AC/DCSusceptibilityoftheHeavy-FermionSuperconductorCePt3SiunderPressure
YoshihiroAoki1,AkihikoSumiyama1∗,GakuMotoyama1,YasukageOda1,TakashiYasuda2,RikioSettai2
andYoshichikaOnuki
¯21
DepartmentofMaterialScience,FacultyofScience,UniversityofHyogo,Ak¯o-gun678-1297
2
GraduateSchoolofScience,OsakaUniversity,Toyonaka560-0043
(ReceivedFebruary1,2008)
Wehaveinvestigatedthepressuredependenceofacanddcsusceptibilities(χacandχdc)oftheheavy-fermionsuperconductorCePt3Si(Tc=0.75K)thatcoexistswithantiferromagnetism(TN=2.2K).Ashydrostaticpressureisincreased,Tcfirstdecreasesrapidly,thenratherslowlynearthecriticalpressurePc=0.6GPaandshowsastrongerdecreaseagainathigherpressures,wherePcisthepressureatwhichTNbecomeszero.Atransitionwidthandadifferenceinthetwotransitiontemperaturesdefinedintheformofstructuresintheout-of-phasecomponentofχacalsobecomesmallnearPc,indicatingthatadoubletransitionobservedinCePt3Siiscausedbysomeinhomogeneouspropertyinthesamplethatleadstoaspatialvariationoflocalpressure.AsuddenincreaseintheMeissnerfractionabovePcsuggeststheinfluenceofantiferromagnetismonsuperconductivity.
KEYWORDS:magneticsusceptibility,pressure,CePt3Si,heavy-fermionsuperconductor,Meissnereffect
1.Introduction
Eversincethediscoveryofheavy-fermionsupercon-ductivityinCePt3Si,1)manystudieshavebeenmadetoclarifyitsunconventionalsuperconductivity.Thetem-peraturedependenceofvariousphysicalproperties,suchasthermalconductivity2)andmagneticpenetrationdepth,3)suggestsagapfunctionvanishingontheFermisurface.Thelargeuppercriticalfield1)andNMRKnightshift4)suggestitsspintripletsuperconductivity,whilethenuclearspin-latticerelaxationratehasacoherenceHebel-SlichterpeakatTc,5)indicatingconventionalsu-perconductivity.Thepossibilityofamixedspinsingletandtripletstatethatisallowedowingtothelackofthecenterofinversionsymmetryinthecrystalstructurehasbeenproposedtoexplaintheseresults.6,7)
Besidesunconventionalsuperconductivity,CePt3Sipossessesacomplexpressure-temperature(P-T)phasediagram.Antiferromagnetism(TN=2.2K)andsuper-conductivity(Tc=0.75K)coexistsatambientpres-sure,1)andbothT8)NandTcdecreasewithanincreaseinpressure.AntiferromagnetismdisappearsabovePc=0.6GPa,whilesuperconductivityisobservedupto1.5GPa.Inaddition,thesuperconductingtransitional-waysshowsalargetransitionwidthat∼0.2K,9,10)andsomesamplesevenshowadoublepeakinspe-cificheatmeasurements.11–13)Althoughthepossibilitythatthesecondtransitionisduetoatraceofantifer-romagneticphase12)orunconventionalsuperconductiv-ity11)hasbeenproposed,ourrecentinvestigationsug-geststhatCePt3SicontainstwosuperconductingphaseswithdifferentTc’s.13)
Inthiswork,weinvestigatethepressuredependenceofthedoublesuperconductingtransitionbymagneticsus-ceptibilitymeasurementsandelucidatewhatcausesthedifferenceinTcinsideCePt3Si.WealsoreportthechangeintheMeissnereffectbelowandabovePc.
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01.191.030.300.120 GPa\"χπ4−0.50.800.65CePt3Si−1Single Crystal0.081.030.800.650.300.120 GPa\"χπ40.041.19000.20.40.60.8Temperature ( K )
Fig.1.Temperaturedependenceofacmagneticsusceptibility(χac=χ′+iχ′′)ofaCePt3Sicrystalunderdifferentpressures.χacwasmeasuredwithanacfieldofHac=1.2mOeat160Hz.Thearrowsindicateadditionalshoulder-likestructuresinχ′′.
0.8) CePtK3Si (Single Crystal) ( %0.6T+c+01TT−Tcχ\"c ,%T90%00.4T−9TTc10% ,−cT 0.2,+cT000.40.81.2Pressure ( GPa )
Fig.2.PressuredependenceoffourTc+characteristictemperatures:
,Tc−,T90%,andT10%.T90%andT10%arethetemperatureswheretheCePt3Sicrystalshows90%and10%offulldiamag-netism,respectively.Asindicated+
andTc−
schematicallyintheinset,Tc
arethetemperatureswhereχ′′reachesamaximumandhasalocalmaximumorashoulder,respectively.Thesolidlinesthroughthedatapointsareguidestotheeye.
transitionisnottherecentlyproposedsecondtransitionthatisfromthedxz-wavetothedxz±idyz-wavestate,sincethelattertransitionshouldbeobservedonlybelowPc.16)
Inordertodemonstratethepressuredependenceofsuperconductingtransitionmoreclearly,wedefinefour
characteristictemperaturesT90%,T10%,T+−
follows:χ′′hasamaximumatT+c,andT+
cas
alocalmaximumorashouldercandbelowTatTcitshows
−
thetemperatureswhereχc,whileT90%and
T10%are′
is90%and10%offulldiamagnetism,respectively.TheresultsareshowninFig.2.Asthepressureisincreased,thefourtemper-aturesfirstdecreasesteeplyuptoP=0.3GPa,thenchangeslowly,andbeginastrongerdecreaseaboveP=0.65GPa.Asimilarbehaviorhasalreadybeenreportedinspecificheatmeasurementsofasinglecrystal.8)TheslowdecreaseinTcprobablyreflectsthevanishingofan-tiferromagnetismatPc=0.6GPa.
Inourpreviouspaper,13)wehavereportedAC/DCsusceptibilityofthepresentcrystalandacrystalthat
showstwopeaksatTc+andTc−
inthespecificheat;dia-
magneticsusceptibilityandtheMeissnereffectofthelat-tersampleislargerthanthatofthepresentsamplenear
Tsuggestsc
+,andyetnoanomaliesisobservedatTthatthedoublepeaksinthespecificc−.Thisresultheatisas-cribedtothecoexistenceofsuperconductingphaseswithdifferentTc’sratherthanthesuccessivechangeofasu-perconductingphaseintoanotherstateatT−
peakscontainsagreateramountc;thecrystalwiththedoubleofthe
superconductingphasewithT+
thethesuperconductingphasecandasmalleramountof
withTwiththepresentcrystalthatshowsasinglec−
incomparison
peakatT−
inthespecificheat.However,theoriginofthedifferencecinTcwasstillunclear.
InFig.2,thedifferencebetweenT+−
width∆T=TcandTcaswellasthetransition90%−T10%becomessmallatpressuresbetween0.30GPaand0.65GPawhereTcdependslittleonpressure.Thisresultsuggeststhatsomeinhomogeneousproperty,suchasthestrainfieldaroundcrystallographicdefectsandadeviationfromthestoichiometriccomposition,causesavariationinlocalpressureandtheresultantTcdifferenceaccordingtotheP−Tccharacteristics.Evenifsuchapressurevariationexists,thedifferenceinlocalTcbecomessmallandthetransitionbecomessharp,whentheappliedpressureisnearPcandTcdependslittleonpressure.SinceTcde-terminedbyspecificheatmeasurementscorrespondstoTc−inthissinglecrystal,alargepartofthesamplehasTc−andasmallparthasTc+probablybecauseoflowerlocalpressures.Onepossibleexplanationforsuchalocalreductioninpressureisanegativepressurecausedbylatticedefectsorpartialreplacementofelements.
Theresultthatanincreaseinpressurereducesthetransitionwidth∆T=T90%−T10%atleastbelow0.3GPacontrastswithwhatisobservedinresistivitymea-surements;theonsettemperaturechangeslittle,andthetransitionbecomesbroader15)orshowsacomplexbehav-ior9)withincreasingpressure.Sinceonlyasmallamountofsuperconductingphasecancauseadropinresistivity,atraceoflowpressureregion(P∼0GPa)thatisonlydetectableinresistivitymeasurementsmaystillremainunderpressure.
Althoughacdiamagneticsusceptibilityreflectsbulksuperconductivityincomparisonwithzeroresistivityinthesensethattheshieldingcurrentonthewholesurfaceisdetected,dcsusceptibilitymeasurementsthatdetecttheMeissnereffectgivesmoreinformationaboutbulkproperties,asshowninFig.3.Themeasuringprocedureisasfollows.ThesamplewasfirstcooleddowntothelowesttemperatureinzeromagneticfieldandthenHdcwasapplied.Thediamagneticsusceptibilityduetotheshieldingcurrentwasmeasuredduringthewarmingpro-cessuptotemperatureswellaboveTc(ZFC:zero-fieldcooled).Inthesamefield,theMeissnereffectwasmea-suredduringthecoolingprocess(FC:fieldcooled).
ApartfromaslightdecreaseinTcduetoalargerap-pliedfield,theZFCsusceptibilityshowsabehaviorsimi-lartotheacsusceptibilityχ′inFig.1.TheFCsuscepti-bility,ontheotherhand,showsacomplicatedbehavior.Atambientpressure,theincreasingrateoftheMeiss-nereffectwithdecreasingtemperatureslightlychangesatabout0.5K,indicatingthesecondtransition.When
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FullPaperAuthorName3
01.19Zero−Field Cooled1.03cdχ0.800.120 GPaπ4−0.50.650.30CePt3Si−1Single Crystal0.051.19Field Cooled1.03c00.30dχ0.80π40.120 GPa−0.050.65−0.100.20.40.60.8Temperature ( K )
Fig.3.TemperaturedependenceofχdcunderdifferentpressuresfortheCePt3Sicrystal,asobtainedbythefield-cooledandthezero-fieldcooledmethods.Theappliedfieldsis0.12Oe.
0
Zero−Field Cooled
c0.83
0.60
0.310 GPa
dχπ4−0.5
CePtPolycrystal3Si−1Field Cooled
0
cdχπ4−0.020.830.600.310 GPa−0.04
0
0.2
0.40.60.8
Temperature ( K )
Fig.4.TemperaturedependenceofχdcunderdifferentpressuresforaCePt3Sipolycrystal,asobtainedbythefield-cooledandthezero-fieldcooledmethods.Theappliedfieldis0.12Oe.
pressureisapplied,thesecondtransitionisdifficulttoobserveinFCsusceptibilitymeasurementsprobablybe-causethesuperconductingtransitionbecomessharp.Inaddition,aparamagneticsignalappearsbelow0.6Katpressuresabove0.3GPa,whichiscanceledoutbyadia-magnetic(Meissner)signalbelowTc.Themagnitudeandthetemperaturewheretheparamagneticsignalappearsdependslittleonpressure.
InordertotestwhethertheobservedparamagneticanomalyisascribedtobulkCePt3Siorsomeimpurityphase,wehavemeasureddcsusceptibilityofapolycrys-tallinesample,asshowninFig.4.Theparamagneticsig-nalthatappearsunderhighpressuresinFig.3hasnotbeenobservedforthepolycrystallinesample,indicatingthatitisasample-dependentproperty.Theparamag-neticsignalforthesinglecrystalisremarkableonlyintheFCsusceptibilityandresemblestheferromagneticanomalythatisobservedat3KforsampleswithsmallvariationsinthecompositionofCe1+xPt3+ySi1+z.14)
01.19Field Cooledrenss0 GPai1.030.12eMχπ−0.05c0.04FC1.19 GPa4d0.80χπ40.02−0.10.300ZFC0.6500.4T ( K )0.800.20.40.60.8Temperature ( K )
Fig.5.TemperaturedependenceofχMeissnerfortheCePt3Sicrystal,whereχMeissnervaluesatP=0and0.12GPaarethesameasFC(FieldCooled)χdcinFig.3.AtP≥0.30GPa,FCχdcatP=1.19GPa,whichisshownintheinset,issubtractedfromFCχdcbelow0.6Kinordertoremovetheparamagneticcontribution.
ConsideringalsothecomplexityoftheCe-Pt-Siternaryphasediagram,17)atraceofsomesecondphasemaycausetheparamagneticanomalyobservedonlyforthesinglecrystal.Otherdifferencesbetweenthetwosam-pleswillbediscussedlater.
Inthefield-coolingprocessinFig.3,theparamag-neticsignalthatappearsabove0.30GPashowsalmostthesametemperaturedependenceuntilthesupercon-ductingtransitionstarts.SinceatP=1.19GPaonlyaslightchangeduetosuperconductivityisobservedbelow0.12K,weregardFCχdcatP=1.19GPabelow0.6KastheunderlyingparamagneticcontributionandsubtractitfromFCχdcatP≥0.30GPatoextracttheMeissnereffect.TheresultisshowninFig.5.ItisobviousthattheparamagneticcontributionisoverestimatedforχdcatP=0.30GPaandtheMeissnerfraction−4πχMeissnershouldbealittlesmaller.TheresultthattheMeissnerfractionatthelowesttemperaturesisalmostthesamebetweenP=0.12and0.30GPasuggeststhattheemer-genceoftheparamagneticsignaldoesnotchangethemagnitudeoftheMeissnereffect.Incontrast,theabruptincreaseintheMeissnereffectbetweenP=0.30and0.65GPaisclearlyseen,indicatingthatitoriginatesfromthedisappearanceofantiferromagnetismatPc=0.6GPa.Evenifthewholevolumeissuperconducting,theMeissnerfractioninrealsamplesoftype-IIsupercon-ductorsisusuallymuchsmallerthan1becauseofvortexpinning.TheresultthattheMeissnerfractionatambientpressurehasnotchangedbeforeandaftertheapplica-tionofpressuresuggeststhattheabruptincreaseabovePccannotbeattributedtopressure-inducedirreversiblechangeofthelatticethatactsasapinningsite.Sincevortexpinningoccursbythelocalvariationofthefreeenergyofafluxlinethatdependsoncoherencelengthξ,penetrationdepthλandcriticalfieldHc,thedisappear-anceofantiferromagnetismmaycauseanabruptchangeinthesesuperconductingproperties.Onepossibleexpla-nationforsuchachangeisthatsomeofthenodesintheenergygapofCePt3Sivanishwhenantiferromagnetismdisappears.16)
InFig.4,thepolycrystallineCePt3Siunderpressureshowsalessdecreaseintheonsettemperatureandconse-quentlyabroadertransitionwidththanthesinglecrys-tal,suggestingthatthepolycrystallinesampleislessho-
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mogeneouswithrespecttolocalpressurethanthesinglecrystal.Apartialtransitionat0.3KmaybeexplainedbytheP−TcharacteristicsinFig.2;thepressurerangeinwhichTciscloseto0.3Kisrelativelywide,sothatmanypartstendtohavelocalpressurevaluesinthisrangeandthetransitionat0.3Koccurs.Thismayalsoexplainthedropoftheonsettemperaturefrom0.8Kto0.3Kob-servedinresistivitymeasurementsunderpressure.9)
andantiferromagnetism.Acknowledgments
ThisstudywaspartlysupportedbyaGrant-in-AidfromtheMinistryofEducation,Culture,Sports,Sci-¯enceandTechnology(MEXT),Japan.Oneofus(Y.O.)
wasfinanciallysupportedbytheGrant-in-AidforCOEResearch(10CE2004)oftheMEXT,Japan.
Sincethegrainboundariesinapolycrystalactasad-ditionalpinningsites,theMeissnerfractiontendstobesmallerthanthatofasinglecrystal,asseeninFigs.4and5.TheymayalsopreventtheincreaseintheMeiss-nerfractionabovePc;evenifmoremagneticfluxesareexpelledfromthecrystalgrainsbytheabsenceofanti-ferromagneticorder,thegrainboundariesprobablytrapatleastapartofthem.ThecomparisonofFCχdcwellabovePcindicatesthattheMeissnerfractionatP=0.80GPaislargerthanthatbelowPcatthelowesttemper-aturesforthesinglecrystal,whiletheMeissnerfractionatP=0.83GPaissmallerthanthatbelowPcforthepolycrystal,althoughbothsamplesshowabout90%offulldiamagnetisminZFCχdc.Moreover.theonsetofsuperconductivityinZFCχdcis0.3Kforthepolycrys-tal,indicatingacertainamountofthesuperconductingphasemaystillcoexistwithantiferromagnetism.Thein-homogeneousdistributionoflocalpressuretogetherwiththevortexpinningatthegrainboundariesinthepoly-crystalmakesitdifficulttoobservetheanomaliesnearPcthatappearedforthesinglecrystal:thedecreaseinthetransitionwidthandthechangeintheMeissnerfraction.4.Conclution
Inconclusion,acanddcmagneticsusceptibilitymea-surementsofCePt3SiunderpressurehaverevealedthatthedecreaseintheslopeofthepressuredependenceofTcandthedecreaseinthesuperconductingtransitionwidthoccurataboutthecriticalpressurePcwhereco-existingantiferromagnetismvanishes.Thelargetransi-tionwidthandthesample-dependentsecondtransitionatambientpressurearewellexplainedontheassump-tionthataspatialvariationoflocalpressureexistsinCePt3Si.AnotheranomalynearPc,thatis,theabruptincreaseintheMeissnerfractionabovePcprovidessomeinformationontherelationbetweensuperconductivity
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