The complex resistivity $\hat{\rho}(\omega)$ of the vortex lattice in an untwinned crystal of 93-K $\rm YBa_2Cu_3O_7$ has been measured at frequencies $\omega/2\pi$ from 100 kHz to 20 MHz in a 2-Tesla field $\bf H\parallel c$, using a 4-probe RF transmissi

Collapseofthevortex-latticeinductanceandshearmodulusatthemeltingtransition

inuntwinnedYBa2Cu3O7.

arXiv:cond-mat/0205466v1 [cond-mat.supr-con] 22 May 2002

2

DepartmentofPhysics,PrincetonUniversity,Princeton,NewJersey08544and

DepartmentofPhysics,McGillUniversity,3600UniversityStreet,Montr´eal,Quebec,CanadaH3A2T8

(Dated:February1,2008)Thecomplexresistivityρ (ω)ofthevortexlatticeinanuntwinnedcrystalof93-KYBa2Cu3O7hasbeenmeasuredatfrequenciesω/2πfrom100kHzto20MHzina2-Tesla eldH c,usinga4-probeRFtransmissiontechniquethatenablescontinuousmeasurementsversusωandtempera-tureT.AsTisincreased,theinductanceLs(ω)=Imρ (ω)/ωincreasessteeplytoacuspatthemeltingtemperatureTm,andthenundergoesasteepcollapseconsistentwithvanishingoftheshearmodulusc66.Wediscussindetailtheseparationofthevortex-latticeinductancefromthe‘volume’inductance,andotherskin-depthe ects.Toanalyzethespectra,weconsideraweaklydisorderedlatticewithalowpindensity.Close tsareobtainedtoρ1(ω)over2decadesinω.Valuesofthepinningparameterκandshearmodulusc66obtainedshowthatc66collapsesbyover4decadesatTm,whereasκremains nite.

PACSnumbers:74.60.Ge,74.72.Bk,72.15.Gd,64.70.Dv

1

PeterMatl1, ,N.P.Ong1,R.Gagnon2,andL.Taillefer2,

I.INTRODUCTION

TheinvestigationoftheresponseofvorticesintypeIIsuperconductorstoanalternatingdrivingcurrenthashadalongandfruitfulhistory,beginningwiththeexper-imentofGittlemanandRosenblum(GR)onPbInandNballoys[1].Incupratesuperconductors,theseinves-tigationshavebeenperformedonYBa2Cu3O7(YBCO)overabroadrangeoffrequenciesextendingfrom100kHztoafewTHz.Atfrequenciesωbelowafew100MHz,thevortexresponseisobtainedbydirectlymeasuringthesample’scomplexresistivityρ (ω).Atmicrowavefrequen-cies(10to100GHz),cavityperturbationtechniqueshavebeentheprimaryapproach,althoughbolometricabsorp-tiontechniqueshavebeenmoreusefulatthehighmi-crowaveend.

Theoccurenceofthevortexsolid-to-liquidmeltingtransitioninthecupratesisoneofthemostinterest-ingphenomenaintheinvestigationof‘vortexmatter’insuperconductorsThemeltingtransitionatTmhasbeeninvestigatedinsomedetailbyhigh-resolutionmea-surementsofthemagnetization[3,4],heatcapacity[5]anddcresistivityInanysolid-to-liquidtransition,thekeyquantityofinterestistheshearmoduluswhichvanishesintheliquid.Theresistivitypro le(ρvs.T)inacrystalofBi2Sr2CaCu2O8inwhichalternatingstrongandweakpinningchannelsarecreatedbyionirradiationwasinterpretedasalossofshearstrengthatTm[8].Thee ectofthevanishingshearmodulusatTmonρwhenthe eldHistiltedrelativetothetwinboundariesintwinnedYBCOcrystalswasalsodemonstratedThestandardapproachtoinvestigatinghowtheshearmoduluschangesinasystemundergoingasolid-to-liquidtransitionisbyobservingitsdynamicalresponsetoanos-cillatingdrivingforce.Thefrequencydependenceofρ (ω)inthevortexstateinYBCOhasbeeninvestigatedbyseveralgroupsatfrequenciesinthe1to100MHzrange.Initialmeasurementsusingthin- lmsamplesfoundthat

ρ (ω)=ρ1(ω)+jρ2(ω)displaysstrong,featurelessdis-persionatthesefrequencies13].However,theresponseinhigh-puritysinglecrystalsisqualitativelydif-ferent.Wu,Ong,GagnonandTaillefer(WOGT)[10]investigatedtheacresponseinuntwinnedcrystalsofYBCOintheMHzrange,andfoundthattheinductancevs.Hexhibitsastep-wisechangeatthemelting eld.Asaliquidcannotproduceaninductiveresponse,thestep-wisechangeintheinductanceisdirectevidenceforacollapseoftheshearmodulusc66atTm.

The2-probeexperimentsofWOGTwereperformedat xedTversusH.ThisapproachcannotbeextendedtomeasurementsinwhichTiscontinuouslyvariedin xedHbecausevariationsinthebackgroundsignal(fromT-dependentstraycablereactances)swampthesamplesig-nal.WereportresultsobtainedbytheuseofanRF4-probetechniquethatcircumventsthisobstacle.The4-probetechniqueallowshigh-resolutionimpedancemea-surementsversuseachofthethreequantitiesω,HandT.We ndthatthecollapseoftheinductanceisevenmoreabruptwhenTisscannedat xedH.Whilewelargelycon rmthe xed-TresultsofWOGT,theswept-Tex-perimentsprovideamoredirectpictureofthebehaviorofthevortexresistivityandinductanceasTisincreasedabovethemeltingline.Withthebroaderperspective,wecorrectapreviousinferenceregardinga‘remanent’shearmodulusinthevortexliquidstate.Adetaileddiscussionofhowthevortex-latticeinductanceisseparatedfromthe‘volume’inductanceisprovided.TogetherwiththemeasurementsofWOGT,thepresentresultsprovideacompleteexperimentalpictureofthelinearresponseofthepinnedlatticeinahigh-puritycupratecrystaltoanacdrivingcurrentintheMHzfrequencyrange.Thetwodistinguishingfeaturesarethestrongdispersionofρ (ω)observedevenatlowω(justbelowthemeltingtemper-atureTm)andthestrikingabruptcollapseoftheinduc-tanceatTm.

Tounderstandthespectra,wehaveadoptedamodelin