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On the metallic conductivity of the delafossites PdCoO and PtCoO 2 2 ∗ Volker Eyert, Raymond Frésard, and Antoine Maignan Laboratoire CRISMAT, UMR CNRS-ENSICAEN(ISMRA) 6508, 6 Boulevard Maréchal Juin, 14050 Caen Cedex, France (Dated: February 4, 2008) The origin of the quasi two-dimensional behavior of PdCoO2 and PtCoO2 is investigated by means of electronic structure calculations. They are performed using density functional theory in the generalized gradient approximation as well as the new full-potential augmented spherical wave 8 method. We show that the electric conductivity is carried almost exclusively by the in-plane Pd 0 (Pt) d orbitals. In contrast, the insulating CoO2 sandwich layers of octahedrally coordinated Co 0 atoms mayberegarded ascharge carrier reservoirs. Thisleads toa weak electronic coupling of the 2 Pd (Pt) layers. The obtained nearly cylindrical Fermi surface causes the strong anisotropy of the electric conductivity. n a PACSnumbers: 71.20.-b,72.15.Eb,73.90.+f J Keywords: electronicstructure,low-dimensionalcompounds, geometricfrustration 6 2 I. INTRODUCTION ] i c s Transition metal oxides attract a lot of attention due - to a great variety of physical phenomena, most of which l r go along with the ordering of some microscopic degrees t m of freedom as a function of, e.g., temperature, pressure, or doping. Prominent examples are the striking metal- . at insulator transitions of the vanadates1, high-Tc super- m conductivity in the cuprates, or the colossal magnetore- sistance observed in the manganates2,3,4,5. Cobaltates - d have arousedmuch interest due to the occurrence of dif- n ferent spin states6,7,8. In addition, they are promising o materials for thermoelectric applications9,10. c [ Known since 1873, when Friedel discovered the min- eral CuFeO2, the delafossites ABO2 keep on generating 1 astrongandeverincreasinginterest11,12,13,especiallyaf- v ter Kawazoe et al. evidenced simultaneous transparency 7 7 and p-type conductivity14, which laid groundfor the de- 0 velopment of transparent optoelectronic devices. Fur- 4 thermore,thequasitwo-dimensionalityofthelatticeand 1. the triangular coordination of atoms gave rise to such 0 exciting physical properties as strong anisotropies of the 8 electrical conductivity and magnetic frustration effects. 0 ThedelafossitestructurehasthespacegroupR¯3mand : v results from a stacking of monoatomic triangular layers, i seeFig.111,13. Inparticular,theB-atomsareatthe cen- X tersofdistortedoxygenoctahedra,whichshareedgesand ar form the characteristic BO2 sandwich layers. These tri- FIG. 1: (Color online) Crystal structure of PdCoO2. Palla- dium,cobalt,andoxygenatomsareshownasgreen,blue,and layers are interlinked by linear O–A–O bonds, resulting red (light, big dark, and small dark) spheres, respectively. in a twofold coordination of the A-atoms. However, the latter have, in addition, six in-plane nearest neighbour A-atoms. For this reason, the structure may be likewise regardedas formedfromsingle A-atomlayers,whichare (O–Pt–O) dumbbells15. intertwined by the octahedral sandwiches. For PdCoO In general, interest in the delafossite-type compounds 2 andPtCoO ,wewillfindthislatterpointofviewpartic- has concentrated quite much on the triangular arrange- 2 ularlyuseful. Finally,theoxygenatomsaretetrahedrally mentofthetransition-metalatomsandtheresultingpos- coordinatedbyoneA-atomandthreeB-atoms. Pressure sible frustration effects, which arise once localized mag- studies revealanincreaseofthe structuralanisotropyon netic moments are established. While most of these compression indicating the high mechanical stability of oxides have been found to be antiferromagnetic semi- both the octahedral sandwich layers and the O–Pd–O conductors, other class members like PdCrO , PdCoO , 2 2 2 PdRhO , and PtCoO attracted interest due to their 2 2 TABLEI:Experimentalandcalculatedlatticeparameters(in ratherhighmetallicconductivity. Inparticular,PdCoO 2 ˚A) and atomic positions. has been shown to possess one of the lowest electric re- sistivities ofnormal-stateoxides,evenlowerthanthatof compound a c zO Pd metal at room temperature11,12,16. Yet, the conduc- PdCoO2 exp. 2.8300 17.743 0.1112 tivityisstronglyanisotropic11,16. Inparticular,theratio calc. 2.8767 17.7019 0.1100 oftheresistivitiesparallelandperpendiculartothecaxis PtCoO2 exp. 2.8300 17.837 0.1140 canbeaslargeas200inPdCoO 16. Photoemissiondata calc. 2.8989 17.458 0.1128 2 indicate that the density of states at the Fermi energy can be exclusively attributed to the Pd 4d states12,13,17. Fromthecombinationofphotoemissionspectroscopyand tooptimizethebasisset,additionalaugmentedspherical inverse photoemission spectroscopy several authors con- waves were placed at carefully selected interstitial sites. cludedthattheFermienergyislocatedatashallowmin- The choice of these sites as well as the augmentation imumofthedensityofstatesanddopingmightthuslead radii were automatically determined using the sphere- to rather high values of the thermoelectric power16,17,18. geometryoptimizationalgorithm34. Self-consistencywas Despitetheirsimplechemicalformulaethedelafossites achieved by a highly efficient algorithm for convergence may be regarded as prototypical superlattices where the acceleration35. The Brillouinzoneintegrationswereper- composition of both the A and B layers can be used to formed using the linear tetrahedron method with up to strongly influence the behavior of the whole system. For 1469 k-points within the irreducible wedge33,36. instance, in CuCrO2, the Fermi energy falls into the Cr In the present work, we used a new full-potential ver- 3d band, but since the Cr layers order magnetically this sion of the ASW method, which was implemented only compound is a magnetic semiconductor. In contrast, as very recently37. In this version, the electron density and will be shown below, in PdCoO2, the Co layers only act relatedquantities are given by a spherical-harmonicsex- a charge reservoirs, and conduction takes place almost pansion inside the muffin-tin spheres. In the remaining exclusively in the Pd layers. interstitial region, a representation in terms of atom- Asamatteroffact,quiteafewelectronicstructurecal- centered Hankel functions is used38. However, in con- culationsfordelafossitecompoundshavebeenreportedin trast to previous related implementations, we here get theliterature19,20,21,22,23,24,25,26,27,28. ForPdCoO2,there away without needing a so-called multiple-κ basis set, existlinearmuffin-tinorbitalscalculationsbySeshadriet which fact allows for a very high computationalspeed of al.aswellasbyOkabeetal.21,25. Whileaccordingtothe the resulting scheme. former authors, who also investigated PtCoO , the den- 2 sity of states at E is mainly due to the Pd 4d states F with only small contributions from the Co 3d and O 2p III. RESULTS AND DISCUSSION orbitals, the results by Okabe et al. are not very specific in this respect. For this reason, the role of these or- Whilethepreviouscalculationswerebasedonthecrys- bitals for the metallic conductivity is not yet completely talstructure data by Prewitt et al.11, we here calculated clear. In order to resolve the issue and to make closer these parameters from a minimization of the total en- connectionwiththe photoemissiondata,we applyinthe ergy. To this end, in a first step for each compound the present work the new full-potential augmented spherical lattice was relaxed and after that the oxygen parame- wavemethodto study the electronicpropertiesof the ti- ter was optimized. The results for both compounds are tle compounds. We concentrate especially on the strong summarizedinTab.I. Notethatthedeviationofthecal- anisotropies and on the influence of the different species culated structuralparametersfrom the measuredones is and orbitals on the electronic properties. 2.4%atmost, whichis verywellwithin the knownlimits of the GGA and an excellent proof of the validity of the new full-potential ASW method. II. THEORETICAL METHOD In order to discuss the electronic properties, we first concentrate on PdCoO and only after that discuss the 2 The calculations are based on density-functional the- changes coming with the substitution of Pt for Pd. The oryandthegeneralizedgradientapproximation(GGA)29 electronic bands along selected high-symmetry lines of with the local-density approximation parametrized ac- the first Brillouin zone of the hexagonal lattice, Fig. 2, cording to Perdew and Wang30. They were performed are displayed in Fig. 3. The corresponding partial den- using the scalar-relativistic implementation of the aug- sities of states (DOS) are shown in Fig. 4. The rather mentedsphericalwave(ASW)method(seeRefs.31,32,33 complicated structure of both the electronic bands and and references therein). In the ASW method, the wave the DOS results from the energetical overlap of the rel- functionisexpandedinatom-centeredaugmentedspher- evant orbitals in the energy interval shown. While the icalwaves,whichareHankelfunctions andnumericalso- lower part of the spectrum is dominated by O 2p states, lutions of Schrödinger’s equation, respectively, outside the transition metal d states lead to rather sharp peaks and inside the so-called augmentation spheres. In order in the interval from −3.5eV to +2eV. In particular, we 3 ...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................k...............................................................................................................x.....................................................................................................................................................................................................................................................................................LM..................................................................................................................................................u.......u..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................uu..................................................................k(cid:0)A...................................................................................................................................z........................................................................................................................................................................................................................................................H.....................................................................................................................................................................................................................................................................................uu...............................................K........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................k......................................y DOS (1/eV) 3456789 CCoo 3P3Oddd t24e2pdgg FIG. 2: First Brillouin zone of the hexagonal lattice. 2 1 6 0 -10 -8 -6 -4 -2 0 2 4 6 4 (E - E ) (eV) F 2 V) 0 FIG. 4: (Color online) Partial densities of states (DOS) of ) (eF -2 PdCoO2. Selection of Co 3d orbitals is relative to the local E rotated reference frame, see text. E - -4 ( 4.5 -6 4 Pd 4dxy,x2-y2 -8 Pd 4dxz,yz 3.5 Pd 4d3z2-r2 -10 Γ M K Γ A L H A 3 ) V e 2.5 FIG. 3: (Color online) Electronic bandsof PdCoO2. (1/ S 2 O D 1.5 recognizethe t and e manifolds ofthe Co 3dstates as 2g g 1 resultingfromtheoctahedralcoordination. Inrepresent- ing these partialDOS we haveused a localrotatedcoor- 0.5 dinate system with the Cartesian axes pointing towards 0 theoxygenatoms. σ-typeoverlapoftheO2pstateswith -10 -8 -6 -4 -2 0 2 4 6 the Co 3d e orbitals leads to the rather sharp contribu- g (E - E ) (eV) tion of the latter near −5.8eV. In contrast, due to the F much weaker π-type overlap of the O 2p states with the t orbitals, these states give rise to sharp peaks in the FIG. 5: (Color online) Partial Pd 4d DOS of PdCoO2. 2g interval from −2eV to E . Since the Fermi energy falls F right between the t and e manifolds, Co turns out 2g g to be in a d6 low-spin state. Our results thus provide −6.2,−5.2,+0.6,1.5,and+4.2eVarecomplementedby further support to the picture that Co is trivalent while contributions of the O 2p partial DOS of similar shape Pd is in a monovalent d9 configuration11,12,13. Further- reflecting the strong σ-type d-p overlapalong the c axis. more, the Co and O states give only a tiny contribution In contrast, the short in-plane Pd-Pd distances of about totheelectricalconductivity,whichismaintainedalmost 2.83˚A(experimentalvalue),whichareonlyby3%longer exclusively by the Pd 4d states. The latter are further thanthoseinmetallicPd,leadtothebroadPddxy,x2−y2 analyzed in Fig. 5, which displays the five Pd 4d par- bands visible in the interval from −4.5 to 2eV in Fig. 5. tialDOS.SincePdislinearlycoordinatedbytwooxygen Inaddition,thesebandsgiverisetothelargestcontribu- atomsparalleltothe c axisandhassixPdneighboursin tion at E , whereas the d states do not contribute F xz,yz thea-bplaneweusedtheglobalcoordinatesystemtorep- at all. In contrast, the contribution from the d3z2−r2 or- resentthesepartialDOS.Withthischoice,contributions bitals is rather similar to that of the dxy,x2−y2 orbitals. from the dxy and dx2−y2 as well as from the dxz and dyz However,accordingtoak-resolvedanalysis,theirweights states are identical. The Pd 4d partialDOS are strongly vary on the Fermi surface. At about +0.6eV, the con- influenced by the aforementioned coordination. In par- tributionofthedxy,x2−y2 orbitalsis stronglysuppressed, ticular, the six peaks of the d3z2−r2 states near −8.0, and the small dispersion along the line M-K causes the 4 sharp d3z2−r2 peak seen in Fig. 5. 10 The strong quasi two-dimensionality of the electronic Pt 5d statesisreflectedbytheFermisurfacedepictedinFig.6. Co 3d t2g 8 Co 3d e Apartfromtheverysmallbendingparalleltothecdirec- g O 2p ) V 6 e 1/ ( S O 4 D 2 0 -10 -8 -6 -4 -2 0 2 4 6 (E - E ) (eV) F FIG. 7: (Color online) Partial densities of states (DOS) of PtCoO2. Selection of Co 3d orbitals is relative to the local rotated reference frame, see text. ladium system. However, the larger extent of the Pt 5d FIG. 6: (Color online) Fermi surface of PdCoO2. orbitals as compared to the Pd 4d states leads to an in- creased width mainly of the in-plane d bands as well as tion, it gives rise to completely in-plane Fermi velocities anincreasedoverlapofthesestateswiththe O2pstates. and explains the strong anisotropy in electric conductiv- Asaconsequence,theanisotropyoftheelectricalconduc- ity. However,notethat,accordingtotheelectronicbands tivity will be somewhat reduced in PtCoO as is indeed 2 shown in Fig. 3, the dispersion parallel to the direction observed11. Γ-A in general is not negligible. In passing, we mention In passing, we mention additional GGA+U calcula- the negligible dispersion along M-K, which is typical of tions for PdCoO , which however, confirmed the GGA 2 tight-binding bands in a triangular lattice. These bands results without any noticeable changes. give rise to the sharp peak at about +0.6eV in Fig. 5 and can thus be attributed to the Pd d3z2−r2 states. Overall, our results are in good agreement with the previous calculations by Seshadri et al. and by Okabe et IV. SUMMARY al.21,25. In particular, Seshadri et al. obtained a distri- bution of states at EF, whichis similar to ours. Further- In summary, we have shown that the strongly more, our results are in agreement with the photoemis- anisotropic metallic conductivity of PdCoO and 2 sion data by Tanaka et al. and Higuchi et al.12,17, who PtCoO is almost exclusively due to the Pd (Pt) layers. 2 attribute the metallic conductivity almost exclusively to In contrast, the octahedrally coordinated CoO sand- 2 the Pd 4d states. It has been argued by several au- wiches are insulating. As Co was found in a low-spin d6 thors, that the dominant contribution is due to the Pd configuration, these CoO complexes strongly suppress 2 d3z2−r2 orbitals, which hybridize with the Pd 5s states. theelectroniccouplingbetweenthePd(Pt)metalliclay- While we find indeed a 5s contribution of the order of ers, and the Co3+ layers merely act as charge reservoirs. 0.02states/eV, hence, of the order of 10% of the d3z2−r2 Inaddition,theypronouncethequasitwo-dimensionality partialDOSatEF,we stillpointto the in-planedxy and ofthesystem. Itmaybespeculatedhowtheintroduction dx2−y2 states,whichplayanevengreaterroleatEF than of impurities into the cobalt layers,i.e. replacing,e.g. Fe the d3z2−r2 states. As aconsequence,ourresultsdemon- or Ni for Co, alters the electronic properties locally and stratethatthemetallicconductivityismaintainedbythe might thus be used to design nano-structured materials. in-plane dxy anddx2−y2 orbitalsandthe in-plane partof Work along this line is in progress. In this context one the d3z2−r2 orbitals to a similar degree with a somewhat mightaskto what extentthe structuralchangesinduced greaterinfluence oftheformer. Thisfindingisconfirmed by the introduction of impurities with different covalent by the calculations for PtCoO2, where the DOS at EF is radii as compared to Co might be damped by the inter- again almost exclusively due to the in-plane states. mediate oxygen layers. This would provide a situation, In general, the partial DOS obtained for PtCoO , where chemical substitution only acts on the electronic 2 which are displayed in Fig. 7, resemble those of the pal- degrees of freedom. 5 V. ACKNOWLEDGEMENTS was supported by the Deutsche Forschungsgemeinschaft throughSFB484. Figs.1and6weregeneratedusingthe We gratefully acknowledge many fruitful discussions XCrysDen software (Ref. 39). with T. Kopp, C. Martin, and W. C. Sheets. 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