3D-2D phase transition in vortex lattice of layered high-temperature superconductors of BSC

(Bi1.7Pb0.3Sr2Ca2Cu3O4)

J.G.Chigvinadze,A.A.Iashvili,T.V.Machaidze

E.AndronikashviliInstituteofPhysics,380077Tbilisi,Georgia

(February1,2008)

Abstract

Usingthehigh-sensitivemechanicalmethodofmeasuring[1]thedissipationprocessesinsuperconductors,the3D-2Dphasetransitioninmagneticfieldwasinvestigatedinthevortexlatticeofstronglyanisotropichigh-temperaturesuperconductorsofBi(2223)system.Itwasshownthatwiththeincreaseofexternalmagneticfieldthedissipationconnectedwithamotionofvortexesrelativetothecrystallatticeofasample,firstincreases,reachingthemaxi-mumandthenwithafurtherincreaseofthemagneticfieldsharplyreducesasaresultofpinningenhancementinconnectionwiththetransitionofthree-dimensionalvortexsysteminquasi-two-dimensional”pancake”one.PACSnumber:74.60.-w,74.60.Ge,74.80.Dm

TypesetusingREVTEX

1

Withahelpofcomputercalculationsitwasshownrecentlyin[2]thatinthelayeredhigh-temperaturesuperconductorsofBCCOsystemthedisintegrationofthree-dimensionalvortexesinto”pancake”ones-theso-called3D-2Dtransitioncouldtakeplace.

Thistransitionmustbeaccompaniedbyasharpincreaseofcriticalcurrentthatinitsturnmeansasharpincreaseofapinningforceaccompanyingthedisintegrationofvolumevortexesinto”pancake”-likeones.Thisalsoshouldstronglyaffectthedissipationprocessesaccompanyingthemotionofvortexsystem.

Naturally,atthistransition,asaresultoftheincreaseofthepinningforce,theenergyofdissipationshouldalsosharplydiminish.

Ifonemeasuresthelossesinavortexsystemtheirstrongdecreasewouldbeobtainedatthe3D-2Dtransition.

Theexperimentoninvestigationsofsuchtypephenomenawasmadebyususingtheorientedlayeredhigh-temperaturesuperconductorsamplesofBi1.7Pb0.3Sr2Ca2Cu3Oy[BSCCO(Bi2223)]system.

Layeredhigh-temperaturesuperconductorsarecharacterizedbyastronganisotropyoftheirsuperconductiveproperties.Fromthispointofviewthelayeredhigh-temperaturesuperconductorsofBCCOsystemareparticularlydistinguished.Theyarecharacterizedbyahighdegreeofanisotropy[3–5]withanisotropyparameterΓ=M/m≫1,(whereMistheeffectivemassalongc-axis,andmistheeffectivemassintheab-plane)andamountstoΓ≈103.

WhenouterfieldHisdirectedalongc-axis,H󰀈c,thenbelowadefinitefieldB=B2Dthevortexsystembehavesasthree-dimensionalone,andaboveB>B2ditbehaveslikequasi-two-dimensionalsystem.

The3D-2DtransitionfieldB=B2Dcanbeevaluatedbyexpression[3]:

B2D≈

Φ0

conductorbehaviortothequasi-two-dimensionalonetakesplacewhen

ξ⊥=d,

whereξ⊥isthecoherencelengthperpendiculartotheab-plane,thatisthecoherencelengthalongc-axis

ξ⊥=ξc,

anddisthedistancebetweenlayers(d=c/2).Fromthisconditionwecoulddefinetheso-calledcrossovertemperature-Tcr[5]whichprovestobeequal:

Tcr=1−

󰀁

22ξc(0)

initsturn,wassuspendedonthethinelasticthread3.Intheupperpartoftherod,lightorganicglassdisk5ofdiameterR=1cmandmassm=0.4gwasfixed.

ThemomentofinertiaofthesuspendsystemwasI=0.5g·cm2.Therecordingofvibra-tionswasmadeusingmirror6gluedtothesuspendsystem,andphotoresistivetransducers,mountedonscale7.Thescalewithtransducerswasseparatedfrommirror6atadistanceofl=200cmandthemaximalvibrationamplitudeinourexperimentsdidn’texceedϕ≈3·10−1rad.

Thelogarithmicdampingdecrementδofthevibrationsofasuspendedsystemwasmea-suredbyrecordingthetimeofflightofalightspot,reflectedfromthevibratingmirror,betweentwotransducers[7].Thepartofcryostat,whereasuperconductivesamplewasplaced,wasfilledwithliquidheliumorliquidnitrogen,andplacedina8kOemagneticfieldperpendiculartothesuperconductivecylindricalsampleaxis.Electromagnet8wassup-portedbyasystemofbearingsandcouldrotatearounditsaxis.Thesystemofcoils9,10,11canprovidebothlongitudinalandtransversefieldsinrespecttosample’saxis.Inthecaseofnecessitythesecoilsalsocouldbeusefulforapplicationtothesampleofadditionalpulsedandoscillatingmagneticfields.Thesamplewasgluedtothecrystalholderinsuchawaythatitsc-axiswasdirectedalongthemagneticfieldHperpendiculartothevibrationsystemaxis.Byrotatingofelectromagnet8onecouldsetthedirectionofmagneticfieldalongc-axisusingthediamagneticmomentofforcesactingonthec-orientedsample[8].Ifnecessary,wecouldalsomeasuretheanisotropyofelastic-viscouspropertiesofvortexsystem.

Thesmallaxialvibrationsofsampleweremeasuredduringwhichitsc-axisexperiencedsmalldeviationswithrespecttothemagneticfield.Themaximalamplitudeofvibrationswasnotmorethanϕmax≈3·10−1rad.ThedependenceoflogarithmicdampingdecrementofthevibrationsontheoutermagneticfieldtensionHdirectedalongc-axisofstronglyanisotropiclayeredhigh-temperaturesuperconductorsystemBi1.7Pb0.3Sr2Ca2Cu3Oywasinvestigated.

InFig.2thedependenceofdontheoutermagneticfieldtensionHispresented.Asit

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isseenfromthefigure,intheweakfieldsuptoapproximatelyH=140Oethedampingδwithanincreaseofthemagneticfieldtensionincreases,butthenbeginningfrom175Oeitsharplydecreasesandalreadyatmagneticfieldsoftheorderof1250Oeitbecomesequaltothedampingvalueattheabsenceofamagneticfield.

Furtheraslowreductionfollows,andatfieldH=1750Oeandhigheritturnsouttobeslightlylessthanattheabsenceofmagneticfield.

Asharpreductionofdampingprocessesatfields>175Oe,toouropinion,isrelatedwiththe3D-2Dphasetransitioninthevortexsystem,whenvolume3Dvortexestransforminquasi-two-dimensional2Dvortexesandtheincreaseofcriticalcurrentconnectedwiththistransitionand,correspondingly,ofthepinningforce,stronglyreducesthedissipationprocesses,connectedwiththemotionofvortexsystem.The175-1750Oeintervalisatransitionrange.Thepossibilityof3D-2Dtransitionwasdiscussedintheveryinterestingwork[9]inconnectionwiththetransformationofV-IcharacteristicsofTl2Ba2Ca2Cu3O10−δinthemagneticfieldrange1500-1600Oe.Theestimationof3D-2DtransitioncriticalfieldvalueB2Daccordingtoformula(1)andusingthedataof[4,11]:Γ=3·103,andd=18.5˚A,givesB2D≈2000Oebeinginouropinioninagoodagreementwiththeexperiment.TheestimationofthecrossovertemperatureTcrbyformula(2)usingtheresultsofworksAresultsinTcr=105.7K.A,andd=18.5˚[4,11,12]:Tc=107K,ξc(0)=1.4˚

BeginningfromT=90KuptoT=105Ktheδ(H)dependencecharacterpresentedinFig.2isnotchanged.ButatT=106Ktheδ(H)valueissharplyreducedandbasicallychangedthatpointstothecorrectnessofourestimationofTcr.

Inouropinion,thetransitionrangepresentedintheincreasedscaleintheinsertiontoFig.2deservesanattention.

AsitisseeninFig.2attheweakfieldsH<1kOetheδ(H)dependenceshowsthepresenceofpeakswhichcanbeconnectedwithphasetransitionsinthevortexsystem,forexample,thetransitionofAbrikosovvortex[10]intoglassystateoritsmelting.Theestimationofvortexlatticemeltingfield[13]gives:

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Bm(T)≈βm

whereβm≈5,CL≈0.2

4CL

Tc

󰀄2

(3)

Gi=

󰀅

Tc

2ε0(0)dΦ0

(4)

ε0(0)=

22πξab(0)

(6)

whereξab(0)indifferentexperimentsfallsintherange15÷17˚A.

Oneobtains:Hc2(0)=(114÷146,5)T.Hence,usingformulas(3),(4)and(5)oneobtains:Bm(T)≈275÷315OeatT=100K.

ThisvalueisinagoodagreementwiththesecondmaximumoflogarithmicdampingdecrementofvibrationsintheinsertionofFig.2whichisseenatH≈280Oe.

So,thedampingpeakobservedbyusinthetransitionrangeofmagneticfieldscanberelatedwiththeAbrikosovvortexmelting,i.e.withthemeltingof3Dvortexes[13].Itshouldbepointedthatthe3D-2Dtransitionatincreasingmagneticfield,predictedbyM.Fisherandcollaborators[15]inthestronglyanisotropiclayeredmaterials,canberealizedalsoinsuperconductorswithnotsoextremelyhighvalueofanisotropyfactor,asinBSCCO,butwithitscomparativelylowvalue.

Asanillustrationonecanconsidertheinterestingwork[16]oninvestigationofthe3D-2DtransitioninthefinelayersofYBa2Cu3O7−δ.

Inconclusion,itshouldbepointedthatthesharpdecayofdissipationatfieldsB>175OeobservedbyusisprobablyconnectedwithasharpincreaseofpinningforcebecausetheamplitudeeffectsofdissipativeprocessessharplydecreaseatstrongfieldsB>2000Oe.Thus,thisphenomenon,initsturn,pointsagaintothepossiblephasetransitioninthe3D-2DvortexstructureinfieldsB>2000Oe.

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Wehavestartedexperimentsonthedirectmeasurementofpinningforceatthe3D-2Dphasetransition.

And,finally,authorsareexpressingtheirsinceregratitudetoM.J.Chubabriaforprepar-ingthesamples,andtoN.G.SuramlishviliandYu.G.Mamaladzeforthediscussionofexperimentalresults.

ThisworkismadewithsupportofInternationalScientificandTechnologyCenter(ISTC)throughGrantG-389.

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REFERENCES

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8

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FIGURES

FIG.1.

Thediagramoflow-temperaturepartofinstrument:1-sample,2-crystalholder,

3-thread,4-glassrod,5-discus,6-mirror,7-scalewithphotoresistivetransducers,8-electromagnet,9-11-coils.

FIG.2.LogarithmicdampingdecrementδofthevibrationsofasuspendedsystemasafunctionoftheexternalmagneticfieldH.

10

Fig.1

0.250.20

0.250.20δ

0.150.100.050.00

0δ0.15H/2c10.100.050.000200400600800 H (Oe)10002000300040005000

H (Oe)

Fig.2