Pairingstateinthe rutheno-cuprate superconductor RuSr GdCu O : 2 2 8 A pointcontact Andreev reflection spectroscopy study S. Piano, F. Bobba, F. Giubileo and A. M. Cucolo, M. Gombos, A. Vecchione 6 Physics Department and INFM-CNR SUPERMAT Laboratory, 0 University of Salerno, Via S. Allende, 84081 Baronissi (SA), Italy 0 (Dated:February2,2008) 2 The results of Point Contact Andreev Reflection Spectroscopy on polycrystalline RuSr2GdCu2O8 pellets n arepresented. ThewidevarietyofthemeasuredspectraareallexplainedintermsofamodifiedBTKmodel a consideringad-wavesymmetryofthesuperconductingorderparameter. Remarkablylowvaluesoftheenergy J gap∆=(2.8±0.2)meV andofthe2∆/kBTc ≃2ratioareinferred. Fromthetemperatureevolutionofthe 0 dI/dV vsV characteristicsweextractasublineartemperaturedependenceofthesuperconductingenergygap. 3 Themagneticfielddependenceoftheconductancespectraatlowtemperaturesisalsoreported. Fromthe∆vs H evolution,acriticalmagneticfieldHc2 ≃30T isinferred. Toproperlyexplainthecurvesshowinggap-like ] featuresathighervoltages,weconsidertheformationofaJosephsonjunctioninserieswiththePointContact n junction,asaconsequenceofthegranularityofthesample. o c - PACSnumbers:74.50.+r,74.45.+c,74.20.Rp,74.72.-h r p u I. INTRODUCTION rationconditionswith some reportsshowingtransition onset s . ashighas50K6. TheRu-1212alsoshowsa magneticphase t a PointContactSpectroscopy1isaversatiletechniquewidely below135K. Ithasbeenreportedthatthemagneticorderof m used to study the basic properties of superconductors, such theRumomentsispredominantlyantiferromagneticalongthe - as the density of states at the Fermi level and the supercon- caxis7,whileaferromagneticcomponenthasbeenobserved d ductingenergygap. The techniqueconsistsin establishinga intheRuO2 planes,thatactaschargereservoir8. Atthemo- n contactbetweena tipof a normalmetal(N)anda supercon- ment,duetocomplexityofthiscompound,anexhaustivede- o c ductingsample(S),thusformingasmallcontactareathatisa scription of the interaction between the magnetic and super- [ “PointContact”junction. Byvaryingthedistanceand/orthe conductinglayersis still missing as wellas an unambiguous pressure between tip and sample it is possible to obtain dif- evaluationofthesymmetryoftheenergygap. 2 ferent tunnel barriers, that is different conductance regimes. Thepaperisorganizedasfollows: inSec.IIwebrieflyre- v 6 Indeed,quasiparticletunnelspectroscopyisobtainedforhigh viewtheresultsoftheBTKmodel9foraconventionals-wave 4 barriers, while Point Contact Andreev Reflection (PCAR) superconductorandtherecentextensions10 foranisotropics- 3 spectroscopy is achieved in case of low barriers. Often in waveandd-wavesymmetryoftheorderparameter.InSec.III 9 the experiments, intermediateregimesare realized, in which we describe the point contact experimentsin polycrystalline 0 throughtheN/Scontactbothquasi-particletunnelingandAn- Ru-1212pelletsshowingavarietyofconductancecurvesob- 5 dreevreflectionprocessesoccur. tained at T = 4.2K. Satisfactory theoretical fittings are 0 / AndreevReflections2,3takeplaceattheN/Sinterfacewhen achieved by using a modified BTK model for d-wave sym- at an electron, propagatingin the normalmetal with an energy metryoftheorderparameter. InSec.IVweshowthat,dueto m lower thanthe superconductingenergygap, entersin the su- thegranularityofthesamples,insomecases,theformationof perconductorformingan electron pair (Cooperpair) while a aJosephsonjunctioninserieswiththeN/Scontactoccurs.In- - d hole, with opposite momentum with respect to the incident deed,conductancecurvesshowinggap-likefeaturesathigher n electron,isreflectedinthenormalmetal. A singlereflection voltagesanddipsinthespectraarewellexplainedbythisas- o correspondstoanetchargetransferof2e,whereeistheelec- sumption.InSec.Vwereportthetemperatureevolutionofthe c troncharge,fromthenormalmetaltothesuperconductor. In conductancecurvesofaverystablejunction. Allthespectra : v the limitof lowbarriersat low temperatures,allthe incident arewellreproducedbythed-wavemodifiedBTKmodel,and Xi electrons at the N/S interface with energy eV < ∆ are An- weinferfromtheexperimentsthetemperaturedependenceof dreevreflectedandtheconductancedoublesthenormalstates thesuperconductingenergygap∆. InSec.VIweanalyzethe r a value. magnetic field behavior of the measured conductance spec- InthispaperwereportonPCARstudiescarriedoutinthe tra, providingan estimation of the upper critical field of the hybrid rutheno-cuprate RuSr GdCu O (Ru-1212) system4. Ru-1212 compound. Finally, in Sec. VII we summarize our 2 2 8 resultsanddrawsomeconclusions. Thiscompoundhasrecentlydrawngreatattentionamongthe- orists and experimentalists in the field of solid state physics due to the coexistence at low temperaturesof superconduct- ingandmagneticordering5. TheRu-1212structureissimilar II. THEBTKMODELANDITSEXTENSION tothatofYBa Cu O withmagnetic(2D)RuO planessub- 2 3 7 2 stitutingthe(1D)Cu-Ochains. Thesuperconductingcritical In this section, for sake of clearness, we review the main temperatureinthiscompoundstronglydependsontheprepa- resultsoftheoriginalBlonder-Tinkham-Klapwijk(BTK)the- 2 oreticalmodel9,asdevelopedforelectronictransportthrough a Point-Contactjunctionbetween a normalmetal and a con- Z = 0 Z = 0.5 Z = 5 s ventional BCS superconductor. We also summarize the 2m a) 3 b) 4c) -w Kashiwaya-Tanaka10extensionforasymmetrics-waveandd- VNor 2 3 av d1 2 e wavesuperconductors.Indeed,aclosecomparisonofthecal- dI/ 1 1 culatedconductancespectraisusefulforabetterunderstand- 0 0 0 ing of the peculiar transport processes that occur at an N/S -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3 interfacedependingonthesymmetryofthesuperconducting 2 d) 3 e) 4 f) d odrifdFfeeorrlelponawtriaainmlgceotthenred.uocrtiagnincaelcphaaprearc,twereiswticristefothreaeNx/pSrecsosniotancotfthtahte, dI/dV1Norm ==0/8 12 123 -wave =/4 accordingtotheBTKmodel9,isgivenby: 0 0 0 -3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3-3 -2 -1 0 1 2 3 eV/ eV/ eV/ a dI(eV) n GGNNNS(ZeV−+∞)∞=dE[d1V+A=(E)−B(E)](cid:20)−df(dE(e+Ve)V)(cid:21) (1) dI/dV12Norm g) ==0/8 12h) 1234 i) isotropic s-w =/4 a where eV is the applied potential, G = 4/(4 + Z2) is 0-3 -2 -1 0 1 2 30-3 -2 -1 0 1 2 30-3 -2 -1 0 1 2 3ve NN the normal conductance expressed in term of Z, a dimen- FIG. 1: Conductance characteristics, at low temperatures, for dif- sionless parameter modeling the barrier strength, f(E) is the ferentbarriersZ asobtainedbytheBTKmodelforaPointContact Fermi functionand A(E) and B(E) are, respectively, the An- junctionbetweenanormalmetalandas-wave(a,b,c),ad-wave(d,e,f) dreev reflection and normal reflection probabilities for an andananisotropics-wavesuperconductor(g,h,i). electron approaching the N/S interface. Eq.(1) shows that, whileordinaryreflectionsreducethetransportcurrentthrough thejunction,Andreevreflectionsincreasethisbytransferring E− E2−∆2 ± twoelectrons(Cooperpair)inthesuperconductingelectrode Γ± = q , (5) on the other side of the barrier. The case Z = 0 corre- ∆± sponds to a completely transparent barrier so that the trans- ∆± = ∆cos[2(α∓ϕ)]. (6) portcurrentispredominantlydueto Andreevreflectionsand G (V < ∆)/G (V >> ∆) = 2 is found(Fig.1a). By So,atagivenenergyE,thetransportcurrentdependsboth NS NN increasingZ,theAndreevreflectionsarepartiallysuppressed ontheincidentangleϕoftheelectronsattheN/Sinterfaceas andtheconductancespectratendtothecaseofaN/I/Stunnel well as on the orientationangle α, that is the angle between junctionshowingpeaksateV =±∆(Figs. 1b,c). thea-axisof thesuperconductingorderparameterandthe x- Recently, Kashiwaya and Tanaka10 extended the BTK axis.WhenapplyingEqs. (2)-(6)toPCARexperiments,there model by considering different symmetries of the order pa- isnopreferentialdirectionofthequasiparticleinjectionangle rameter. Indeed, for a d-wave superconductor, the electron- ϕintothesuperconductor,sothetransportcurrentresultsby likeandhole-likequasiparticles,incidentattheN/Sinterface, integration over all directions inside a semisphere weighted experience different signs of the order parameter, with for- by the scattering probability term in the current expression. mationofAndreevBoundStatesattheFermilevelalongthe Moreover,because our experimentsdeal with policrystalline nodaldirections.ThepresenceofAndreevBoundStatesmod- samples,theangleαisapureaveragefittingparameter,which ifythetransportcurrentandtheexpressionofthedifferential dependsontheexperimentalconfiguration. conductanceisgivenby: Incase ofd-wave symmetry,forZ → 0, the conductance curves at low temperatures show a triangular structure cen- +∞dE +π2 dϕσ(E,ϕ)cosϕ −df(E+eV) tered at eV = 0, quite insensitive to variations of α with GNS(V)= R−+∞∞dER−−π2df(E+eV) +π2 dϕσh (ϕd)(ceVos)(ϕi), (mFaigx.im1du)m.Haomwpelivteurd,efoGrhNiSgh(Verb=arr0ie)/rsG,tNheNc(oVnd>uc>tan∆ce)c=har2- R−∞ h d(eV) iR−π2 N (2) acteristics show dramatic changes as function of α. In par- ticular as soon as α 6= 0, the presence of Andreev Bound where StatesattheFermilevelproducesstrongeffectsmoreevident σ(E,ϕ)=σN(ϕ)(1+σN(1(ϕ+))(Γσ2+N+(ϕ()σ−N(1ϕ)Γ)+−Γ1−))(2Γ+Γ−)2, a0l)o/nGgNthNe(Vno>da>l d∆ir)ec>tio2nis(αfou=ndπ(/F4ig)sf.o1rew,f)h.ich GNS(V = (3) For comparison, we report the conductance behavior for isthedifferentialconductanceand anisotropics-wave superconductor,in whichonlythe ampli- tude of the order parameter varies in the k-space, while the phaseremainsconstantandEq. (6)reducesto: 1 σ (ϕ) = , Z˜(ϕ)=Zcos(ϕ), (4) N 1+Z˜(ϕ)2 ∆+ =∆− =∆cos[2(α−ϕ)]. (7) 3 Again, in the limit Z → 0, an increase of the conductance 1.6 1.3 forE < ∆with a triangularprofileisfoundwith maximum 1m.5 Z==00..468 a) Z==00..591 b) (aFmigp.l1itgu)d.eOGnNthSe(oVthe=rh0a)n/dG,NfoNrh(Vigh>er>Z,∆w)e=ob2taianttzuenrnoebliinags V1Nor.4 D=y2ne.s8=m0.e6VmeV 1.2 D=y3ne.s0=m0.e7VmeV d1.3 conductancespectra that show the characteristic “V”-shaped dI/1.2 1.1 profile in comparison to the classical “U”-shaped structure 1.1 foundforanisotropics-waveorderparameter(Figs.1h,i). We 1.0 1.0 notice that in this case all the curves are quite insensitive to -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 variationoftheαparameterandazerobiaspeakisobtained V(mV) V(mV) onlyforlowbarriers. 2.0 1.6 Z=0.85 c) d) IIEI.XPPECRAIMRESPNETCSTARNODSTCHOEPOYROENTRICUASLR2FGITDTCIUN2GOS8: dI/dV11Norm..24 D==y02ne..s46=3m0.e1V3meV 111 ...468 ZD===y020ne...s384=9m50meVeV ZRD===Jy/020nRe...s484P=C4m50=.e00V.80m5eV 1.2 IJ=30A 1.0 1.0 The Ru-1212 samples used for this study were direction- ally solidified pellets, grown by means of the Top-Seeded -15 -10 -5 0 5 10 150.8-15 -10 -5 0 5 10 15 V(mV) V(mV) Melt-Textured method starting from Ru-1212 and Ru-1210 (RuSr GdO )powdermixtureswitharatioRu-1212/Ru-1210 = 0.2.2The6details of the preparationprocedure are reported 1m.15 Z==00..3795 e) 22..02 Z==01..975 f) 1el2s1e2whpehraes.e11wIansthfoeuXnd-.RaIyn tdhieffrraecstiisotinviptyattmerenass,uaremsinegnltes vReur-- dV1Nor.10 RD=Jy/3nRe.s0P=Cm1=.e18V.m14eV 11..68 RD=Jy/3nRe.s0P=Cm0=.e31V.m5eV sus temperature, the onset of the superconducting transition dI/1.05 IJ=6.4A 11..24 IJ=30A was observed at Tocn ≃ 43K with Tc(ρ=0) ≃ 24K and 1.00 1.0 ∆T = 12K (∆T is defined as the difference between the 0.8 c c -40 -30 -20 -10 0 10 20 30 40 -40 -30 -20 -10 0 10 20 30 40 temperatures measured at 90% and 10% of the normal state resistance). Wenoticethatabroadeningofthesuperconduct- V(mV) V(mV) ingtransitionisoftenobservedinpolycrystallinesamplesand FIG. 2: (Color online) The dI/dV vs V characteristics measured itisusuallyrelatedtotheformationofintergrainweakJoseph- in different Ru-1212/Pt-Ir PC junctions at 4.2K. The experimental sonjunctions5,12,13. Weaddressthispointinthenextsection. data(dots)areshowntogetherwiththebesttheoreticalfittings(solid lines)obtainedbyamodifiedBTKmodelforad-wavesymmetryof To realizeourexperimentswe useda Pt-Ir tip, chemically thesuperconductingorderparameter. etchedina40%solutionofHCl,whileRu-1212sampleswere cleaned in an ultrasound bath in ethyl alcohol. Sample and tip were introduced in the PCAR probe, in which three mi- crometricscrewsareallocated,eachdrivenbyitsowncrank. structure, the main features appearing for each contact with Two screws allow to vary the distance between tip and sam- differentshapes, amplitudesandenergywidths. Quite often, ple, with a precision of 1µm and 0.1µm, respectively. The oscillationsare observedon the conductancebackground,as thirdscrewisdevotedtochangetheinclinationofthesample shownin Figs. 2 c–f. We observethatthe ZBCP appearsas holder varying the contact area on the sample surface. The a simple structure in Fig. 2b, while in the remaining spec- PointContactjunctionswereformedbypushingthePt-Irtip tra it results to be structured with variationsof slope or sec- on the Ru-1212 pellet surface with the probe thermalized in ondary maxima, as in Fig. 2e. The maximum conductance the liquid He4 bath. The Current-Voltage (I vs V) charac- ratio GNS(V = 0)/GNN(V >> ∆) is less than 2 for all teristics were measured by using a conventional four-probe the curves, howeverGNS(V = 0)/GNN(V >> ∆) ≃ 2.2 method and a lock-in technique with an amplitude of the ac for the data in Fig. 2f. In addition to this, the energywidth current less than 1µA was used to measure the differential ofthemainzerobiastriangularstructureislowerthan10mV conductance(dI/dV vsV)spectraasfunctionoftheapplied in Figs. 2a–d while it results wider, around 40mV, in Figs. voltage. 2e,f. At a first qualitative analysis, these data appear quite In Fig. 2, we show a variety of normalized conductance puzzlingandcouldbeinterpretedintermoflocal,largevari- spectra obtainedat T = 4.2K byestablishingdifferentcon- ations of the superconductingenergy gap. In the following, tactsondifferentareasofthesameRu-1212pellet. Thejunc- wewillshowthatthetheoreticalfittingsofallthespectragive tionresistancesvariedbetween10Ωand100Ω. Byusingthe clearindicationofad-wavesymmetryofthesuperconducting Sharvin relation,14 it has been possible to achive an estima- orderparameter,withconsistentvaluesoftheinferredampli- tion of the size of the contact area. Indeed R = ρl/4a2, tudeoftheenergygap. whereρ = 0.4mΩcmisthelowtemperaturesresistivityand Firstofall,letusquantitativelyanalyzethecurvesofFigs. l≈1000A˚,asestimatedinRef.11.Inourcase,wehavefound 2a–d. Wewerenotabletoreproducetheconductancespectra thatthetypicalcontactsizevariedbetween300A˚ and1000A˚. reportedinFig. 2a,bbyusingeithertheconventionals-wave We observe that all the reported spectra are characterized modelortheanisotropicone,evenbyconsideringsmallZval- by a Zero Bias Conductance Peak (ZBCP) with a triangular ues, indicativeof low barriers. On the otherhand, as can be 4 observedinFig.1,thes-wavefittingscannotmodelthestruc- tancecurvesreportedinFigs. 2e,f,withawiderZBCP.Inthis tured conductances reported in Figs. 2 c,d. The solid lines respect, we observe that, due to the granularity of the com- inthefiguresarethetheoreticalfittingsobtainedbyconsider- pound,insamecases,anintergrainJosephsonjunctioncanbe ingad-wavesymmetryoftheorderparameterinthemodified formedinserieswiththePointContactone,asschematically BTK model, Eqs. 2-6. A satisfactory agreementis obtained drawn in Fig. 3. This topic has been recently addressed in byusingasfittingparametersthesuperconductingenergygap PCARstudiesonMgCNi 17andMgB 18. 3 2 ∆,thebarrierstrengthZ,theangleαandaphenomenological To provide a quantitative evaluation of the conductance factorΓDynes15totakeintoaccountpairbreakingeffectsand spectra, we consider a real configuration in which the Pt-Ir finitequasiparticlelifetime16.Wenoticethatintheconsidered tiprealizesaPCjunctiononasingleRu-1212grain,which,in spectra, both quasiparticle tunneling and Andreev reflection turn,isweaklycoupledtoanothergrain,soformingaJoseph- processestake place, since intermediateZ valueshave to be sonjunction.Inthiscasethemeasuredvoltagecorrespondsto usedtosimulatethebarrierstrength(0.45≤Z ≤0.9).More- thesumoftwoterms: over,theangleαvariesbetween0.39and0.51,indicatingthat theaveragetransportcurrentmainlyflowsalonganintermedi- V (I)=V (I)+V (I), (8) measured PC J atedirectionbetweenthenodalone(α=π/4)andthatofthe maximumamplitudeoftheenergygap(α=0).Themodified whereV andV arethevoltagedropsattheN/SPointCon- d-waveBTKmodelallowstosatisfactorilyreproducethevari- PC J tactjunctionandattheS/I/SintergrainJosephsonjunction,re- ationsofslopearound±1mV ofthestructuredZBCPinFigs. spectively.ThislastcontributioncanbecalculatedbytheLee 2a,c,dwithalightdiscrepancyinmodelingthefullheightof formula19which,inthelimitofsmallcapacitanceandatlow thepeakinFig. 2d. Weshowinthenextsectionthatamore temperatures,reducestothesimplifiedexpression20: satisfactory fitting for this contactcan be obtainedby taking intoaccountanadditionalinseriesintergrainjunction. 0 forI <I ; We remark that the values of the superconducting energy V = J (9) gap, inferred from the theoretical fittings, are all consistent J (cid:26)RJIJ [(I/IJ)2−1] forI ≥IJ . andenableustoestimateanaveragevalueoftheamplitudeof p theorderparameter∆=(2.8±0.2)meV. Thisvalueissur- Atthe same time, forthe PointContactcontribution,we use prisinglylowincomparisonwiththeamplitudeoftheenergy againtheextendedBTKmodelforad-wavesuperconductor. gapinothercupratesuperconductors,howeverthepossibility TheI(V)characteristicisthencalculatedbyinvertingEq.(8) that the presence of the RuO magnetic planes can play an andtheconductancespectrumisgivenby: 2 importantroleinthecomplexRu-1212systemhastobetaken into account. We notice that the ratio between the smearing dI dV dV −1 PC J factorΓDynes andthesuperconductingenergygapresultsal- σ(V)= = + . (10) dV (cid:18) dI dI (cid:19) ways less than 20% and it vanishes for the fitting shown in Fig. 2d. We consider this fact as an indication of the good By applying this simple model we have satisfactory fitted qualityofourpoint-contactjunctions. the experimental data reported in Figs. 2e,f. Remarkably, for both spectra, the best fittings have been obtained by us- ing ∆ = 3.0 meV, consistently with the average value ex- IV. ROLEOFTHEINTERGRAINCOUPLING tractedfromtheothercurvesinFigs. 2a–d. Weobservethat, inthismodel,twomoreparametersareneeded,namelythere- To complete our discussion about the spectra measuredat sistanceR andthecriticalcurrentI oftheJosephsonjunc- J J lowtemperatures,wenowaddresstheanalysisoftheconduc- tion.However,thechoiceofthesetwoparametersisnotcom- pletelyarbitrary,sincetheconditionR +R = R has J PC NN tobefulfilled,whereR isthemeasurednormalresistance NN tip N I andtheproductRJIJ necessarilyresultslowerthan∆21. Insomecases,ithasbeenpointedoutthatdipsinthecon- ductance spectra can be related to the presence of intergrain VPC junctions17,18,andforsakeofcompleteness,wehaveapplied grain S ourmodelalso to the spectra of Figs. 2 a–d. We notice that N/I Vmeasured for different junctions, the effect of the intergrain coupling V J results more or less evident, depending on ratio R /R . grain S For the conductances shown in Figs. 2a–c this effeJct tuPrCns outto benegligible,however,some improvementofthe the- oreticalfitting is obtainedin the case of Fig. 2d (see dashed FIG.3: (Color online) Intergrain coupling effect inpolycrystalline line). Remarkably,bythislastfittingwehavefoundthesame samples. ThemeasuredvoltageVmeasuredisthesumoftwoterms: valueofthesuperconductingenergygappreviouslyinferred, VPC, the voltage drops between tipand sample, the N/S PC junc- ∆ = 2.8meV, with a ΓDynes/∆ ratio less than 3% and tion,andVJ,thevoltagedropsbetweentwosuperconductinggrains, R /R =0.05. formingtheS/I/SJosephsonjunction. J PC 5 V. TEMPERATUREDEPENDENCEOFTHE 2.0 CONDUCTANCESPECTRA T To achieve informationon the temperature dependenceof thesuperconductingenergygapintheRu-1212system,inthis 1.0 4.4K section we analyze the temperature behavior of the conduc- 4.7K tancespectrumshowninFig. 2d. Indeed,thisPCARjunction resultedtobeverystablefortemperaturevariations. 5.0K InFig.4weshowtheconductancecharacteristicsmeasured 5.6K in the temperaturerange4.2K ≤ T < 35K. We firstly no- tice that the ZBCP decreases for increasing temperatureand m 6.3K disappearsat aboutT ≃ 30K, that we estimate as the local or N 7.9K criticaltemperatureTl ofthesuperconductingRu-1212grain V c d in contact with the Pt-Ir tip, consistently with the resistivity I/ 10.4K measurements11. Thisfactprovidesfurtherevidencethatthe d ZBCPisaconsequenceofthesuperconductingnatureofRu- 13.7K 1212andisnotduetospuriouseffectslikeinelastictunneling 17.5K via localized magneticmomentsin the barrierregion22. The experimentaldataforeachtemperaturearethencomparedto 21.8K the theoretical fittings calculated by using the d-wave modi- 22.5K fiedBTKmodelwithasmallcontributionofJosephsonjunc- tioninseries. Forallthecurves,wefixedthestrengthofthe 28.2K barrier and the angle α to the values obtained at the lowest 33.8K temperature. Theresultingtemperaturedependenceofthesuperconduct- -15 -10 -5 0 5 10 15 ing energy gap ∆(T) is reported in Fig. 5, where vertical V(mV) bars indicate the errors in the gap amplitude evaluation, that FIG. 4: (Color online) Temperature evolution of the conductance increasewhenapproachingthecriticaltemperature. Contrar- spectrum of Fig. 2c from T = 4.2K to up the critical tempera- ily to what expected for BCS superconductors, we observe ture(dots). Thesolidlinesarethetheoreticalfittingsobtainedbya thattheenergygap,atlowtemperatures,decreasesrapidlyfor modified d-wave BTK model with the energy gap as only free pa- increasing temperatures and goes to zero at Tl in a sublin- c rameter. ear way. We notice that the same temperature evolution for the superconducting energy gap is found trough the d-wave BTK modelwith orwithoutconsideringanyintergrainjunc- tioninseries;remarkably,inthislastcase,thesuperconduct- ingenergygap∆remainstheonlyvaryingparameter.Asim- 3.0 1.0 ilartemperaturedependencehasbeenreportedbyG.A.Um- G GNS(0,T)/GNS(0,T=4.2K) NS marinoetal.23,howevertheseauthorsgivealargerestimation 2.4 0.8 (0 ofthemaximumgapamplitude. ,T V) )/G Fromtheaveragevalueofthesuperconductingenergygap (me11..28 00..46 NS(0,T= ∆pmeurac=thurs2em.8aTlcllmere≃tVha3na0ntKdhe,frpwormeedoitchbteteadimnBeCaasSruarvteiaodlu2leo∆caan/ld(kcaBrlistToiccla)sml ≃taelmle2-r 4.2 thanthevaluesfoundforhigh-Tc cupratesuperconductors24. 0.6 0.2 K) Againwe speculate thatthe simultaneouspresenceofsuper- conducting and magnetic order is an important key for un- 0.0 0.0 derstanding the behavior of the Ru-1212 system. Coexis- 0 5 10 15 20 25 30 35 tence of superconductivity and antiferromagnetism is found T(K) amongcuprates,howeveritiscommonbelievethatferromag- FIG.5:(Coloronline)Temperaturedependenceofthesuperconduct- netism and superconductivityare mutually excludingorders. ingenergygapasinferredfromthetheoreticalfittingsshowninFig. Recently, it has been found that in conventional Supercon- 4. Thesolidlineisaguidefortheeyes. Therighthandscalerefers ductor/Ferromagnetic (S/F) structures, proximity effect give to the temperature evolution of the measured height of the ZBCP risetoanoscillatorybehaviorofthesuperconductingT asa c normalizedtothe4.2Kvalue. function of the thickness of the F layer25,26. There are con- ditionsforwhichachangeofsignoftheorderparameteroc- curs,producingtheπ-junctionphenomenon27. Inadditionto this,adramaticsuppressionoftheamplitudeoftheorderpa- rameterisexpectedforhighT superconductorsinclosecon- c 6 tactwithaferromagneticmaterial28 andvariousexamplesof the other hand, as observed in Muon Spin Rotation (µSR) anomalous temperature behavior are found in the literature. experiments8, they show quite homogeneous ferromagnetic Gaplesssuperconductivitycanbeachieved,thatcaninducea orderbelowT . Aweakinteractionbetweenthetwoorderpa- c sublineartemperaturedependenceofthesuperconductingen- rameters,ferromagnetismintheRuO planesandsupercon- 2 ergygap. IntheRu-1212system,ithasbeenprovedthatthe ductivityintheCuO planes,hasbeensuggestedandrecently 2 RuO planes are conducting, however these do not develop severalexperimentsappeartoconfirmthishypothesis29. De- 2 superconductivityat any temperature29. By means of differ- spiteofthehugeexperimentalandtheoreticaleffortsfocused entexperimentaltechniques,it hasbeeninferredthat a large on the study of the interplay between superconductivityand fractionof the chargecarriersis notcondensedin the super- magnetism, to the best of our knowledge no spectroscopic conductingstateevenatlowtemperatures29.Bothfindingsare studiesinmagneticfieldofthesuperconductingorderparam- consistentwithareducedvalueofthe2∆/(k T )ratiointhis eterinRu-1212havebeenreportedinliteraturesofar. B c compound. In Fig. 6 we show the PCAR spectra measured by apply- In Fig. 5 we also report(righthandscale) the temperature ing an external magnetic field, parallel to the tip, with in- evolutionoftheheightoftheZBCPnormalizedtoitsvalueat tensity H varying from 0T to 2T. The dI/dV vs V curves T = 4.2K. ItisworthtonoticethatG (V = 0,T),asdi- refer to the contact reported in Fig. 2b. A reduction of the NS rectlymeasuredfromtheexperiments,and∆(T),asinferred ZBCPforincreasingmagneticfieldsisobserved,thatinfirst fromthetheoreticalfittings,showasimilarscalingwithtem- approximationcanbereproducedbyaphenomenologicalap- perature. This correspondence is easily verified for Z = 0 proach. Indeed,addressingtheproblemofthemagneticfield incaseofas-wavesuperconductor,howeveritisaquitenew dependenceoftheconductancecharacteristicsisnonconven- resultsinceithasbeenfoundforintermediatebarriersandun- tionalsuperconductors,isaquitedifficulttaskandacomplete conventionalsymmetryofthesuperconductingorderparame- treatmentofPCARspectroscopyinmagneticfieldwouldre- ter. quiretheuseofanappropriatedensityofstatesincalculating theBTK expressionforthe reflectionandtransmissioncoef- ficientsattheN/Sinterface. Dueto thelack ofananalytical model,Miyoshietal.33 presentedatwofluidmodeltorepro- VI. MAGNETICFIELDDEPENDENCEOFTHE ducethe effectof normalvortexcoresin PCAR junctionsin CONDUCTANCESPECTRA conventionalsuperconductors,assumingthatthecontactarea contains multiple randomly distributed individual junctions As we already observed, one of the most interesting fea- (non-Sharvinregime14). These authors propose a simplified tures of the Ru-1212is the coexistenceof the superconduct- expression for the conductance, written as a sum of normal ing phase and magnetic order. Indeed, from Nuclear Mag- andsuperconductingchannels: netic Resonance (NMR)30,31 and magnetization32 measure- ments,ithasbeenfoundthatinthiscompoundrutheniumoc- G (V)=(1−h)G +hG (V) NStot NN NS cursinamixedvalencestateRu4+,Ru5+ withsomehigher Ru5+ concentration. The RuO2 planes, from one side, act where h = H/Hc2 and Hc2 is the critical field. This ap- aschargereservoirforthesuperconductingCuO planes,on proach,however,cannotbe appliedto ourexperimentssince 2 we dealwith policrystalline,unconventionalsuperconductor, exhibitinginternalmagneticordering. In this case, the mag- netic induction B is not simply proportional to the external magneticfieldH andasaconsequencethedensityofvortices 1.25 H=0T 3.0meV) isnotlinearlyrelatedtoH. ( An alternative way to perform a theoretical fitting is ob- 1.20 H=2T 2.9 tainedbyusinganadditionalpairbreakingparametertosim- m ulate the effect due to the magnetic field34,35. In this case, VNor 1.15 2.8 0.0 0.5 1.0 1.5 2.0 the total broadening effect Γ is considered as the sum of d H(T) two terms: Γ = ΓDynes +Γext where ΓDynes is the intrin- dI/ 1.10 sic broadening due to the quasiparticle lifetime, as used in 1.05 thepreviousfittings,whileΓext mimicsthepairbreakingef- fectdue to the externalappliedmagnetic field. The curveat 1.00 H = 0T (see Fig. 2b) has been fitted by using the d-wave modified BTK model with ∆ = 3.0 meV. For increasing 0.95 magneticfieldswekeepconstant,inthenumericalcomputa- -10 -5 0 5 10 tion,thestrengthofthebarrierZ =0.9,theorientationangle V(m V) α=0.51andtheintrinsicΓDynes =0.7meV,whilevarying FIG.6: (Coloronline)Magneticfielddependenceofthenormalized onlytwoparameters:theenergygap∆andthemagneticfield dI/dV vs V characteristics at T = 4.2 K from 0 T to 2 T (dots) effectΓext. Weobservethatthebesttheoreticalfittings(solid forthespectraofFig. 2b. Thefulllinesarethetheoreticalfittings linesinFig. 6)satisfactorilyreproduceforanyfieldboththe obtainedasdiscussinthetext.Intheinsetthemagneticfielddepen- heightandtheamplitudeofthemeasuredspectra.Intheinset, denceoftheenergygapisreported. wereportthemagneticfielddependenceofthesuperconduct- 7 pellets. Alltheconductancecurvesatlowtemperaturesshow 1.16 0T a Zero Bias Conductance Peak that decreases for increasing 1.14 1T temperaturesand disappears at the local critical temperature 2T Tl ≃ 30K of the superconductinggrain in contact with the 1.12 2.5T c Pt-Irtip. Thetriangularshapeofallthemeasuredspectrahas 0T field switched off 1.10 beenmodeledby usinga modifiedBTK modelfor a d-wave ) -1 1.08 symmetryofthesuperconductingorderparameter. Thisfind- V( ingsuggestsaclosersimilarityoftheRu-1212systemtothe d 1.06 dI/ high Tc cuprate superconductorsrather than to the magnetic 1.04 ruthenateSr RuO compound. However,theremarkablylow 2 4 valuesoftheenergygap∆=(2.8±0.2)meV andofthera- 1.02 tio2∆/k T ≃2indicatemajordifferencesbetweentheRu- B c 1.00 1212andthehighT cuprates.Wespeculatethatthepresence c 0.98 of ferromagneticorder within the superconductingphase re- -60 -40 -20 0 20 40 60 sultsinaneffectivereductionoftheenergygap.Wehavealso V(mV) demonstratedthat,whendealingwithgranularsamples,inter- FIG.7: Normalized conductance curves for the contact of Fig. 2e grain couplingeffectscan play a predominantrole. In some measuredatT =4.2Kinmagneticfieldupto2.5T.Whenthefield cases,anintergrainJosephsonjunctioninserieswiththepoint isswitchedoff,theoriginalspectraarerecovered. contactjunctionisformed.Takingintoaccountthisfeatureas well,allconductancespectrahavebeenproperlymodeledby consideringa d-wavesymmetryof theorderparameter,with ingenergygap(dots)asextractedfromthetheoreticalfittings. consistentvaluesoftheamplitudeoftheenergygap. TheamplitudeoftheenergygapreduceslinearlyforH upto By fixing all the fitting parameters to their values at the 2Tandby a linearextrapolationofthe data, we findthatthe energy gap disappears at about Hext ≃ 30 T, consistently lowestmeasuredtemperature,andbyvarying∆,thetempera- withtheestimatedcriticalfieldreportedinRef.11. turedependenceoftheenergygaphasbeenextractedfromthe conductancecharacteristicsofaverystablejunction.Wehave Wehavealsostudiedtheeffectofthemagneticfieldonthe foundthattheenergygapexhibitsasub-lineardependencein conductance characteristics of the junctions showing wider temperature. The magnetic field behavior of the spectra has ZBCP, that are formedby two junctionsin series. In Fig. 7 been also studied, showing a linear reduction of the energy we reportthe dI/dV vs V curves measured up to 2.5 T for thecontactsofFig. 2e. Inthiscase,weobservethatthecon- gapforfieldsupto2T,fromwhichacriticalfieldHc2 ∼ 30 T is inferred. We have found that both the superconducting ductance curves dramatically change with the application of featuresandthenormalbackgroundintheconductancespec- the magnetic field. As discussed in the previoussection, the tradonotshowanyhysteresisinmagneticfield. Theseobser- Josephson current due to the intergrain coupling is immedi- vationsseem to suggesta weak couplingbetween the super- atelysuppressedbythemagneticfield,modifyingthespectra conductingandmagneticorderparameter. towardsthe narrower,non-structured,triangularshape ofthe ZBCP.Inadditiontothis,theoscillatorybehavioroftheback- Ouranalysismaybehelpfulforadeeperunderstandingof ground,duetotheintergraincouplingdisappearsinmagnetic themechanismsenablinghightemperaturesuperconductivity, field. 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