arXiv:cond-mat/0207462v1 [cond-mat.str-el] 18 Jul 2002D.E.MacLaughlin
Abstract
Zero-fieldµSRexperimentsintheheavy-fermionalloysCe1−xLaxAl3,x=0and0.2,examinearecentproposalthatthesystemexhibitsastronganisotropicKondoeffect.WeresolveadampedoscillatorycomponentforbothLaconcentrations,in-dicativeofdisorderedantiferromagnetism.Forx=0.2theoscillationfrequencydecreasessmoothlywithincreasingtemperature,andvanishesatthespecificheatanomalytemperatureT∗≈2.2K.OurresultsareconsistentwiththeviewthatT∗isduetoamagnetictransitionratherthananisotropicKondobehavior.Keywords:anisotropicKondoeffect,heavy-fermionsystems,Ce1−xLaxAl3.
Moreover,aslanthanumisdopedontoceriumsitesthespecificheatcoeffi-cientγ(T)=C(T)/Tisdrasticallymodified,andamaximuminγ(T)atacharacteristictemperatureT∗(≈0.4KinCeAl3)movesupintemperatureandgrowsintoalargepeak[3];T∗=2.2Kforx=0.2.Thisbehaviorwasinitiallytakenasevidencefordevelopmentofaweak-momentmagneticallyorderedphaseofCeAl3,andattributedtoreductionofthehybridizationbe-tweenCefelectronsandligand-derivedconductionelectrons.
Thisinterpretationhasbeencalledintoquestion[4]onthebasisofinelasticneutronscatteringexperimentsonCe0.8La0.2Al3,whichfoundabroadinelasticpeakbelowT∗.ThispeakwastakenasevidenceforapplicabilityoftheAKMtotheCe1−xLaxAl3system.Zero-fieldµ+spinrelaxation(ZF-µSR)experi-ments[5]attheISISpulsedmuonfacility[4]indicatedmagneticfreezingatT=T∗,butthefrozenmomentwasclaimedtobeweak(∼0.05µB/Ceion),principallybecausenoneutrondiffractionpeakwasobserved.RecentZF-µSRstudies[6],alsocarriedoutatISIS,concludethatforx=0.05themagneticfreezingpersiststotemperatureswellaboveT∗.Thisistakenasfurtherevi-dencethatthespecificheatpeakatT∗reflectstheanisotropicKondoeffectandisunrelatedtospinfreezing.
SpecificheatmeasurementsinCe0.8La0.2Al3atappliedfieldsofupto14T[7]disagreewiththetheoreticalbehavioroftheAKM,however.Furthermore,theargumentforapplicabilityoftheAKMdependsstronglyonevidencethatthefrozenmomentsaresmall,viz.,theabsenceofneutronBraggpeaks.Neutrondiffractionwouldnotnecessarilybesensitivetospinfreezingofaglassynatureorshort-rangeorder,however,whereastheZF-µSRrelaxationratereflectsspinfreezingindependentlyofthedegreeoflong-rangeorder.
WehavecarriedoutZF-µSRexperimentsinCe1−xLaxAl3,x=0and0.2,atTRIUMFandPSI.Forx=0.2weobserveastronglydampedbutresolvedoscillationinthemuonasymmetrydataatlowtemperatures,asshowninFig.1.ForbothLaconcentrationstheprecessionfrequencydisappearsatT∗,indisagreementwiththeresultsofRef.[6]forx=0.05,andinagreementwiththeexpectedresultifT∗wereamagneticorderingtransitiontemperature.Thestrongdampingindicatesadistributionofstaticlocalfieldsatmuonsites,asmightbeexpectedinastronglydisorderedsubstitutionalalloy,buttheoscillationreflectsafairlywell-definedaveragelocalfield.ForcomparisonwiththeanalysisofRef.[6]asymmetrydataforbothLaconcentrationswerefitassumingmagneticandnonmagneticvolumefractions;a“dampedcosine”formwasusedfortheprecessingsignal.Theformoftherelaxationfunctionis
G(t)=Am
2
3
exp(−λLt)+AnGKT(t).(1)
Heretherelaxationfromthemagneticvolumefractionfmagismodeledbythe
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ASYMMETRY (%)20Ce0.8La0.2Al3H = 0 T = 0.05 KDAMPED COSINE FIT1000.00.51.0TIME (µs)1.52.0Fig.1.Ce0.8La0.2Al3asymmetryrelaxationfunction.
componentwithasymmetryamplitudeAm.Thestaticfieldatthemuonsiteisassumedtoberandomlyoriented.Relaxationofmuonsintheremainingnon-magneticfractionisduetonucleardipolarfieldsandisdescribedbyastaticKubo-ToyabefunctionGKT(t)[5];thusfmag=Am/(Am+An).TherelaxationratesλTandλLcharacterizethetransverseandlongitudinalrelaxation,re-spectively;theformerisexpectedtobedominatedbystaticdisorderwhereasλLreflectsdynamicspin-latticerelaxation.ThequalitativefeaturesofthefitsareunchangedifthedampedBesselfunctionfoundbyAmatoinCeAl3[8]isused.
ThetemperaturedependenceofthefitparametersisgiveninFig.2.Itcanbeseenthatν(T)(a)isindependentofxatlowtemperatures,(b)decreasesmarkedlyasT∗isapproachedfrombelow,and(c)issuppressedtozeroatT=T∗forx=0.02.UnfortunatelythemuonstoppingsiteinCeAl3isnotknown,otherwisetheorderedmomentµordcouldbeestimatedaccurately.Amato[8]givesarangeµord=0.11–0.5µB/CeioninCeAl3,whichis2–10timeslargerthanthevaluereportedinRef.[4].TheentropyreleaseatT∗impliesµord≈0.3µB/Ceion[3],comparabletovaluesobtainedfromNMRandothermeasurements[9].
InCeAl3ν(T)isnotcompletelysuppressedtozeroandλT(T)increasesrapidlyatT∗.Thisisnotnecessarilyasignofafirst-ordertransitionsinceitcanbeunderstoodasaneffectofinhomogeneityinthetransitiontemperature,asobservedinLa2CuO4[10].NosuchincreaseinbroadeningisobservedinCe0.8La0.2Al3.CeAl3alsoexhibitsadecreaseoffmagasT∗isapproachedfrom
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Ce1-xLaxAl3H = 0Damped cosine fit0.8fmag0.40.04x = 0x = 0.2(a)(b)ν (MHz)1050105020(c)λT (µs)-1λL (µs)(d)-10T*(x=0)12T*(x=0.2)TEMPERATURE (K)Fig.2.Temperaturedependenceof(a)magneticvolumefractionfmag(T),(b)pre-cessionfrequencyν(T),(c)transverserelaxationrateλT(T),and(d)longitudinalrelaxationrateλL(T)fromZF-µSRinCe1−xLaxAl3,x=0and0.2.below;thisisalsonotseeninCe0.8La0.2Al3.Inconclusion,ourZF-µSRdataareconsistentwithascenario[3,7]inwhichthespecificheatanomalyinCe1−xLaxA3isassociatedwiththeonsetofstaticmagnetismbelowT∗,withorwithoutlong-rangeorder.Inparticular,thereisnosignofsuchstaticmagnetismabovethistemperatureinCe0.8La0.2Al3.
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WearegratefultoA.Amato,C.Baines,M.Good,D.Herlach,B.Hitti,S.Kreitzman,P.Russo,andA.Saviciforhelpwiththeexperiments,andtoE.Goremychkin,K.Ingersent,R.Osborn,andB.Rainfordforusefuldiscussions.ThisworkwassupportedinpartbytheU.S.NSF,Grantnos.DMR-9731361andDMR-0102293(UCRiverside),DMR-9820631(CSULosAngeles),andDMR-0104240(U.ofFlorida),andbytheNetherlandsNWOandFOM,andwasperformedinpartundertheauspicesoftheU.S.DOE.
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