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Structural and Magnetic Phase Transitions near Optimal Superconductivity

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Structural and Magnetic Phase Transitions near Optimal Superconductivity

PRL114,157002(2015)

PHYSICALREVIEWLETTERS

weekending17APRIL2015

StructuralandMagneticPhaseTransitionsnearOptimalSuperconductivity

inBaFe2ðAs1?xPxÞ2

DingHu,1XingyeLu,1WenliangZhang,1HuiqianLuo,1ShiliangLi,1,2PeipeiWang,1GenfuChen,1,*FeiHan,3

ShreeR.Banjara,4,5A.Sapkota,4,5A.Kreyssig,4,5A.I.Goldman,4,5Z.Yamani,6ChristofNiedermayer,7MarkosSkoulatos,7RobertGeorgii,8T.Keller,9,10PengshuaiWang,11WeiqiangYu,11andPengchengDai12,1,?

InstituteofPhysics,ChineseAcademyofSciences,Beijing100190,China2

CollaborativeInnovationCenterofQuantumMatter,Beijing,China

3

MaterialsScienceDivision,ArgonneNationalLaboratory,Argonne,Illinois60439,USA

4

AmesLaboratory,U.S.DOE,Ames,Iowa50011,USA

5

DepartmentofPhysicsandAstronomy,IowaStateUniversity,Ames,Iowa50011,USA

6

CanadianNeutronBeamCentre,NationalResearchCouncil,ChalkRiver,OntarioK0J1P0,Canada

7

LaboratoryforNeutronScattering,PaulScherrerInstitut,CH-5232Villigen,Switzerland8

HeinzMaier-LeibnitzZentrum,TechnischeUniversitätMünchen,D-85748Garching,Germany9

Max-Planck-InstitutfürFestkörperforschung,Heisenbergstrasse1,D-70569Stuttgart,Germany

10

MaxPlanckSocietyOutstationattheForschungsneutronenquelleHeinzMaier-Leibnitz(MLZ),D-85747Garching,Germany

11

DepartmentofPhysics,RenminUniversityofChina,Beijing100872,China12

DepartmentofPhysicsandAstronomy,RiceUniversity,Houston,Texas77005,USA

(Received22December2014;published17April2015)

Weusenuclearmagneticresonance(NMR),high-resolutionx-ray,andneutronscatteringstudiestostudystructuralandmagneticphasetransitionsinphosphorus-dopedBaFe2ðAs1?xPxÞ2.Previoustransport,NMR,specificheat,andmagneticpenetrationdepthmeasurementshaveprovidedcompellingevidenceforthepresenceofaquantumcriticalpoint(QCP)nearoptimalsuperconductivityatx¼0.3.However,weshowthatthetetragonal-to-orthorhombicstructural(Ts)andparamagnetictoantiferromagnetic(AF,TN)transitionsinBaFe2ðAs1?xPxÞ2arealwayscoupledandapproachTN≈Ts≥Tc(≈29K)forx¼0.29beforevanishingabruptlyforx≥0.3.TheseresultssuggestthatAForderinBaFe2ðAs1?xPxÞ2disappearsinaweaklyfirst-orderfashionnearoptimalsuperconductivity,muchliketheelectron-dopedironpnictideswithanavoidedQCP.

DOI:10.1103/PhysRevLett.114.157002

PACSnumbers:74.70.Xa,75.30.Gw,78.70.Nx

1

Adeterminationofthestructuralandmagneticphasediagramsindifferentclassesofironpnictidesuperconduc-torswillformthebasisfromwhichamicroscopictheoryofsuperconductivitycanbeestablished[1–5].TheparentcompoundofironpnictidesuperconductorssuchasBaFe2As2exhibitsatetragonal-to-orthorhombicstructuraltransitionattemperatureTsandthenordersantiferromag-neticallybelowTNwithacollinearantiferromagnetic(AF)structure[Fig.1(a)][3,4].UponholedopingviapartiallyreplacingBabyKorNa[6,7],thestructuralandmagneticphasetransitiontemperaturesinBa1?xAxFe2As2(A¼K,Na)decreasesimultaneouslywithincreasingxandformasmallpocketofamagnetictetragonalphasewiththec-axis-alignedmomentbeforedisappearingabruptlynearoptimalsuperconductivity[8–11].Forelectron-dopedBaðFe1?xTxÞ2As2(T¼Co,Ni),transport[12,13],muonspinrelaxation[14],nuclearmagneticresonance(NMR)[15–17],x-ray,andneutronscatteringexperiments[18–23]haverevealedthatthestructuralandmagneticphasetransitiontemperaturesdecreaseandseparatewithincreas-ingx[18–23].However,insteadofagradualsuppressiontozerotemperaturenearoptimalsuperconductivityasexpectedforamagneticquantumcriticalpoint(QCP)0031-9007=15=114(15)=157002(5)

[15,16],theAForderforBaðFe1?xTxÞ2As2nearoptimalsuperconductivityactuallyoccursaround30K(>Tc)andformsashort-rangeincommensuratemagneticphasethatcompeteswithsuperconductivityanddisappearsintheweaklyfirst-orderfashion,thusavoidingtheexpectedmagneticQCP[20–23].

AlthoughaQCPmaybeavoidedinelectron-dopedBaðFe1?xTxÞ2As2duetodisorderandimpurityscatteringintheFeAsplaneinducedbyCoandNisubstitution,phosphorus-dopedBaFe2ðAs1?xPxÞ2providesanalterna-tivesystemtoachieveaQCPsincesubstitutionofAsbytheisovalentPsuppressesthestaticAForderandinducessuperconductivitywithoutappreciableimpurityscattering[24–27].Indeed,experimentalevidenceforthepresenceofaQCPatx¼0.3inBaFe2ðAs1?xPxÞ2hasbeenmounting,includingthelineartemperaturedependenceoftheresis-tivity[28],anincreaseintheeffectiveelectronmassseenfromthedeHaas-vanAlpheneffect[26],magneticpen-etrationdepth[29,30],heatcapacity[31],andnormalstatetransportmeasurementsinsampleswheresuperconductiv-ityhasbeensuppressedbyamagneticfield[32].Althoughtheseresults,aswellasNMRmeasurements[33],indicateaQCPoriginatingfromthesuppressionofthestaticAF

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FIG.1(coloronline).(a)TheAF-orderedphaseofBaFe2ðAs1?xPxÞ2,wherethemagneticBraggpeaksoccuratQAF¼ð1;0;LÞ(L¼1;3;…)positions.(b)Temperaturedependenceoftheresistanceforthex¼0.31sample,whereRRR¼Rð300KÞ=Rð0KÞ?17.InpreviousworkonsimilarP-dopedsamples,RRR?13[28].(c)ThephasediagramofBaFe2ðAs1?xPxÞ2,wheretheOrt,Tet,andSCareorthorhombic,tetragonal,andsuperconductivityphases,respectively.TheinsetshowstheexpandedviewoftheP-concentrationdependenceofTs,TN,and,Tcnearoptimalsuperconductivity.Thecolorbarrepresentsthetemperatureanddopingdependenceofthenor-malizedmagneticBraggpeakintensity.ThedashedregionindicatesthemesoscopiccoexistingAFandSCphases.

ordernearx¼0.3,recentneutronpowderdiffractionexperimentsdirectlymeasuringTsandTNinBaFe2ðAs1?xPxÞ2asafunctionofxsuggestthatstructuralquantumcriticalitycannotexistatcompositionshigherthanx¼0.28[34].Furthermore,thestructuralandmagneticphasetransitionsatallstudiedP-dopinglevelsarefirstorderandoccursimultaneouslywithinthesensitivityofthemeasurements(?0.5K),thuscastingdoubtonthepresenceofaQCP[34].Whiletheseresultsareinteresting,theywerecarriedoutonpowdersamplesand,thus,arenotsensitiveenoughtotheweakstructuralormagneticordertoallowaconclusivedeterminationonthenatureofthestructuralandAFphasetransitionsnearoptimalsuperconductivity.InthisLetter,wereportsystematictransport,NMR,x-ray,andneutronscatteringstudiesofBaFe2ðAs1?xPxÞ2singlecrystalsfocusedondeterminingtheP-dopingevolutionofthestructuralandmagneticphasetransitionsnearx¼0.3.Whileourdataforx≤0.25areconsistentwiththeearlierresultsobtainedfrompowdersamples[34],wefindthatnearlysimultaneousstructuralandmagnetictransitionsinsinglecrystalsofBaFe2ðAs1?xPxÞ2occuratTs≈TN≥Tc¼29Kforx¼0.28and0.29(nearoptimaldoping)anddisappearsuddenlyatx≥0.3.Whilesuperconductivitydramaticallysuppressesthestatic

AForderandlatticeorthorhombicitybelowTcforx¼0.28and0.29,thecollinearstaticAForderpersistsinthesuperconductingstate.OurneutronspinechoandNMRmeasurementsonthex¼0.29samplerevealthatonlypartofthesampleismagneticallyordered,suggestingitsmesoscopiccoexistencewithsuperconductivity.Therefore,despitereducedimpurityscattering,P-dopedBaFe2As2hasremarkablesimilaritiesinthephasediagramtothatofelectron-dopedBaðFe1?xTxÞ2As2ironpnictideswithanavoidedQCP.

Wehavecarriedoutsystematicneutronscatteringexperi-mentsonBaFe2ðAs1?xPxÞ2withx¼0.19;0.25;0.28;0.29;0.30,and0.31[35]usingtheC5,RITA-II,andMIRAtriple-axisspectrometersattheCanadianNeutronBeamcenter,PaulScherrerInstitute,andHeinzMaier-LeibnitzZentrum(MLZ),respectively.Wehavealsocarriedoutneutronresonancespinecho(NRSE)measurementsonthex¼0.29sampleusingTRISPtriple-axisspectrometeratMLZ[36].Finally,wehaveperformedhigh-resolutionx-raydiffractionexperimentsonidenticalsamplesatAmesLaboratoryandAdvancedPhotonSource(APS),ArgonneNationalLaboratory(ANL)(seetheSupplementalMaterial[37]).OursinglecrystalsweregrownusingaBa2As2=Ba2P3self-fluxmethod,andthechemicalcompo-sitionsaredeterminedbyinductivelycoupledplasmaanalysiswith1%accuracy[35].WedefinethewavevectorQat(qx;qy;qz)asðH;K;LÞ¼ðqxa=2π;qyb=2π;qzc=2πÞreciprocallatticeunitsusingtheorthorhombicunitcellsuitablefortheAF-orderedphaseofironpnictides,wherea≈b≈5.6Åandc¼12.9Å.Figure1(b)showstemper-aturedependenceoftheresistivityforx¼0.31sample,confirmingthehighqualityofoursinglecrystals[28].Figure1(c)summarizesthephasediagramofBaFe2ðAs1?xPxÞ2asdeterminedfromourexperiments.Similartopreviousfindingsonpowdersampleswithx≤0.25[34],wefindthatthestructuralandAFphasetransitionsforsinglecrystalsofx¼0.19;0.28,and0.29occursimultaneouslywithinthesensitivityofourmea-surements(?1K).Onapproachingoptimalsuperconduc-tivityasx→0.3,thestructuralandmagneticphasetransitiontemperaturesaresuppressedtoTs≈TN≈30Kforx¼0.28;0.29andthenvanishsuddenlyforx¼0.3;0.31asshownintheinsetofFig.1(c).AlthoughsuperconductivitydramaticallysuppressesthelatticeorthorhombicityandstaticAForderinx¼0.28;0.29,thereisstillremnantstaticAForderattemperatureswellbelowTc.However,wefindnoevidenceofstaticAForderandlatticeorthorhombicityforx¼0.3and0.31atalltemperatures.SinceourNMRmeasurementsonthex¼0.29samplesuggestthatthemagneticordertakesplaceinabout?50%ofthevolumefraction,thecoupledTsandTNAFphaseinBaFe2ðAs1?xPxÞ2becomesahomogeneoussuperconductingphaseintheweaklyfirst-orderfashion,separatedbyaphasewithcoexistingAFclustersandsuperconductivity[dashedregioninFig.1(c)

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FIG.2(coloronline).[(a),(c),(e)]Wavevectorscansalongthe½H;0;3??directionatdifferenttemperaturesforx¼0.19;0.28,0.29,and0.31,respectively.Horizontalbarsindicateinstrumentalresolution.[(b),(d),(f)]TemperaturedependenceofthemagneticscatteringatQAF¼ð1;0;3Þforx¼0.19;0.28,and0.29,re-spectively.(g)NRSEmeasurementoftemperaturedependenceoftheenergywidth(Γisthefull-width-at-half-maximum(FHWM)ofscatteringfunctionand0indicatesinstrumentalresolutionlimited)atQAF¼ð1;0;3Þforx¼0.29.(h)Themagneticorderparametersfromthenormaltriple-axismeasurementonthesame

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sample.

temperaturedependenceofthescatteringat(1,0,3),revealingacontinuouslyincreasingmagneticorderparam-eternearTNandadramaticsuppressionofthemagneticintensitybelowTc.Figures2(e)and2(f)indicatethatthemagneticorderinthex¼0.29samplebehavessimilartothatofthex¼0.28crystalwithoutmuchreductioninTN.Onincreasingthedopinglevelstox¼0.3(SupplementalMaterial[37])and0.31[Fig.2(f)],wefindnoevidenceofmagneticorderabove2K.GiventhatthemagneticorderparametersnearTNforthex¼0.28;0.29sampleslookremarkablylikethoseofthespinclusterphaseinelectron-dopedBaðFe1?xTxÞ2As2nearoptimalsuperconductivity[22,23],wehavecarriedoutadditionalneutronscatteringmeasurementsonthex¼0.29sampleusingTRISP,whichcanoperateasanormalthermaltriple-axisspectrometerwithinstrumentalenergyresolutionofΔE≈1meVandaNRSEtriple-axisspectrometerwithΔE≈1μeV[36].Figure2(h)showsthetriple-axismodedatawhichrepro-ducetheresultsinFig.2(f).However,identicalmeasure-mentsusingNRSEmoderevealthatthemagneticscatteringabove30.7Kisquasielasticandthespinsofthesystemfreezebelow30.7Konatimescaleofτ??=ΔE≈6.6×10?10s[23].Thisspinfreezingtemperatureisalmostidenticaltothoseofnearlyoptimallyelectron-dopedBaðFe1?xTxÞ2As2[21–23].

Figure3summarizesthekeyresultsofourx-rayscatteringmeasurementscarriedoutonsamplesidenticaltothoseusedforneutronscatteringexperiments.TofacilitatequantitativecomparisonwiththeresultsonBaðFe1?xTxÞ2As2,wedefinethelatticeorthorhombicityδ¼ða?bÞ=ðaþbÞ[19,22].Figure3(a)showsthetemperaturedependenceofδforBaFe2ðAs1?xPxÞ2

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with

ToestablishthephasediagraminFig.1(c),wefirstpresentneutronscatteringdataaimedatdeterminingtheNéeltemperaturesofBaFe2ðAs1?xPxÞ2.Figure2(a)showsscansalongthe½H;0;3H??directionatdifferenttemper-aturesforthex¼0.19sample.TheinstrumentalresolutionlimitedpeakcenteredatQAF¼ð1;0;3Þdisappearsat99KaboveTN[Fig.2(a)].Figure2(b)showsthetemperaturedependenceofthescatteringatQAF¼ð1;0;3Þ,whichrevealsarathersuddenchangeatTN¼72.5Æ1Kcon-sistentwiththefirst-ordernatureofthemagnetictransition[34].Figure2(c)plots½H;0;0??scansthroughthe(1,0,3)Braggpeakshowingthetemperaturedifferencesbetween28K(4K)and82Kforthex¼0.28sample.Thereisaclearresolution-limitedpeakcenteredat(1,0,3)at28KindicativeofthestaticAForder,andthescatteringissuppressedbutnoteliminatedat4K.Figure2(d)showsthe

FIG.3(coloronline).Temperatureevolutionofδfor(a)x¼0.19and(b)x¼0.28samples.Thesolidcirclesindicatex-raydatawhereclearorthorhombiclatticedistortionsareseen.Theopencirclesaredatawhereonecanonlyseepeakbroadeningduetoorthorhombiclatticedistortion.Temperaturedependenceofthe½H;0;0??scansfor(c)x¼0.29and(d)x¼0.31.Theverticalcolorbarindicatesx-rayscatteringintensity.ThedatawerecollectedwhilewarmingthesystemfrombasetemperaturetoatemperaturewellaboveTs.

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x¼0.19,obtainedbyfittingthetwoGaussianpeaksinlongitudinalscansalongthe(8,0,0)nuclearBraggpeak(SupplementalMaterial[37]).Wefindthatthelatticeorthorhombicityδexhibitsafirst-order-likejumpbelowTs¼72.5Kconsistentwithpreviousneutronscatteringresults[34,37].Wealsonotethatthelatticedistortionvalueofδ≈17×10?4issimilartothoseofBaðFe1?xTxÞ2As2withTs≈70K[19,22].

Figure3(b)showsthetemperaturedependenceofδestimatedforthex¼0.28sample.Incontrasttothex¼0.19sample,weonlyfindclearevidenceoflatticeorthorhombicityinthetemperatureregionof26≤T≤32.5K[filledcirclesinFig.3(b)](SupplementalMaterial[37]).Theopensymbolsrepresentδestimatedfromtheenlargedhalf-widthofsinglepeakfits(SupplementalMaterial[37]).Althoughthedatasuggestareentranttetragonalphaseandvanishinglatticeorthorhombicityatlowtemperature,thepresenceofweakcollinearAForderseenbyneutronscattering[Figs.2(c)and2(d)]indicatesthattheAF-orderedpartsofthesampleshouldstillhaveorthorhombiclatticedistortion[19,22].Figures3(c)and3(d)showtemperaturedependenceofthelongitudinalscansalongthe½H;0;0??directionforthex¼0.29and0.31samples,respectively.Whilethelatticedistortioninthex¼0.29samplebehavessimilarlytothatofthex¼0.28crystal,therearenoobservablelatticedistortionsintheprobedtemperaturerangeforthex¼0.31sample.

Tofurthertestthenatureofthemagnetic-orderedstateinBaFe2ðAs1?xPxÞ2,wehavecarriedout31PNMRmeasure-mentsunderan8-Tc-axis-alignedmagneticfield(SupplementalMaterial[37]).Figure4(a)showsthetemperaturedependenceoftheintegratedspectralweightoftheparamagneticsignal,normalizedbytheBoltzmannfactor,forsinglecrystalswithx¼0.25and0.29.Forx¼0.25,theparamagneticspectralweightstartstodropbelow60Kandreacheszeroat40K,suggestingafullyorderedmagneticstatebelow40K.Forx¼0.29,theparamagnetictoAFtransitionbecomesmuchbroader,andthemagnetic-orderedphaseisestimatedtobeabout50%atTc¼28.5K.Uponfurthercooling,thepara-magneticspectralweightdropsdramaticallybelowTcbecauseofradiofrequencyscreening.WefindthatthelostNMRspectralweightaboveTcisnotrecoveredatotherfrequencies,suggestingthatthemagnetic-orderedphasedoesnottakefullvolumeofthesample,similartothespin-glassstateofBaðFe1?xTxÞ2As2[21–23].

Figure4(b)showstheP-dopingdependenceoftheorderedmomentsquaredM2inBaFe2ðAs1?xPxÞ2includingdatafromRef.[34].WhileM2graduallydecreaseswithincreasingxforx≤0.25,itsaturatestoM2≈0.0025μ2BattemperaturesjustaboveTcforx¼0.28and0.29beforevanishingabruptlyforx≥0.30.TheinsetinFig.4(b)showstheP-dopingdependenceoftheM2aboveandbelowTcnearoptimalsuperconductivity.While

FIG.4(coloronline).(a)Temperaturedependenceoftheparamagneticspectralweightforx¼0.25and0.29samplesfromNMRmeasurements.Forx¼0.25,therearenopara-magneticphasesbelow40K,suggestingafullymagnetic-orderedphase.AtTcofthex¼0.29sample,therearestill50%paramagneticphasessuggestingthepresenceofmagneticsignaloutsideoftheradiofrequencywindowoftheNMRmeasurement.ThespectralweightlossbelowTcisduetosuperconductivity.TheverticaldashedlinesmarkTNdeterminedfromneutronscattering.(b)TheP-dopingdependenceofM2estimatedfromnormalizingthemagneticBraggintensitytoweaknuclearpeaksassuming100%magneticallyorderedphase.ThebluesolidcirclesarefromRef.[34].TheP-dopinglevelsfordifferentexperimentsarenormalizedbytheirTNvalues.TheinsetshowstheexpandedviewofM2aroundoptimaldopingabove(solidsquares)andbelow(opensquares)Tc.(c)TheP-dopingdependenceofδ,wherethebluediamondsandgreensquaresarefromRefs.[34]and[28],respectively.Forsamplesnearoptimalsuperconductivity,thefilledandopenredcirclesareδaboveandbelowTc,respectively.

superconductivitydramaticallysuppressesM2,itdoesnoteliminatetheorderedmoment.Figure4(c)showstheP-dopingdependenceofδinBaFe2ðAs1?xPxÞ2belowandaboveTc.ConsistentwiththeP-dopingdependenceofM2[Fig.4(b)]andTN[Fig.1(c)],wefindthatδaboveTcapproaches?3×10?4nearoptimalsuperconductivitybeforevanishingatx≥0.3

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SummarizingtheresultsinFigs.2–4,wepresenttherefinedphasediagramofBaFe2ðAs1?xPxÞ2inFig.1(c).WhilethepresentphasediagramismostlyconsistentwiththeearliertransportandneutronscatteringworkonthesystematlowP-dopinglevels[30,34],wehavediscoveredthatthemagneticandstructuraltransitionsstilloccursimultaneouslyaboveTcforxapproachingoptimalsuper-conductivity,andbothorderparametersvanishatoptimalsuperconductivitywithx¼0.3.SinceourNMRandTRISPmeasurementsforsamplesnearoptimalsuper-conductivitysuggestsspin-glass-likebehavior,wecon-cludethatthestaticAForderinBaFe2ðAs1?xPxÞ2disappearsintheweaklyfirst-orderfashionnearoptimalsuperconductivity.Therefore,AForderinphosphorus-dopedironpnictidescoexistsandcompeteswithsuper-conductivitynearoptimalsuperconductivity,muchliketheelectron-dopedironpnictideswithanavoidedQCP.Fromthephasediagramsofhole-dopedBa1?xAxFe2As2[8–11],itappearsthataQCPmaybeavoidedthereaswell.WethankQ.SiforhelpfuldiscussionsandD.RobinsonforsupportofoursynchrotronX-rayscatteringexperimentatAPS.TheworkatIOP,CAS,issupportedbyMOST(973project:2012CB821400,2011CBA00110,and2015CB921302),NSFC(11374011and91221303),andCAS(SPRP-B:XDB07020300).TheworkatRiceUniversityissupportedbytheU.S.NSF,DMR-1362219,andbytheRobertA.WelchFoundationGrantNo.C-1839.ThisresearchusedresourcesoftheAPS,aUserFacilityoperatedfortheDOEOfficeofSciencebyANLunderContractNo.DE-AC02-06CH11357.AmesLaboratoryisoperatedfortheU.S.DOEbyIowaStateUniversitythroughContractNo.DE-AC02-07CH11358.WorkatRUCissupportedbytheNSFCunderGrantNos.11222433and11374364.

Noteadded.—WebecameawareofatheorypreprintpredictingthefirstorderAFphasetransitioninBaFe2ðAs1?xPxÞ2afterthesubmissionofthisLetter[38]

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