6 0 0 2 n Na CoO :Enhancedlow-energyexcitationsofelectronsona2D a x 2 J triangularlattice 5 2 ∗ M.Bru¨hwilera, B.Batlogga S.M.Kazakova Ch.Niedermayerb J.Karpinskia l] aLaboratoryforSolidStatePhysics,ETHZu¨rich,CH-8093Zu¨rich,Switzerland e bLaboratoryforNeutronScattering,PaulScherrerInstitute,CH-5232VilligenPSI,Switzerland - r t s . at Abstract m Toelucidatethelow-energyexcitationspectrumofcorrelatedelectronsona2Dtriangularlattice,wehavestudied - d theelectricalresistanceandspecificheatdownto0.5Kandinmagneticfieldsupto14T,inNaxCoO2sampleswith n aNacontentrangingfromx≈0.5to0.82.Twodistinctregimesareobserved:forxfromabout0.6tox≈0.75the o specificheatisstronglyenhanced,withapronouncedupturnofCp/T belowabout10K,reaching47mJ/(molK2). c This enhancement is suppressed in a magnetic field indicative of strong low-energy spin fluctuations. At higher [ Na content the fluctuations are reduced and µSR data confirm the SDW ground state below 22K and the much reducedheatcapacityisfieldindependent. 1 v 0 8 Keywords: NaxCoO2,spinfluctuations,thermodynamicproperties,triangularlattice,SDW,muonspinrotation 5 1 0 In light of the complexity of the ground state due namicsoftheitinerantelectrons.Thisadditionalcom- 6 togeometricfrustrationamonglocalizedmagneticmo- plexitybecomesevenmorerelevantbecauseofthepar- 0 mentsresidingonatriangularlattice,[1]itisofpartic- tialmobilityoftheNaionsevenatambientandmod- / t ularinterest tostudythelow-energy physicsof corre- estlyelevatedtemperature,andtheresultingpossibil- a m lated electrons as they acquire some itineracy on the ityfor theNa ions toorder. The CDW-likeelectronic triangularlattice.NaxCoO2 ismetallic, crystallizesin stateisaclearexampleasithasbeenassociatedwitha - d alayeredstructurewithedge-sharingCoO2octahedra, stripe-likeorderingoftheNaions,[7]andseveralindi- n andCooccupiesatriangularlattice.Originallyknown cationsforNa-orderingatothervaluesofxhavebeen o foritsunusuallylargethermoelectriceffect[2]thiscom- observed(e.g.Ref.[8]).Thusitwillbedesirabletoiden- c pound exhibits a rich phase diagram as a function of tifytheinfluenceoftheFermilevelshiftandthatofthe : temperatureandNacontent.Particularly notableare interactions with the Na ions, even as there is reason v i the superconductivity in water-intercalated material to expect some interplay between them.[9,10] In this X (xnear0.3to0.4),[3]aCDW-likestatenearx=0.5,[4] reportwefocusonthecompositionrangewhereNaor- r andaSDW-likestatenearx=0.8.[5,6] dering appears not to dominate the electronic states, a WhilechangingtheelectroncountintheCoO2layer atleastnotonthelevelasitdoesatx=0.5. byvariationoftheNacontentappearsbothsimpleand Thespecificheatandelectricalresistivityweremea- effective,itisalsotobeexpectedthattheCoulombin- sured in aQuantumDesign PPMS setup with a He-3 teractionwiththeNaionswillinfluencethechargedy- insertanda14Tmagnet.Polycrystallinesampleswere synthesized in a traditional way and the Na content wasconfirmedbytheunitcellparameters,inparticu- ∗ Corresponding author. Tel: +41 44 633 23 39 fax: +41 44 lar by thec/a ratio. µ+SR studies were performed at 6331072 thePaulScherrerInstituteandwereparticularlyhelp- Emailaddress: [email protected] fultocheckthemagnetichomogeneityofthesamples. (M.Bru¨hwiler). PreprintsubmittedtoElsevierScience 6February2008 the measured electronic Cp/T for the superconduct- ing compound at lower x,[13] or the x = 0.82 sam- 90 70 plealso shown inthefigure.Forcomparison, anearly 60 LDAcalculationforNa0.5CoO2gaveaCp/T ofroughly 80 50 11mJ/(molK2).[14]ThemeasuredCp/T thussuggests 2 ) 40 two contributions to the low-energy excitation spec- /K 70 30 trum.Onewithatypicalenergyscaleofabout1meV, mol 20 which is suppressed in a magnetic field, and an other J/ 60 10 thatextendstoasignificantlyhigherenergy. m The situation is different at higher Na composition 0 ( 50 0 T 0 5 10 15 20 25 whereaSDWdevelops,markedbyadistinctanomaly T / at 22K.[6,12] In the present study we have focused )uc 40 x = 0.64 on the low-T region and the dependence on a mag- n C netic field. The µ+SR results of such a sample reveal -p 30 theexcellent qualityin terms of themagnetic volume C 14 T fraction. Afitoftheµ+SRdatausingthreeexponen- ( 20 tial relaxation functions and a KuboToyabe function x = 0.82 indicates that over 80% of the muons experience a 10 staticmagneticfield.Belowabout2KCp/T saturates andat0.5Kamountsto11mJ/(molK2).Interestingly, 0 within theexperimentaluncertaintyof a few percent, 1 10 this value remains constant in fields up to 14T. The T (K) same also holds truefor theentiretemperaturerange covered:It isworth notingthat neitherthetransition Fig.1. Low-temperaturespecificheatCp/T oftwoNaxCoO2 temperature at 22K nor the broad hump near 5 to samplesrepresentingtheregionsofcontrastingelectroniclow-T 10K,whichhasbeenassociatedwithanothermagnetic states.Thenuclearcontributionhasbeensubtractedforclar- transition,[12]aremodifiedinafieldupto14T. ity.Thex=0.64sampleisfromthebroadcompositionregion where Cp/T increasesbelowabout 10K, indicativeof strong The low-temperature electrical resistivity ρ in the lowenergyspinfluctuations,whicharesuppressedbyamag- spinfluctuationregion(x=0.7)significantlydeviates neticfield.The x=0.82 sample undergoesaSDW-like tran- from a T2 behavior. At low T, it follows a tempera- isnititohneaspti2n2-flKu.ctTuhaetiolonwr-eTgiovna,luaendofisCnpo/tTiniflsumenucchedlobwyearmthaagn- ture dependence ρ = ρ0+A˜Ta, with a smaller than neticfield.TheinsetshowsthesamedataonalinearT scale. 2.Theexponentastartsatabout1.3inzerofieldand increases rapidly with increasing field reaching about Theessential features of thelow-T specificheat for 1.8at14T. two representative compositions are shown in the fig- This study was partly supported by the Swiss Na- ure.Awelldefinednuclearcontributionstemmingpre- tionalScienceFoundation. dominantly from Co has been subtracted for clarity. Thesamplewithx=0.64isrepresentativeofsamples with a sodium content in the range from x ≈ 0.6 to x ≈ 0.75. Zero field µ+SR spectra down to 1.7K in a x=0.7sampleindicatetheabsenceofmagneticorder. References Forthiscomposition range,thespecificheatrevealsa [1] A.P.Ramirez,Annu.Rev.Mater.Sci.24(1994)453–480. highdensityoflowenergyexcitations,givingrisetoan increase of Cp/T below about 10K to reach values as [2] I.Terasakietal.,Phys.Rev.B56(1997)R12685. large as 47mJ/(molK2), which has been observed in [3] K.Takadaetal.,Nature422(2003)53–55. variousstudies(e.g.[11,12]).Additionalinsightscome [4] M.L.Fooetal.,Phys.Rev.Lett.92(2004)247001. frommeasurementsinanexternalmagneticfield.Ina [5] J.Sugiyamaetal.,Phys.Rev.B67(2003)214420. magnetic field,these excitations aresignificantly sup- pressed, shown in thefigure as the set of data for 0T [6] T.Motohashietal.,Phys.Rev.B67(2003)064406. to 14T with 2T intervals. The suppression tends to [7] H.W.Zandbergenetal.,Phys.Rev.B70(2004)024101. saturateinhighfieldsandfromanextrapolationato- [8] J.L.Gavilanoetal.,Phys.Rev.B69(2004)100404. tal reduction by about 20mJ/(molK2), correspond- [9] M.Indergandetal.,cond-mat/0502116. ingtoasmuchas43%,canbeestimated.Apparently, [10]P.Zhangetal.,cond-mat/0502072. thelow-energyexcitationsareofmagneticorigin.The residualvalueofCp/T is26to28mJ/(molK2)andit [11]M.Bru¨hwileretal.,cond-mat/0309311. isstillenhancedbyaboutafactoroftwocomparedto [12]H.Sakuraietal.,J.Phys.Soc.Japan73(2004)2393. 2 [13] R.Jinetal.,Phys.Rev.Lett.91(2003)217001. [14] D.J.Singh,Phys.Rev.B61(2000)13397. 3