Pairing state in the rutheno-cuprate superconductor RuSr2GdCu2O8: A point contact Andreev Reflection Spectroscopy study

2.4 MB·English

by  Samanta Piano

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. Remarkably,forthejunctionsofbothFigs. 6,7thepe- anditsinterplaywithmagneticorderinunconventionalsuper-
culiarfeaturesofthespectratogetherwiththenormaljunction conductorslikerutheno-cuprates.
resistance,arerecoveredwhenthemagneticfieldisswitched
off,andnohysteresisisfoundforincreasing/decreasingfields.
Acknowledgments
VII. CONCLUSIONS
The authorsthank Y. Maeno, Y. Tanaka and G. Deutscher
WehaveanalyzedthePCARconductancespectraobtained forhelpfuldiscussionsandF.Vicinanzaforthetechnicalsup-
insuperconductingRuSr GdCu O (Ru-1212)policrystalline port.
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