrO compound.

ACKNOWLEDGEMENTS

JC is supported by DOD-ARO Grant No. 0402-17291. JSZand JBG is supported by NSF Grant. No. DMR-1122603. TS-D would also like to thank, CSIR and DST, India for funding.Work at the Advanced Photon Source, Argonne is supported bythe U.S. Department of Energy, Office of Science under GrantNo. DEAC02-06CH11357. JGC acknowledges the supportfrom NSFC, MOST, and Chinese Academy of Sciences (GrantNos. 11304371, 2014CB921500, and Y2K5016X51). Wethank Dr. Shalinee Chikara and Prof. Gang Cao for sharingdata on reference samples Rh2O3 and Sr2RhO4.

∗ Electronic address: Experimental: dmeyers@uark.edu, Theoreti-cal: t.sahadasgupta@gmail.com

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(2013).

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CuCo CuRh CuIr

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Figure 1: (Color online) a) Crystal structure of A-site ordered per-ovskites. Connection between CuO4 planes and IrO6 octahedra shownin the bottom right corner. b) Temperature dependent transport datafor the B = Co, Rh, Ir samples displaying the anomalous behavior inthe crossover region.

CaCu3Ir4O12

CaCu3Rh4O12

CaCu3Co4O12

a

d9L

d9

d8

12

10

8

6

4

2

0

Inten

sity

(a.u

.)

945940935930925 Energy (eV)

Cu L - edge

Energy (eV)

CCIrO

CCRhO

CCCoO

4

3

2

1

0

Inten

sity

(a.u

.)

534532530528526 Energy (eV)

b

Inte

nsity

(a.u

.)

O K - edge

Figure 2: (Color online) a) Soft XAS on the Cu L-edge for allsamples showing the changing Cu valence. (Note: CCCoO dataoriginally published here[22]) b) Enhanced view of the ionically d8

peak highlighting the change in the relative intensity. c) Soft XAS onthe O K-edge showing both the reduction of the prepeak on O and theshifting of the O 2p - Cu 3d and O 2p - B-site d hybridized orbitals.

7

4+

SrRhO3

CCRhO

Rh K-edge

8

6

4

2

0

Inten

sity

(a.u

.)

11.3011.2511.2011.15 Energy (keV)

Ir L3-edge

SrIrO3

CCIrO

a b

4+

4+/3+

2.5

2.0

1.5

1.0

0.5

0.0

Inte

nsity

(a.u

.)

23.2823.2423.20 Energy (eV)

Figure 3: (Color online) a) Rh K-edge measurements on the CCRhOand SrRhO3 (4+) standard. The lines are used to show the strongsimilarity of the edge positions despite change in line shape. c) XASon the Ir L-edge for both CCIrO and a SrIrO3 standard evidencingthe nearly identical line shape and position indicating the 4+ valency.The grey line shows the excellent agreement of the peak positions.

CCuCoO CCuRhO CCuIrO

OCuB

Co Rh IrCuO

magnetically ordered heavy fermion

mixed valence Fermi liquid 𝜖B - 𝜖Cu

TTRKKY TKondo

CuIr CuRh CuCo

⟨n⟩Cu

∼T / T*I II

b

a

Figure 4: (Color online) a) Top panels: Plots of effective Wannierfunctions for O p, Cu dx2−y2 orbitals for CCCoO, CCRhO and CCIrO.Plotted are the constant value surfaces with lobes of different signscolored as cyan and magenta. The Cu, B and O sites are shownas green, red and blue colored balls. Bottom panels: Energy levelpositions of Cu d, B d and O p states for CCCoO, CCRhO andCCIrO. b) Doniach phase diagram showing the dependency on the Cuoccupation.