We argue that the method, which was used for the analysis of equilibrium magnetization data in the original publication, is not adequate to the experimental situation. As a result, the temperature dependencies of the upper critical field Hc2(T) and the mag

Commenton”Holeconcentrationdependenceofpenetrationdepthanduppercritical

eldinBi2Sr2(Ca,Y)Cu2O8+δextractedfromreversiblemagnetization”

1

I.L.Landau1,2H.Keller1

Physik-InstitutderUniversit¨atZ¨urich,Winterthurerstrasse190,CH-8057Z¨urich,Switzerlandand

2

KapitzaInstituteforPhysicalProblems,117334Moscow,Russia

(Dated:February2,2008)

arXiv:cond-mat/0512441v2 [cond-mat.supr-con] 4 Apr 2006

Wearguethatthemethod,whichwasusedfortheanalysisofequilibriummagnetizationdataintheoriginalpublication,isnotadequatetotheexperimentalsituation.Asaresult,thetem-peraturedependenciesoftheuppercritical eldHc2(T)andthemagnetic eldpenetrationdepthλ(T),obtainedinthiswork,areincorrect.Usingadi erentapproach,wereanalyzethepresentedexperimentaldataanddemonstratethatthenormalizedHc2(T)curvesareratherdi erentfromthosepresentedintheoriginalpublicationanddonotfollowpredictionsoftheWerthamer-Helfand-Hohenbergtheory.AnotherinterestingobservationisthattheHc2(T)dependenciesfortwosampleswithcloselevelsofdopingareratherdi erent.

PACSnumbers:74.25.Op,74.25.Qt,74.72.-h

InRef.1,theequilibriummagnetizationM(H,T)inthemixedstateofseveralpolycrystallineBi2Sr2(Ca,Y)Cu2O8+δ(Bi-2212)sampleswasinves-tigated.Theresultswereanalyzedbyemployingthevortex uctuationmodel.2,3,4Wedisagreewiththisanalysis.Below,wereanalyzethedataofRef.byamoreappropriateapproachanddemonstratethattemperaturedependenciesoftheuppercritical eldHc2areratherdi erentfromthoseobtainedintheoriginalpublication.ThismeansthattheconclusionofRef.1thatHc2(T=0)hasamaximumvaluewhentheholeconcentrationpisaround0.19isnotreallybasedonpresentedexperimentaldata.

Thereareseveraltheoreticalmodels,2,5,6whichareusuallyemployedforevaluationofHc2fromexperimen-talmagnetizationdata.Allthesemodelsassumecon-ventionalsuperconductivity(anisotropicsuperconduct-ingorderparameter)andauniformsamplewithazerodemagnetizingfactorn.Neitheroftheseconditionsissatis edinpolycrystallineHTSC’s.Becausethedi er-encesbetweentheoreticalassumptionsandexperimentalsituationsarerarelydiscussedintheliterature,wecon-sidertheminsomedetails.

(i)Demagnetizingfactor.IfthesamplemagnetizationMismuchsmallerthananappliedmagnetic eldH,demagnetizinge ectsareusuallyneglected.Thisisnotcorrect.TherelationbetweenHandthemagneticinduc-tionBinthesampleisalwaysdependentonthevalueofn.Thus,ifn=0,B≡HandM≡0,independentoftheappliedmagnetic eld,temperatureorthenatureofthesample.

(ii)Pairingsymmetry.Symmetryoftheorderparam-eterisalsoimportant.Inthecaseofunconventionald-pairing,whichisexpectedinhigh-Tcsuperconductors(HTSC),thedistributionoftheorderparameteraroundvortexcoresandthecorrespondingcontributiontothefreeenergyisdi erentfromthatforconventionalsuper-conductors.Thisiswhytheoreticalcalculationsbasedonconventionals-pairingshouldbeusedwithcautioniftheyareappliedfortheanalysisofexperimentaldata

collectedonunconventionalsuperconductors(iii)Polycrystallinesamples.HTSC’sarehighlyanisotropic.Insuchmaterials,ifthedirectionofanex-ternalmagnetic elddoesnotcoincidewithoneoftheprincipleaxesofthecrystal,themagneticinductioninthesampleisnotexactlyparalleltotheappliedmagnetic eld.Insamplesconsistingofrandomlyorientedgrains,thisleadstoanadditionalfreeenergyandmayin u-encethesamplemagnetization.Itshouldalsobenotedthat,becausemagnetizationsofdi erentgrainsaredif-ferent,thereissomemagneticinteractionbetweentheneighboringgrains.Thesituationisevenmorecomplexathighertemperatures.Indeed,accordingtocalcula-tionsofBrandt,6themagnetic elddependenceofMisalinearfunctionoflnH(Londonlimit)onlyinmagnetic eldsH<0.1Hc2(seealsoFig.3inRef.12).Attem-peratures,T>～0.8Tc,theupperlimitofthemagnetic eldrangeisusuallyhigherthanthisvalue.Inthiscase,deviationsofM(H)fromthepredictionsoftheLondonmodelhavetobeaccountedforandasimpleaveraging,whichwasproposedinRef.3andusedinRef.1,isnotapplicable.

Inordertoavoidabove-mentioneduncertainties,weusehereadi erentmethodofanalyzingmagnetizationdata.Inthisscalingapproach,developedinRef.8,noparticularM(H)dependenceisassumedapriori,anditcanbeappliedtosinglecrystalsaswellastopolycrys-tallinesamples,independentofthepairingmechanismorthesamplegeometry.9ThedisadvantageofthisanalysisisthatitdoesnotprovidetheabsolutevaluesofHc2butonlyitsrelativevariations.Thisistheprizetopayforitsuniversality.

ThescalingprocedureisbasedontheassumptionthattheGinzburg-Landauparameterκistemperature10Inthiscase,themixed-statemagneticsusceptibilitymaybewrittenas

χ(H,T)=χ(H/Hc2),

(1)

i.e.,thetemperaturedependenceofχisonlyduetotem-peraturevariationofHc2.Eq.(1)isalreadysu cientto