Current-InducedSwitchingofPerpendicularlyMagnetizedMagneticLayersUsing - PDF document

Current-InducedSwitchingofPerpendicularlyMagnetizedMagneticLayersUsingSpinTorquefromtheSpinHallEffectLuqiaoLiu,O.J.Lee,T.J.Gudmundsen,D.C.Ralph,andR.A.BuhrmanCornellUniversity,Ithaca,NewYork14853,USAKavliInstituteatCornell,Ithaca,NewYork,14853(Received24April2012;published29August2012)Weshowthatinaperpendicularlymagnetizedbilayerthespin-Halleffect(SHE)inPtcan FIG.1(coloronline).(a),(b)Current-inducedswitchingina generateshystereticmagneticswitchingbetweenthestates,withthepositivecurrentfavor-or-1(a)].Ifthesmallconstantin-planemagneticÞeldisreversed,thecurrent-driventransitionsinvert,withthepositivecurrentnowfavoringdespitethefactthatthein-planeÞeldstilldoesnotfavoreithermagneticstateintheabsenceofacurrent[Fig.Thecurrent-generatedOerstedmagneticÞeldcannotex-plainthisresult,asitisorientedin-plane.WewillshowthatthefullswitchingphasediagramasafunctionofthecurrentandmagneticÞeldcanbeexplainedquantitativelybySHEtorquefromthePtlayer,andthatpreviouslyproposedRashbaeffectswithintheCo[]donotmakeanymeasurablecontributiontothemagneticorien-tationinoursamples.Phasediagramofamacrospinmodel.—ToexplainhowaSHEtorquecanrotateandswitchthemagneticorienta-ofaperpendicularlymagnetizedlayer,weÞrstsolveasimplezero-temperaturemacrospinmodel.WeconsiderbilayerintheplanewithaColayerofthicknessandconstantmagnetization,ontopofaPtlayerofof1(e)].Forpositivecurrent(electronsßowinginthedirection)theSHEinducesaspincurrentwithinthePtlayersuchthatspinmo-mentspointinginthedirection(spinangularmo-mentumalong)ßowupwardinthedirection.Attheferromagnetinterface,thespincomponentperpendicu-lartocanbeabsorbedbytheferromagnet,impartingaspin-transferÔÔtorqueÕÕperunitmoment ,orientedalong.WewillanalyzethecaseofanappliedmagneticÞeld(themodelisgeneralizabletoarbitrarydirec-tions).Inadditiontothespintorque,wemustalsotakeintoaccountthetorques(perunitmoment)duetotheexternalmagneticÞeld,,andtheperpendicularanisotropyÞeld,Þ¼.Theequilibriumorientationsofsatisfythecondition.Weusemacrospinsimulationsoftheequationofmotion[todistinguishstablefromunstableequilibria.Forcurrentscorrespondingtosmalltomoderatevaluesofspintorque,canremainwithintheplaneaslongas.Inthiscaseallthreetorques)arecollinearinthedirectionandthetorquebalanceequationthatdeterminesthemagnetizationrota-tionangletakesasimplescalarform,andtheappliedÞeldangledeÞnedasinFig..AsthecurrentisrampedfromzeroforÞxed,thedominanteffectofistorotatewithintheplane,shiftingcontinuously,until,forsufÞcientlylargecurrents(relativetotheanisotropystrength),Eq.()predictsabrupthystereticswitching.InweshowmagnetichysteresiscurvespredictedbythismacrospinmodelforÞxedin-planemagneticÞelds.Justasobservedexperimentally[Figs.],thesignofthehysteresisreverseswhenthein-planeÞeldcomponentisreversed.Thereasonforthisreversalisthatalthoughanin-planemagneticÞelddoesnotfavoreithermagneticorientationbyitself,anin-planeÞeldbreaksthesymmetryintheresponsetotheSHEtorque.WithamagneticÞeldinthein-planedirection,thebarrieragainstclockwiserotationoffromthetothestateisdifferentthanforclockwiserotationfromtothestate,withtheresultthatthedirectionofthein-planeÞelddetermineswhichout-of-planemagneticorientationwillbefavoredbyagivensignofSHEtorque[Fig.Forverylargespintorques,,theSHEtorqueisgreaterthanthemaximumrestoringtorquefromthemagneticanisotropy,andforsufÞcientlysmallthereisnosolutionforinEq.(),meaningthatcannotremainintheplane.Bysolvingthefullvector,weÞndthatforlargethereisacurrent-stabilizedregimeinwhichdevelopsacompo-nentinthedirectionforpositivetiltstowardfornegative.Inourexperiments,wehavenotyetbeenabletoapplylargeenoughsteady-statecurrentsto FIG.2(coloronline).(a)Predictionsforcurrent-inducedmag-neticswitchingwithinthemacrospinmodel.(b)IllustrationofthetiltedmagneticstatesthatarestableintheabsenceofacurrentwhenaÞxedin-planemagneticÞeld(left)isapplied.ThetiltangleisexaggeratedcomparedtoFigs..Current-inducedswitchingdependsonthesignofasshown.(c),measuredduringcoherentrotationfor12mA,whenthemagneticÞeldisintheplaneat.(d)Points:measuredvaluesofasdeÞnedinthetext,determinedfromthedatain(c).Lines:Þtstothemacrospinmodeltodetermine.(e)measuredfordifferentvaluesof(f)asafunctionoftheappliedÞeldwhenisappliedalongthedirection,for10mA.Thecurvesareindistinguishable,allowingustosetalimitonthein-planeRashbaÞeld. 096602(2012)PHYSICALREVIEWLETTERSweekending31AUGUST2012 achievethisstate.However,theSHE-inducedrotationofoutoftheplanepredictedinthisregimehasthecorrectsymmetrytoexplainobservationsofstochasticdomainreversalinresponsetolargepulsedcurrents[],asapossiblealternative[]tothemechanismoflargein-plane)RashbaÞeldsproposedbyMironetal.ThefullswitchingphasediagramforthemacrospinmodelcanbecalculatedasdescribedintheSupplementaryMaterial[];weillustrateparticularsec-tionsthroughthephasediagraminFigs.MeasurementsofSHEtorqueandtheRashbaeld.—Beforeanalyzingtheexperimentalswitchingdata,weconsidermeasurementsinwhichtheComagneticmomentrotatescoherently.Byanalyzingthedirectionandmagni-tudeofcurrent-inducedrotationwecandistinguishtheSHEtorquefromanin-planeRashbaÞeld[]andmeasuretheSHEtorque.WeÞrstapplyintheplanewithasmallanglerelativetotheaxis[Fig.].Inthiscase,theÞeld-inducedtorqueisparalleltosoitaddstoorsubtractsfromtheSHEtorque,dependingonthesignof.Thenonzeroanglesuppressesdomainformationsothatthemagnetizationrotatescoherently,andthemacrospinmodelapplies.WecompareÞeldsweepsforthesamemagnitudeofcurrent,positiveandnegative[12mAinFig.2(c)sothatOhmicheatingshouldbeidentical.WedeÞneasthevalueofrequiredtoproduceagivenvalueofispositiveandasthecorrespondingquantityforisnegative.FromEq.(,sothat.Theangleisknownforourapparatuswithanaccuracyofof25]andcanbedeterminedaccuratelyfrom.Therefore,bytakingthedifferenceofthetwoexperimentalversuscurves(for(for2(d)]andperformingaone-parameterÞt,wecan7mT12mA06mT.WeÞndthatisapproximatelyindependentofof2(e)].Acurrentof12mAcorre-spondstoachargecurrentdensityassumingforsimplicitythatthecurrentdensityisuniformthroughoutthebilayerandtheAlisfullyoxidized.withthemeasuredvalue,ourvalueofat12mAcorrespondsto,or2nmAfteraccountingforacorrectionassociatedwiththefactthatthePtthicknessiscomparabletothespindiffusionlength,thisvalueof2nmcorrespondstoabulkvalue¼1ÞÞ25].Thisagreesquantitativelywithmeasurementsforin-plane-polarizedPermalloybilayers[].Asimilaranalysisofallowsadeterminationofasafunctionfunction25]:B0an¼280mTanddecreasessig-niÞcantlyasafunctionofincreasing,reßectingheating.NextwedescribeasimilarexperimentwithIfthereisanycurrent-inducedRashbaÞeld,itshouldbeprimarilyinthedirection[],yieldingcurrent-inducedshiftsincurves.Figure2(f)showsrepresentativedatafor10mA,acurrentdensity.Weobservenomeasurableshiftbe-tweenthetwocurvesforanyvalueof,fromwhichweconcludethatanyRashbaÞeldinoursamplehasamagni-tudethatislessthanoursensitivity,.ThisresultisinstrikingcontrasttoRef[],wherean-orientedRashbaÞeld75timeslargerthanourupperboundwasreportedforsimilarsamples.[The-orientedOerstedÞeld,whichAmpereÕslaw,islessthanourmeasurementsensitivity.]Analysisofexperimentalswitchingphasediagrams.—Representativesectionsofourmeasuredroom-temperatureswitchingphasediagrams(SPDs)areplottedinFigs..Qualitatively,theseSPDshaveshapesandsym-metriesverysimilartothestabilityboundariesinthemacrospinmodel[Figs.],supportingourassertionthattheswitchingcanbeexplainedbytheSHE-torque.However,toanalyzetheeffectsoftheSHE-torquequantitatively,itisnotappropriatetouseazero-temperaturemacrospinmodelfortworeasons:(i)current-inducedheatingcanbesigniÞcantand(ii)magneticswitchingoccursbymeansofaspatiallynonuniformreversalprocess.Nonuniformswitchingisevidenteven FIG.3(coloronline).(a),(b)SPDcalculatedinthezero-temperaturemacrospinmodelfor(a)appliedalongtheaxisand(b)Þxedatvariedcontinuously.Switchingboundariesforthestates(solidlines).Limitsofstabilityforthestates(dashedlines).(c),(d)SPDdeterminedexperimentallyby(c)sweepingÞxedvaluesofalongtheaxis,and(d)Þxing40mTandsweeping.Thesolidlinesin(c)and(d)representswitch-ingboundariescalculatedusingthemodiÞedStoner-Wohlfarthmodel.Inallpanels,thesymbol,not 096602(2012)PHYSICALREVIEWLETTERSweekending31AUGUST2012 ,inthattheeasyaxisswitchingÞeld[17mT,seeFig.]ismuchlessthanthevalueexpectedwithinthemacrospinmodel(280mT,determinedabove).Nevertheless,wecanachieveareasonablequantitativemodelingoftheSPDsbyincludingtheeffectsoftheSHEtorquewithinamodi-ÞedStoner-Wohlfarthmodel[]thataccountsapproxi-matelyforthereducedswitchingthresholdforÞeldsinthedirectionbysubstitutingareducedperpendicularcoer-civeÞeldinplaceof[seeEq.(S23)in[]].Weexperimentallybymeasuringtheswitch-ingÞeldasafunctionofperpendiculartothesampleplane,theangleforwhichspin-torqueeffectsareweakest[].TheonlyotherparametersinthemodelaretheSHE-torquestrength33mTasdeterminedabove.Withtheseinputs,switchingcurrentscanbecalculatedinthemodiÞedStoner-WohlfarthmodelforallÞeldvaluesandcomparedtotheexperimentwithnoadjustmentofÞttingparameters[solidlinesinFigs.].WeÞndremarkableagreementconsideringthesimplicityofthemodel.Inparticular,theskewedshapeofthehystereticregioninFig.reproducedwithnoÞttingparameters.WeconcludethattheSHEtorqueincombinationwithheatingprovidesadescriptionforthecurrent-drivenswitching.Heatingalonecannotexplainthedata,sinceheatingdependsonandwemeasureoppositesignsofswitchingforoppositesignsofBecauseourmeasurementsofbothmagnetizationrota-tionandswitchingareexplainedquantitativelybythesamevalueof,andthisnumberisinagreementwithpre-viousexperiments,wearguethattheSHE-torquemecha-nismfullyexplainsthecurrent-inducedswitching,withnoevidencefortheout-of-plane()RashbaeffectproposedinRef.[](seeadditionaldiscussionin[]).TheoreticalcalculationsindicatethatanyRashbaÞeldintherectionshouldbeaccompaniedbyanevenlargerRashbaÞeldalongalong27Ð30],sothelackofameasurableRashbaÞeldinourrotationexperimentsgivesadditionalreasontoquestiontheexistenceofalargeRashbaÞeld.Wehavealsomeasuredcurrent-inducedswitchingin(Fig.S4in[,andsamples(thicknessesinA).Thisshowsthattheswitchingdoesnotdependonthepresenceofanoxidecappinglayer,andoccursforferromagnetthicknessesupto15Aandforferromagnetswithdifferentchemicalcompositions.TheseobservationssuggeststronglythatitisthePtÞlmwhichdrivesswitching,ratherthanaRashbaÞeldwithintheTheSHEtorqueisattractiveforappli-cationsbecause,inprinciple,itcanbemoreefÞcientthanconventionalspintorquefromspin-polarizedcurrentspro-ducedbyspinÞltering.Inaconventionalspin-torquede-vice,theefÞciencyofthetorquecannotexceedoneunitoftransferredperelectroninthecurrent.However,forSHEtorqueinthegeometryofFig.,wherethechargecurrentßowsthroughasmallin-planeareaandthespincurrentactsthroughamuchlargerperpendicularareatheratioofthetotalspincurrenttothetotalchargecurrentis.ThiscanbegreaterthanoneevenwhenthespinHall(SH)angle,meaningthatforeveryelectronchargepassingthroughthedevicemanyunitsofangularmomentumcanßowperpendiculartotheÞlmtoapplyaspintorquetothemagneticlayer.UnderstandingthattheSHEtorqueexplainscurrent-inducedswitchingofperpendicularlypolarizedmagneticlayersenablesquantitativeestimatesforhowtooptimizetheeffect.ForasufÞcientlysmallsample,themacrospinmodelshouldapply.Weassumeamagneticlayeroflength,width,andthicknessforwhichtheperpendicularanisotropyÞeldisoptimizedtoprovideanenergybarrierisBoltzmannÕsconstantand300K),correspondingtoaretentiontimeof10yr[Thesmall,Þxed,symmetry-breakingin-planemagneticÞeldneededtosetthedirectionofthespin-HallswitchingcanbeappliedeasilybythedipoleÞeldfromanearbymagneticlayer.AsimpleanalysisyieldsacriticalcurrentforSHEswitching[ ¼1Þ isthePtthickness,aretheconductivitiesoftheferromagnetandPt,andisthePtspindiffusionlength.Forasamplewith200nm2nm6nm¼1ÞÞ3], sf¼1:4nmm21],andassumingforsimplicity,weconcludethatshouldbeevenintheabsenceofanyassis-tancefromheating-inducedthermalactivation.Thecriticalcurrentswouldbereducedevenfurtherwithheating,orbyusingmaterials[]thatgeneratestrongerSHEtorques.SwitchingcurrentsfortheSHEtorquethereforehavethepotentialtobecompetitivewiththeoptimumswitchingcurrentsformagnetictunneljunctions)controlledbycon-ventionalspin-transfertorque[].Comparedtocon-ventionalmagnetictunneljunctions,spin-Hallswitcheddeviceshaveanadvantagethatchargecurrentsdonotneedtoßowthroughtunnelbarriersthataresensitivetoelectricalbreakdown.TheSHEtorquemayalsohaveanimportantinßuenceoncurrent-drivenmagneticdomainwallmotioninnano-wiresmadefromlayeredheavy-metalÐferromagnetstructures,where,e.g.,thenonadiabatictorquehasbeenmeasuredtobeanomalouslystrong[WeacknowledgesupportfromARO,ONR,DARPA,NSF/MRSEC(DMR-1120296)throughtheCornellCenterforMaterialsResearch(CCMR),andNSF/NSEC 096602(2012)PHYSICALREVIEWLETTERSweekending31AUGUST2012 throughtheCornellCenterforNanoscaleSystems.WealsoacknowledgeNSFsupportforT.G.andthroughuseoftheCornellNanofabricationFacility/NNINandtheCCMRfacilities. 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