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APPLIEDPHYSICSLETTERS91,112501͑2007͒

Current-inducedmagneticvortexcoreswitchinginaPermalloynanodisk

Y.Liu

InstitutfürFestkörperforschungIFF-9“ElektronischeEigenschaften,”ForschungszentrumJülichGmbH,D-52425Jülich,GermanyandDepartmentofPhysics,TongjiUniversity,200092Shanghai,People’sRepublicofChina

S.Gliga,R.Hertel,a͒andC.M.Schneider

InstitutfürFestkörperforschungIFF-9“ElektronischeEigenschaften,”ForschungszentrumJülichGmbH,D-52425Jülich,Germany

͑Received2February2007;accepted25July2007;publishedonline10September2007͒TheauthorsreportontheswitchingofamagneticvortexcoreinasubmicronPermalloydisk,inducedbyashortcurrentpulseappliedinthefilmplane.Micromagneticsimulationsincludingtheadiabaticandnonadiabaticspin-torquetermsareusedtoinvestigatethecurrent-drivenmagnetizationdynamics.Theypredictthatacorereversalcanbetriggeredbycurrentburstsatenthofananosecondlong.Thevortexcorereversalprocessisfoundtobethesameaswhenanexternalfieldpulseisapplied.Thecontrolofavortexcore’sorientationusingcurrentpulsesintroducesthetechnologicallyrelevantpossibilitytoaddressindividualnanomagnetswithindensearrays.©2007AmericanInstituteofPhysics.͓DOI:10.1063/1.2780107͔

Patternedsoft-magneticthinfilmelementswithlateralextensionaboveacriticalsizenaturallyformflux-closurepatterns,1whichcontainmagneticvortices,i.e.,smallre-gions,wherethemagnetizationdirectioncirculatesinthefilmplanearoundananometer-sizedcore.2Atthecenterofthiscore,themagnetizationpointsperpendiculartotheplane.3Thestudyofthestaticanddynamicpropertiesofvorticesandvortexcoresinparticularhasrecentlyemergedasadynamicfieldofinvestigation.2–8Magneticvortexcoreshaveindeedbeenconsideredaspossiblecandidatesformag-neticdatastorage9duetoseveralattractiveproperties:theirsizeisofonlyafewtensofnanometers,2theyexhibitperfectbistability͑pointingeitherupwardsordownwards,definingthevortexpolarization͒,andtheyformnaturallyandulti-matelyhaveahighthermalstability.Allthesefeaturesrep-resentimportantprerequisitesforpossibleapplicationstodatastorage.Inordertostoreinformationusingavortexcore,mechanismsforacontrolledswitchingofitsorientationarerequired.Thedirectreversalofvortexcoresbymeansofanappliedfieldorientedperpendiculartotheplanerequireslargefieldvaluesofmorethan200mT,9whichgivesanideaofthehighstabilityofthesestructures.Recently,ithasbeendemonstratedthatthevortexcorecouldbeswitchedbymeansofsinusoidallowfieldpulsesappliedintheplaneofthesample.6Inthiscase,thegyrotropicresonancewasexploited—alow-frequencymodewherethevortexrotatesarounditsequilibriumposition.5,7,8,10Inordertousetheresonantpropertiesofthevortex,ithastobebroughtonitsgyrotropicorbit.Thetimerequiredforthisdependsonthegyrotropicfrequency,whichisapproximatelyproportionaltothesample’saspectratioandhastypicalvaluesofaboutagigahertzorbelowforthin-filmelements.7Inpractice,theswitchingtimecanbedefinedasthetimebetweentheappli-cationofthefieldandthecompletionofthecoreswitch.Inthissense,theswitchingtimeoftheresonantschemeisoftheorderofnanoseconds.Basedonmicromagneticsimula-tions,afasterroutetoachievecorereversalhasbeenpro-a͒

posedrecently.11,12Inthiscase,whichdoesnotusethegy-rotropicresonance,thereversalisinducedbyasuitablyshapedunipolarin-planemagneticfieldpulseonlyafewpicosecondslong.Therequiredamplitudeofthefieldpulseislarger͓approximately70mT͑Ref.11͔͒thaninthecaseofresonantswitching͑approximately2mT,6͒butthisswitch-ingschemeismuchfaster.Inspiteoftheirrespectiveadvan-tages͑lowfields,highspeed͒boththeresonantandthenon-resonantswitchingmodesexhibitacommonproblemintermsofapplicability:thelackofselectivityoftheindividualelements.Reliablyaddressingasinglenanodiskinsideadensearrayisverydifficultusingexternalfields.Inthislet-ter,wepresentafastandsimplemethodtoswitchmagneticvortexcoresbyapplyingshortelectriccurrentpulses,only100pslong.Theelectriccurrentpulseisappliedintheplaneoftheelement.Wethusshowthatafasttogglecoreswitch-ingmechanismcanbetriggeredinarelativelysimplewaywhichiscompatiblewithintegratedcircuits,therebysolvingtheissueofselectivity.

Theresultswereobtainedusingmicromagneticfinite-elementsimulationsbasedontheLandau-Lifshitz-Gilbertequation.Ourmicromagneticcodeusedinprevioussimulations13hasbeenextendedtoconsiderthespintorqueexertedbyanelectriccurrentflowingthroughthesample.Thiseffectofcurrent-drivenmagnetizationdynamicsismodeledbyincludingtheadiabaticandthenonadiabaticspintorqueterms14,15intotheGilbertequation,

dmdm

=−␥mϫHeff+␣mϫ−͑u١͒mdtdt

+␤mϫ͓͑u١͒m͔,

͑1͒

wherem=M/Msisthenormalizedlocalmagnetization͑Msthesaturationmagnetization͒,Heffistheeffectivefieldcon-tainingtheexchangeandthedipolarfield,␤isadimension-lessparameterdescribingthestrengthofthenonadiabaticterm,and␣istheGilbertdampingconstant.Thevectoruispointingparalleltotheelectronflowdirectionandhasanamplitudeofu=jPg␮B/͑2eMs͒,15wherejisthecurrentden-sity,Pisthedegreeofelectronpolarization,gistheLandé

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Electronicmail:r.hertel@fz-juelich.de

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FIG.1.͑Color͒Current-inducedvortexcorereversalinaPynanodiskof200nmdiameterand20nmthickness.AGaussiancurrentpulseisappliedinthesampleplanewithastrengthof7.4ϫ1012A/m2andawidth␴=100ps.Themagneticvortexstructureatequilibriumisshownontheleft.Inthethreeframesontheright,theevolutionofthemagnetizationisshownforasmallregionaroundthevortexcore,whereavortex-antivortexpairnucleates.Asthevortexisshiftedinthedirectionoftheelectronflowpriortothepaircreation,theseframesarenottakeninthesameareasofthesample.Thearrowsrepresentthein-planemagnetizationdirection,whilethecolorcodedisplaysthezcomponentofthemagnetization.Theblueandredribbonsarethemx=0andmy=0isosurfaces,respectively.Thetimeismeasuredfromthemomentthepulseisapplied͑seeFig.2͒.

splittingfactor,␮BistheBohrmagneton,andeistheelectroncharge.Asamodelsystem,weconsideradisk-shapedPermalloy͑Py͒sampleofd=200nmdiameterandt=20nmthickness,asusedinRef.11.TheparametersusedinthesimulationareA=13pJ/m͑exchangeconstant͒,␮0Ms=1.0T,␣=0.03,P=0.7,␤=0.02,15K=0͑anisotropyconstant͒.Thesampleisdiscretizedintoapproximately216000irregulartetrahedralelements,correspondingtoacellsizeofabout3nm.Ahomogeneouscurrentdensitydis-tributionisassumed,aswasdonerecentlyinasimilarstudybyKasaietal.,16wheretheresonant,current-pulseinducedgyrotropicvortexcoremotionwasinvestigated.

Thecurrent-inducedvortexcorereversalisstudiedforshortGaussian-shapedcurrentpulses͑␴=100ps͒ofvaryingstrengths.Inallcases,themaximumstrengthisreachedat300ps.Toobtainacorereversal,wefoundthatforthecon-sideredsampletheamplitudeofthesepulsesmustexceedaminimumvalueofj=6.7ϫ1012A/m2.Althoughsuchahighcurrentdensitymightendangerthestructuralstabilityofthesampleifitwasappliedcontinuously,thedamagingeffectsofthecurrentshouldbesmallinthepresentcasewhereonlyultrashortpulsesareused.

AtypicalexampleofthevortexcorereversalprocessisshowninFig.1,startingwithavortexwhosecorepointsinthepositivezdirection.Themicromagneticprocesseslead-ingtothevortexcorereversalareidenticaltotheonesde-scribedinRef.11,wherefieldpulseswereused.Anisosur-facerepresentationasintroducedinRef.17isusedtopreciselylocatethevortexcore.Thein-planemagnetizationisfirstheavilydistortedandapronounced“dip”isformed16,18asaresultofthecurrentrunningthroughthesample.About460psaftertheapplicationofthepulse͑i.e.,160psafterthemaximumhasbeenreached͒,thedistortionleadstothecreationofavortex-antivortexpair,whichcanunambiguouslyberecognizedbythetwoadditionalcross-ingsofthemx=0andmy=0isosurfaces.Bothcoresofthenewpairarepointingintheoppositezdirectionoftheinitialcore.11Thenewlyformedantivortexandtheoppositelypo-larizedinitialvortexsubsequentlyannihilate.17Thelattersubprocessunfoldsoverapproximately10psandleavesasinglevortexcore,whichisoppositelypolarizedwithrespecttotheinitialone.Theformationofvortex-antivortexpairsafterapplicationofshortcurrentpulsesisconsistentwithrecentexperimentalobservationsbyKläuietal.19

Figure2showstheevolutionintimeofthesample’sspatiallyaveragedenergydensityinthecaseofanapplied

currentpulseof7.4ϫ1012A/m2and␴=100ps.Theex-changeenergyrapidlydecreasesaftertheannihilationofthevortex-antivortexpair,leadingtoasuddendropinthetotalenergy.11

Byincreasingthepulsestrength,itispossibletoproducemultipleswitches,asshowninFig.3.Multipleswitchesarearepeatedseriesofvortex-antivortexpaircreationandanni-hilationprocesses.Inallcases,thetotalenergyisseentoimmediatelydecreasefollowingeachcorereversal.How-ever,iftheenergysuppliedbythecurrentpulseafteracorereversalissufficienttoovercompensatedissipation,theen-ergycanstillincreasebeforefurtherswitchesoccur.Adoublecoreswitchingisobtainedwithcurrentpulsesofabout8.5ϫ1012A/m2,whiletripleandquadrupleswitchesoccurwithpulsesof10ϫ1012and11ϫ1012A/m2,respec-tively.Ultimately,forverylargecurrents͑above20ϫ1012A/m2͒,thevortexcoreisexpelledfromthesample.20

ThediagraminFig.3͑b͒showsthenumberofcoreswitchesasafunctionoftheappliedcurrent’sstrength.Clear“steps”areobserved.Whilethecorereversalmechanismismediatedbytheformationofavortex-antivortexpair,itistheannihilationprocesswhichleavesthevortexwithanop-positelypolarizedcore.AsshowninRef.17,suchananni-hilationismediatedbyamagneticsingularity͑Blochpoint͒whichisinjectedthroughthesample.SincetheenergyofformationofaBlochpointisuniquelyafunctionofthe

FIG.2.Evolutionasafunctionoftimeofthetotal,magnetostatic,andexchangeenergydensitiesinthePydiskfollowingacurrentpulseofadurationof␴=100psandapeakvalueof7.4ϫ1012A/m2.

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FIG.3.͑a͒Totalenergyasafunctionoftimeformultiplecoreswitches.͑b͒Numberoftimesthevortexcoreswitchesdependingontheappliedcurrentdensity.

exchangeconstant,21theannihilation͑andthusthereversal͒processcanonlyoccuratspecificenergyvalues,resultingintheobservedsteps.

Inconclusion,wehavepresentedthepossibilityofre-versingthepolarizationofamagneticvortexcoreusingshortcurrentpulses.Themagnetizationreversalprocess,whichconsistsofacomplicatedsequenceofvortex-antivortexpaircreationandannihilationevents,unfoldsonatimescaleofapproximately40ps,i.e.,shorterthanthedurationofthepulsesappliedinthisstudy.Furtherinvestigationsarere-quiredtoexplorethelimitsoftheoperationalrangeforacontrolled,singletoggleswitchingintermsofpulsedurationandpulsestrength,andtodeterminehowshortacurrentpulsecanbetotriggeravortexcorereversal.Thecurrent-inducedvortexcorereversalopensthepossibilityofaddress-ingindividualmagneticelementsinavortexstatewithinan

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arrayofnanoelements.Thisfeaturecouldmakevortexcoresinterestingcandidatesfordatastoragepurposesinfuturede-vices.

Aftersubmissionofthisletter,experimentalevidenceforcurrent-driven22

vortexcoreswitchinghasbeenreportedbyYamadaetal.Oneoftheauthors͑Y.L.͒acknowledgesfinancialsupportfromtheAlexandervonHumboldtFoundation.

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