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Editedby WenqingLiu
RoyalHollowayUniversityofLondon,Egham,UnitedKingdom
UniversityofYork,Heslington,UnitedKingdom
YongbingXu
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1.1Spinandspinordering.........................................................................................2
1.2Thediscoveryofgiantmagnetoresistanceandtunnelling
1.3Semiconductorspintronics:dilutemagneticsemiconductorandspin field-effecttransistor..........................................................................................11 1.42Dmaterialsandmagnetismin2Dmaterials...................................................16
2.1.1FromDiractoPauli
2.2.1Energydispersionandspintexture
2.2.3Quantumoscillations ................................................................................37
2.2.4Weakantilocalization ...............................................................................39
2.3Spin orbittransport...........................................................................................41
2.3.1Spin-chargeconversioneffects .................................................................41
2.3.2Persistentspinhelix ..................................................................................42
2.3.3Spinandchargepumping .........................................................................42
2.3.4Zitterbewegungeffect ...............................................................................43
2.3.5QuantumanomalousHallandmagnetoelectriceffects ..............................43
2.3.6Floquetphysicsinspin orbitcoupledsystems
2.4Rashbadevices...................................................................................................45
2.4.1Aharonov Casherinterferometer .............................................................45
2.4.2Datta Dasspinfield-effecttransistor .......................................................45
2.4.3Spin orbittorquesdevices .......................................................................47
2.4.4Spin orbitQubits.....................................................................................47
2.5Outlookandconclusion.....................................................................................47
Chapter3:Two-dimensionalferrovalleymaterials ..................................................65 Xin-WeiShen,HeHuandChun-GangDuan
3.1Valleytronicsin2Dhexagonallattices..............................................................65
3.2Valleypolarizationinducedbyexternalfields..................................................67
3.3Ferrovalleymaterialswithspontaneousvalleypolarization.............................70
3.3.1VSe2-Ferrovalleymaterialsinducedbyferromagnetism ...........................70
3.3.2BilayerVSe2-antiferrovalleymaterials......................................................77
3.3.3GeSe-Ferrovalleymaterialsinducedbyferroelectricity ............................83
3.4Summaryandoutlook........................................................................................90 References...................................................................................................................91
Chapter4:Ferromagnetismintwo-dimensionalmaterialsviadoping anddefectengineering .........................................................................95
YirenWangandJiabaoYi
4.1Introduction........................................................................................................95
4.2Ferromagnetismingraphene..............................................................................99
4.3Ferromagnetisminboronnitride.....................................................................101
4.4Ferromagnetisminphosphorene......................................................................105
4.5Ferromagnetismoftransition-metaldichalcogenide:MoS2 ............................110
4.6Ferromagnetismintwo-dimensionalmetaloxide:SnO..................................114
4.7Conclusionandprospective.............................................................................118
Chapter5:Charge-spinconversionin2Dsystems
YongPu
5.1Overview..........................................................................................................125 5.2Introduction......................................................................................................126
5.3Spingeneration.................................................................................................128
5.3.1Spin-polarizedchargecurrent .................................................................128
5.3.2 Spininjectionintononmagneticmaterials ..............................................129
5.3.3Purespincurrent .....................................................................................130
5.4Spindetection...................................................................................................131
5.4.1Spinaccumulationvoltage
5.4.2InversespinHalleffect ...........................................................................133
5.4.3Magnetoresistance ..................................................................................133
5.5Outlook.............................................................................................................135
5.5.1Newmaterialsandheterostructures ........................................................135
5.5.2Newtechniquesandcharacterizations.....................................................135
5.5.3Newdevicearchitecturesandfunctionalities ..........................................135
Chapter6:Magneticpropertiesofgraphene
NujiangTang,TaoTang,HongzhePan,YuanyuanSun,JieChen andYouweiDu
6.1Significanceofmagneticgraphene..................................................................137
6.2Primarytheoryofmagnetismofgraphene—Lieb’stheorem.........................138
6.3Generalmethodsforinducinglocalizedmagneticmomentsingraphene......139
6.3.1Vacancyapproach ..................................................................................139
6.3.2Edgeapproach
6.3.3Thesp3-typeapproach
6.4Conclusionandoutlook...................................................................................158 6.5Acknowledgments............................................................................................158
Chapter7:Experimentalobservationoflow-dimensionalmagnetismin graphenenanostructures ....................................................................163
MinghuPanandHuiYuan
7.1Introduction......................................................................................................163
7.2Electron electroninteractioningraphene......................................................164
7.3Magnetisminfinitegraphenefragment..........................................................167
7.4Edgesingraphenenanoribbons.......................................................................174
7.5Magnetisminducedbydefectsingraphenenanostructures............................183
7.6Summaryandoutlook......................................................................................187 References.................................................................................................................188
Chapter8:Magnetictopologicalinsulators:growth,structure,andproperties ........191
LiangHe,YafeiZhao,WenqingLiuandYongbingXu
8.1Introduction......................................................................................................192
8.2Crystalstructureandthinfilmgrownbymolecular-beamepitaxy................192
8.2.1Crystalstructures ....................................................................................192
8.2.2Thinfilmgrownbymolecular-beamepitaxy ..........................................193
8.3Magnetictopologicalinsulator........................................................................197
8.3.1Transitionmetal dopedtopologicalinsulator ........................................197
8.3.2Magneticproperties ................................................................................197
8.3.3Novelphenomenabasedonmagnetictopologicalinsulators ..................200
8.4Magneticproximityeffectintopologicalinsulator basedheterojunctions...201
8.4.1Topologicalinsulators/ferromagneticmetal ............................................201
8.4.2Topologicalinsulators/ferromagneticinsulators ......................................203
8.4.3Dopedtopologicalinsulators/ferromagneticmetal ..................................205
8.4.4Dopedtopologicalinsulators/ferromagneticinsulators ............................207
8.5Spin-transfertorque/spin orbitaltorqueintopologicalinsulators.................209
8.5.1Spin momentumlockingintopologicalinsulators ................................210
8.5.2Theoreticallypredictedspin-transfertorque/spin orbitaltorque intopologicalinsulators ..........................................................................214
8.5.3Spin orbitaltorqueintopologicalinsulators ..........................................215
8.5.4Magneticrandomaccessmemorybasedontopologicalinsulators ..........219
8.6Summaryandoutlook......................................................................................221
Chapter9:Growthandpropertiesofmagnetictwo-dimensionaltransition-metal chalcogenides .....................................................................................227 WenZhang,PingKwanJohnnyWong,RebekahChuaand AndrewThyeShenWee
9.1Introduction......................................................................................................228
9.2Fundamentalsofmolecularbeamepitaxyfortwo-dimensional transition-metalchalcogenides.........................................................................229
9.2.1Uniquenessofmolecularbeamepitaxy...................................................229
9.2.2ConceptofvanderWaalsepitaxy ..........................................................229
9.2.3TechnicalaspectsofvanderWaalsepitaxy............................................232
9.3Growthandpropertiesofmagnetictwo-dimensionaltransition-metal chalcogenides...................................................................................................233
9.3.1Extrinsicmagnetismintwo-dimensionaltransition-metal chalcogenides .........................................................................................233
9.3.2Intrinsicmagnetismintwo-dimensionaltransition-metal chalcogenides .........................................................................................234
9.4Opportunitiesandchallenges...........................................................................239
9.4.1FundamentalissuesofvanderWaalsepitaxy .........................................240
9.4.2Moleculardoping ....................................................................................241
9.4.3Hybridthree-dimensional/two-dimensionalstructures .............................241 9.5Summary...........................................................................................................242
Chapter10:Spin-valveeffectof2D-materialsbasedmagneticjunctions
MuhammadZahirIqbal
10.1Introduction....................................................................................................253
10.3Growthoftwo-dimensionalmaterialsanddevicefabrication......................258
10.4Tungstendisulfide basedspin-valvedevice................................................260 10.5Molybdenumdisulfide basedspin-valvedevice.........................................261
10.6Spin-valveeffectinFe3O4/MoS2/Fe3O4 ........................................................263
10.7Comparisonbetweentransitionmetaldichalcogenide’swithdifferent two-dimensionalmaterials-basedspinvalves...............................................264 10.8Summary.........................................................................................................268
Chapter11:Layeredtopologicalsemimetalsforspintronics ..................................273 XuefengWangandMinhaoZhang
11.1Introduction....................................................................................................273
11.1.1IntroductiontoSpintronics .................................................................273
11.1.2Topologicalsemimetals ......................................................................277 11.2Thestrongspin orbitalcouplingintopologicalsemimetals.......................285
11.3.1FermiarcsinWTe2 ............................................................................288
11.3.2FermiarcsinMoxW1 xTe2 ................................................................289
11.4Two-dimensionaltopologicalinsulators........................................................291
11.4.2Two-dimensionaltopologicalinsulatorsinWTe2 ...............................291
11.4.3Two-dimensionaltopologicalinsulatorsinZrTe5 ...............................292
11.5Majoranafermions.........................................................................................294
11.6Summaryandoutlook....................................................................................294
Listofcontributors MatthewT.Bryan DepartmentofElectronicEngineering,RoyalHolloway,UniversityofLondon, Egham,UnitedKingdom
JieChen PhysicsDepartment,NationalLaboratoryofSolidStateMicrostructures,Jiangsu ProvincialKeyLaboratoryforNanotechnology,NanjingUniversity,Nanjing,P.R.China
RebekahChua DepartmentofPhysics,NationalUniversityofSingapore,2ScienceDrive3, Singapore,Singapore;NUSGraduateSchoolforIntegrativeSciencesandEngineering,Centrefor LifeSciences,NationalUniversityofSingapore,28MedicalDrive,Singapore,Singapore
YouweiDu PhysicsDepartment,NationalLaboratoryofSolidStateMicrostructures,Jiangsu ProvincialKeyLaboratoryforNanotechnology,NanjingUniversity,Nanjing,P.R.China
Chun-GangDuan StateKeyLaboratoryofPrecisionSpectroscopyandKeyLaboratoryofPolar MaterialsandDevices,MinistryofEducation,DepartmentofOptoelectronics,EastChinaNormal University,Shanghai,P.R.China;CollaborativeInnovationCenterofExtremeOptics,Shanxi University,Taiyuan,P.R.China
LiangHe York-NanjingJointCenter(YNJC)forSpintronicsandNanoengineering,Schoolof ElectronicsScienceandEngineering,NanjingUniversity,Nanjing,P.R.China
HeHu StateKeyLaboratoryofPrecisionSpectroscopyandKeyLaboratoryofPolarMaterialsand Devices,MinistryofEducation,DepartmentofOptoelectronics,EastChinaNormalUniversity, Shanghai,P.R.China
MuhammadZahirIqbal NanotechnologyResearchLaboratory,FacultyofEngineeringSciences, GIKInstituteofEngineeringSciencesandTechnology,Topi,Pakistan
WenqingLiu York-NanjingJointCenter(YNJC)forSpintronicsandNanoengineering,Schoolof ElectronicsScienceandEngineering,NanjingUniversity,Nanjing,P.R.China;Departmentof ElectronicEngineering,RoyalHolloway,UniversityofLondon,Egham,UnitedKingdom
AurelienManchon MaterialScienceandEngineering,PhysicalScienceandEngineeringDivision, KingAbdullahUniversityofScienceandTechnology,Thuwal,SaudiArabia
HongzhePan PhysicsDepartment,NationalLaboratoryofSolidStateMicrostructures,Jiangsu ProvincialKeyLaboratoryforNanotechnology,NanjingUniversity,Nanjing,P.R.China;Schoolof PhysicsandElectronicEngineering,LinyiUniversity,Linyi,P.R.China
MinghuPan SchoolofPhysics,HuazhongUniversityofScienceandTechnology,Wuhan, P.R.China
YongPu NanjingUniversityofPostsandTelecommunications,Nanjing,Jiangsu,China
Xin-WeiShen StateKeyLaboratoryofPrecisionSpectroscopyandKeyLaboratoryofPolar MaterialsandDevices,MinistryofEducation,DepartmentofOptoelectronics,EastChinaNormal University,Shanghai,P.R.China
YuanyuanSun PhysicsDepartment,NationalLaboratoryofSolidStateMicrostructures,Jiangsu ProvincialKeyLaboratoryforNanotechnology,NanjingUniversity,Nanjing,P.R.China;Schoolof PhysicsandElectronicEngineering,LinyiUniversity,Linyi,P.R.China
NujiangTang PhysicsDepartment,NationalLaboratoryofSolidStateMicrostructures,Jiangsu ProvincialKeyLaboratoryforNanotechnology,NanjingUniversity,Nanjing,P.R.China
TaoTang PhysicsDepartment,NationalLaboratoryofSolidStateMicrostructures,Jiangsu ProvincialKeyLaboratoryforNanotechnology,NanjingUniversity,Nanjing,P.R.China;Collegeof Science,GuilinUniversityofTechnology,Guilin,P.R.China
XuefengWang SchoolofElectronicScienceandEngineering,andCollaborativeInnovation CenterofAdvancedMicrostructures,NanjingUniversity,Nanjing,P.R.China
YirenWang SchoolofMaterialsScienceandEngineering,CentralSouthUniversity,Changsha, P.R.China
AndrewThyeShenWee DepartmentofPhysics,NationalUniversityofSingapore,2Science Drive3,Singapore,Singapore;CentreforAdvanced2DMaterials(CA2DM)andGraphene ResearchCentre(GRC),NationalUniversityofSingapore,6ScienceDrive2,Singapore,Singapore PingKwanJohnnyWong CentreforAdvanced2DMaterials(CA2DM)andGrapheneResearch Centre(GRC),NationalUniversityofSingapore,6ScienceDrive2,Singapore,Singapore YongbingXu York-NanjingJointCenter(YNJC)forSpintronicsandNanoengineering,Schoolof ElectronicsScienceandEngineering,NanjingUniversity,Nanjing,P.R.China;Departmentof ElectronicEngineering,TheUniversityofYork,York,UnitedKingdom;Spintronicsand NanodeviceLaboratory,DepartmentofElectronicEngineering,UniversityofYork,York,United Kingdom;Nanjing-YorkJointCenterinSpintronics,NanjingUniversity,Nanjing,China
JiabaoYi GlobalInnovativeCentreforAdvancedNanomaterials,SchoolofEngineering,The UniversityofNewcastle,Callaghan,NSW,Australia
HuiYuan SchoolofPhysics,HuazhongUniversityofScienceandTechnology,Wuhan, P.R.China
MinhaoZhang SchoolofElectronicScienceandEngineering,andCollaborativeInnovation CenterofAdvancedMicrostructures,NanjingUniversity,Nanjing,P.R.China
WenZhang DepartmentofPhysics,NationalUniversityofSingapore,2ScienceDrive3, Singapore,Singapore
YafeiZhao York-NanjingJointCenter(YNJC)forSpintronicsandNanoengineering,Schoolof ElectronicsScienceandEngineering,NanjingUniversity,Nanjing,P.R.China
Preface “Spin”isanintrinsicformofangularmomentumuniversallycarriedbyelementary particles,compositeparticles,andatomicnuclei.Itisasolelyquantumphenomenonand hasnocounterpartinclassicalmechanics.Manyfundamentalquestionsoftheelectrons’ spinremainopenissuesuptothisdate:thespin orbitalcoupling,spin photoninteraction, andspin-wavetransmissiontonameafew.Significantly,thediscoveryofgiant magnetoresistanceeffect,celebratedbythe2007NobelPrize,hasgeneratedarevolutionary impactonthedatastoragetechnologies.Thistriggeredtheriseofspintronics,an interdisciplinarysubjectdedicatedforthestudyofspin-basedotherthanorinadditionto chargeonly basedphysicalphenomenaofelectronicsystems.
Two-dimensional(2D)materialswithstrongintrinsicspinfluctuationshaveintroducednew physicalparadigmsandenabledthedevelopmentofnovelspintronicdevices.These cleavablematerialsprovideanidealplatformforexploringspinorderinginthe2Dlimit, wherenewphenomenaareexpected,andrepresentasubstantialshiftinourabilityto controlandinvestigatenanoscalephases.Withsteadyimprovementingrowthtechniques, spintronic2Dmaterialscanbenowassembledinachosensequencewithone-atomic-plane precision.Combiningtheminverticalstacksfurtheroffersenormousamountofpossibilities tobroadentheversatilityof2Dmaterials,allowingforachievingunusualmaterial propertiesthatcannotbeobtainedotherwise.
Withcontributionsfromtheworld-leadingscientists,thisbookaimstoprovideanoverview oftheresearchinspintronic2Dmaterials.Thisstartswith2Dmagnetismfundamentaland coversthedevelopmentofthemostrepresentativespintronic2Dmaterialsuptodate.It providesbackground,introduction,thelatestresearchresults,andanextensivelistof referencesineachchapter.Itishopedthatthecollectionofthesematerialsinonebookwill enablethechallengesandresearchprogressin2Dspintronicstobeseenincontext,while theindividualchaptersaredesignedtobeself-contained.Theeditorswishtothankallthe authorsforwritingtheirchaptersandthededicatedElsevierpublicationteamforpublishing thebook.
Introductiontospintronicsand2D materials WenqingLiu1,MatthewT.Bryan1 andYongbingXu2,3
1DepartmentofElectronicEngineering,RoyalHolloway,UniversityofLondon,Egham, UnitedKingdom, 2SpintronicsandNanodeviceLaboratory,DepartmentofElectronicEngineering, UniversityofYork,York,UnitedKingdom, 3Nanjing-YorkJointCenterinSpintronics,Nanjing University,Nanjing,China
ChapterOutline
1.1Spinandspinordering2
1.2Thediscoveryofgiantmagnetoresistanceandtunnellingmagnetoresistance7
1.3Semiconductorspintronics:dilutemagneticsemiconductorandspinfield-effect transistor11
1.42Dmaterialsandmagnetismin2Dmaterials16
1.5Overviewofthisbook22
References22
Spin-basedphenomenaarerichinfundamentalphysicsandimportanttoinformation technology.Manyaspectsofelectronspindynamicsremainopenquestions,including spin orbitalcoupling,spin photoninteraction,spinorderingatlowdimensions,andspinwavetransmissiontonameafew.Sincethediscoveryofthegiantmagnetoresistanceeffect (GMR),celebratedbythe2007NobelPrizeinPhysics,spin-basedelectronics—or “spintronics”asitquicklybecameknown—hasdevelopedintoaninterdisciplinaryfield dedicatedtothestudyofspin-basedeffectsratherthanpurelycharge-basedphysical phenomenapreviouslyassociatedwithelectronicsystems(Fig.1.1).Thiseventuallyledtoa revolutionaryimpactondeviceconcepts,particularlyindatastoragetechnologieswherethe introductionofspintronictechnologiesenabledarapidincreaseinthecapacityofharddrives. Inparallelwiththedevelopmentofspintronicsresearch,newtwo-dimensional(2D) materialshavebecomeavailable.Beginningwiththediscoveryofgraphene,acknowledged bythe2010NobelPrizeinPhysics,anumberof2Dmaterialshavebeenproducedwith uniquepropertiesnotseenelsewhere,eveninbulk(three-dimensional)analogsofthesame materials,duetoconfinementoftheirelectronicbandstructure.Combiningtheseproperties withspintronicscouldproducethenextrevolutioninelectronicstechnology,withpotential
https://doi.org/10.1016/B978-0-08-102154-5.00001-1
Spintronicscombinesthenonvolatileandremotesensingpropertiesofmagneticmaterialswith theprocessingfunctionalityofelectronics.
forminimalpowerdissipationorextremesensitivitytomagneticfields.Thisbookcovers recentadvancesinspintronic2Dmaterials,showinghowmagnetismandlow-dimensional electronicscanbecoupledtoproducenewdeviceconceptsandnovelapplications.
1.1Spinandspinordering Spinisanintrinsicformofangularmomentumuniversallycarriedbyelementaryparticles, compositeparticlesandatomicnuclei.Itisasolelyquantumphenomenonandhasno counterpartinclassicalmechanics.Theearliestsignof“spin”canbetracedbacktothe 1880s,whenAlbertA.Michelsonobservedclosely-spaced,butdiscrete,linesinthe emissionspectraofsodiumgas.Whenatomicspectrawerefirstdiscovered,thesodium spectrumwasthoughttobedominatedbyabrightlineknownasthesodiumD-lineat wavelength λD 5 589.3nm.HoweverMichelsonwasabletoresolvethespectruminfiner detailandfoundthattheD-linewasinfactsplitintotwolines,namely λD1 5 589.6nmand λD2 5 589.0nm,calledthefinestructure.Today,weknowthatthesodiumD-linearises fromthetransitionfromthe3ptothe3slevels,withthefinestructurecausedbyslight differencesinenergylevelsofoppositespinsduetothespin orbitinteraction.
WhileMichelsondidnotrecognizespinastheoriginofthefinestructure,hisobservations markthebeginningofthestudyofspin-basedphenomena.FollowingJosephJ.Thomson’s discoveryoftheelectronasaparticlein1897,nextexperimentalhintofspincamein1912, whenFriedrichPaschenandErnstE.A.Backobservedthatinthepresenceofastrong magneticfieldthesodiumD1-andD2-linesfurthersplitintofourandsixlines, respectively.Thisfield-inducedsplittingoffinestructurespectraduetospin orbiteffects issometimesreferredtoastheanomalousZeemaneffect(orthePaschen—Backeffectat highfields).Inthefollowingyear,NielsBohrpublishedhisatomtheory,whichincluded quantizedenergyshellsandelectronorbitalmomentum.Itprovidedaframeworkto understandmanyofthenewquantumphenomenabeingdiscoveredatthetime,butstill
Figure1.1
lackedaspinangularmomentumterm.Quantizationofangularmomentumwas demonstratedbyOttoSternandWaltherGerlachin1922,bymeasuringthedeflectionofa collimatedbeamofgaseous,electricallyneutralsilveratomspassingthrougha nonhomogeneousmagneticfieldintotwodistinctbands(ratherthanthesingle,broadband expectedfromaclassicaldistributionofangularmomentum).Howeveritwasnotuntil 1925,whenSamuelGoudsmitandGeorgeUhlenbecksuggestedthattheelectronhadan intrinsicquantizedangularmomentum,thattheconceptofspinwasgraspedandusedto explainthefinestructure,andanomalousZeemaneffect.By1929,PaulA.M.Dirachad developedhistheoryofrelativisticquantummechanics,demonstratingthatunlikeorbital angularmomentum,electronicspinwasrestrictedtojusttwoquantizedvalues: S 56 1/2.
InexplainingtheanomalousZeemaneffect,electronicspinisdirectlylinkedtothe magneticmomentofeachatom.Indeed,spinisresponsibleformagneticorderingwithina crystalviaaquantummechanicalinteraction,calledexchange.Fundamentally,the exchangeinteractionmanifestsasanelectrostaticinteractionbetweenneighboringspins:by thePauliexclusionprinciple,particlesinidenticalquantumstatescannotoccupythesame position,soelectronsinthesamebandarerepellediftheyhavealignedspins.Thereforethe spatialdistributionofchargewithinthecrystalisdependentonthealignmentof neighboringspins.Naturally,theinteractionisreciprocal;thechargedistribution determinedbythecrystallatticeinfluencesspindirectiongivingrisetomagneto-crystalline anisotropy(havingapreferredmagnetization“easy”axisoraxes)andmechanical distortionsinthelatticemaycause,orbecausedby,changesinthespindirection(aneffect calledmagnetostriction).Stronginteractionbetweenanelectron’sspinandthemagnetic fielditexperiencesduetoitsorbitaroundachargednucleus(the“spin orbitinteraction”) cancreateanadditionalexchangeterm,calledtheDzyaloshinskii Moriyainteraction (DMI),whichactstoalignspinsperpendiculartoeachother.Sinceitcompeteswithnormal exchange,DMItendstointroduceatopologicalchiralitytoamagnet,favoringaparticular senseofspinrotationwhenevermagnetizationbecomesnonuniform.
Eachinteractioncontributestotheoverallenergyofthesystem,withthelowestenergy statedeterminingthemagnetizationprofile.Atafundamentallevel,theexchange Hamiltonian, H,maybedescribedbytheHeisenbergmodel:
where J istheexchangeconstantand si,j arenearest-neighborspins,andthesummationis overallnearest-neighborpairs.InasystemexhibitingaDMI,thisexchangeHamiltonianis augmentedwithaDMIterm:
where Dij isaconstantdescribingthestrengthoftheDMIbetweentheneighboringspins. AsanalternativetotheHamiltonianform,theexchangeenergydensity(neglectingDMI), Eex,maybeexpressedintermsofthematerialmagnetization, M:
where A istheexchangestiffness(proportionalto J ).Theexchangestiffnessisa measurablepropertyofamaterialandfund amentallyaffectsthemagneticordering. When A . 0,magnetizationdivergenceincreasestheenergy,soexchangeenergyis minimizedwhenneighboringspinsalignpar allelwitheachothertogiveferromagnetic ordering.Thereforeferromagneticmateria lscharacteristicallyhaveaspontaneousnet magneticmoment.
Whileexchangealignsspins,anisotropydeterminesthespindirectionality.Therearea numberofdifferent(andsometimescompeting)mechanismsthatinduceanisotropy,and thereforedeterminespinormagnetizationdirection.Magneto-crystallineanisotropy dominatesinmanymaterials,suchthatthealignmentdirectiondependsonthecrystal structure.Foruniaxialmaterials,magneto-crystallineenergy, EK,isgivenby:
whereascubicmaterialshave
where K1,2 areanisotropyconstantsthatdefinethestrengthofthealignment,and θ and φ arethesphericalpolarcoordinatedirections(withpolardirectionalignedwithaneasyaxis). Internaldemagnetizingfieldscausedbyfreesurfacepolesencouragedivergencein magnetization,resultingintheformationofdomainstructure(inwhichmagnetization withinadomainisaligned,butneighboringdomainsareunalignedandseparatedby boundariescalleddomainwalls)andalsoaneffectcalled“shapeanisotropy”that energeticallyfavorsmagnetizationalignedparalleltostructuralsurfacesandedges. Anisotropycanalsoarisefromexternalstimuli,suchasstress(magnetostriction),providing amechanismtotunemagneticbehaviorinsomematerials.
Incontrasttoferromagneticorder,materialswith A , 0haveantiferromagneticorderingin whichneighboringspinsarealignedantiparallelandthereisnonetmagnetization.Note thatnotallneighborsneedtobeantiparallel;anantiferromagnetmayenteranumberof differentantiferromagneticphasesdependingonstoichiometryandcrystalstructure (Fig.1.2A).Insomecases,theantiferromagneticstatebecomes“canted”andthespins misalignfromantiparallel,developingaslighttiltinonedirectiontogiveasmallnet magnetization(Fig.1.2B).Fromatheoreticalviewpoint,antiferromagnetsmaybe consideredastwosublatticesthathaveoppositemagnetizations(Fig.1.2A).This
Examplesof(A)commonantiferromagneticphases,(B)cantedantiferromagnetalignment,and (C)ferrimagneticconfiguration.Coloringindicatesthedifferentsublattices.
descriptionisalsousefultodescribeathirdmagneticorder,ferrimagnetism,wherethe sublatticesarealignedantiparallel,buthaveunequalmagnetizations(Fig.1.2C).
Magneticorderingcanalsobecausedbyinteractionsthatoccurindirectly,via intermediaries.Superexchangemayoccurbetweentwononneighboringmagneticatoms whentheyhaveacommonnonmagneticneighbor(Fig.1.3A).Inessence,theresponseof thenonmagneticatomtotheonemagneticatomaffectsitsinteractionwiththeother magneticatom,leadingtoanindirectexchangecouplingbetweenthemagneticatoms. Doubleexchangeoccursincompoundswithchemicalbondingstructurethatshares electronsbetweenatomsintheirgroundstate(Fig.1.3B).Sincethese“itinerant”electrons arenotlocalizedtoaparticularatomandsincespinispreservedastheelectronhopsfrom oneatomtothenext,theelectronsmediateexchangebetweenmagneticions.
Ruderman Kittel Kasuya Yosida(RKKY)interactionsinvolveexchangebetweencore electronslocalizedtoanatomandconductionelectrons [1],whicharenotlocalizedtoa particularatom(Fig.1.3C).Byinteractingwithseveralatoms,theelectronsinthe conductionbandmaycoupleatomsthatareseveralunitcellsapart.Importantly, progressivelyincreasingtheseparationbetweenatomsnotonlydiminishesthestrengthof theinteraction,butalsocausesoscillationsinthefavoredalignmentoftheatoms.Thatis dependingontheseparation,theRKKYinteractioncanpromoteeitherferromagneticor antiferromagneticspinalignment(Fig.1.3D).SinceRKKYinteractionsaremediatedby conductionelectrons,theyonlyoccurinconductivematerials.Insulatorsmayexperience long-rangeindirectmagneticorderingviavanVleckparamagnetism.Whereastheprevious indirectexchangemechanismsdiscussedinvolvedmaterialsintheirelectronicground states,thevanVleckmechanismoccursduetoexcitedstatesofvalenceelectrons (Fig.1.3E).Intheabsenceofotherinteractions,nocorrelationbetweenspinsof neighboringionsinthegroundstatewouldbeexpected.Howeverperturbingtheground
Figure1.2
Schematicdiagramsof(A)superexchangebetweenelectronsinoutershellsofmagneticionsviaa nonmagneticintermediary,(B)doubleexchangethroughhoppingofitinerantelectronsinouter shellsbetweenmagneticionsviaanonmagneticintermediary,(C)RKKYinteractionsbetween innercoreelectronsofmagneticions,viaexchangewithdelocalizedoutershellelectrons,(D)the variationoftheRKKYexchangeconstantwithdistancebetweeninteractingions(arrowsshowthe favoredspinalignmentbetweenions),and(E)thevanVleckmechanismofexchangebetweentwo ionsinarelaxedstatefollowingexcitationfromagroundstatewithrandomlyalignedspins.Inall figures,solidarrowsrepresentlocalizedspinsordirectexchangeinteractions,dottedarrows representspinsofitinerantelectronsorthehoppingthatmediatestheinteraction. RKKY, Ruderman Kittel Kasuya Yosida.
state(e.g.,bythermalexcitation)mayresultinthetransferofanelectronbetween neighboringatoms,formingeitheratriplet(S 5 1)orsinglet(S 5 0)statewithinthe unfilledshalloftherecipiention.Crucially,inthevanVleckmechanismtripletstatesare energeticallyfavored,promotingspinalignment [2].Uponrelaxationtothegroundstate, thealignedspinisretainedastheelectronmovesbacktoitsoriginalhostion,sothatthere isaneffectiveferromagneticcouplingbetweentheions.Althoughweakinmanymaterials, thevanVleckmechanismisveryimportantforunderstandingferromagnetismininsulators exhibitinginversionoftheconductionandvalencebands.
Anotherfactorthatplaysacriticalroleindeterminingmagneticorderistemperature.Many materialsmayadoptdifferentmagneticorderingatdifferenttemperatures.Crucially, magneticorderingislostinallmaterialsattemperaturesexceedingacharacteristicordering temperature,calledtheCurietemperatureinferromagneticmaterialsandtheNe ´ el temperatureinantiferromagnets.Abovetheorderingtemperature,materialsbecome
Figure1.3
Introductiontospintronicsand2Dmaterials7
paramagnetic;individualatomsretainmagneticmoments,butthereisnosystematic alignmentbetweenneighborsandthereforenospontaneousmagnetization.Whileindividual momentswillalignwithanappliedmagneticfield,inducingamagnetization,removalofthe fielddestroysthealignmentandthematerialwillreturntozeromagnetizationatremanence.
Materialsmayalsodisplayparamagnetic-likecharacteristicsbelowtheorderingtemperature iftheirdimensionsaresmall(wellbelowthesizeneededtoensuresingle-domain magnetization),aneffectcalledsuperparamagnetism.Superparamagnetismisthe mechanismofspontaneousmagneticreversalcausedbythermalperturbationsovercoming theenergybarrierbetweenmagneticstatesandisimportantwhenthethermalenergy(kBT, where kB istheBoltzmannconstant,and T isthetemperature)isgreaterthanaround 2.5% 4%oftheanisotropyenergy(KV,where K istheanisotropyconstant,and V isthe activationvolume,whichifreversedwillleadtothewholesamplemagnetization switching).Sincethermalfluctuationsarerandom,superparamagneticmagnetization reversalmaybeexpectedtooccurwithinatime-period, τ ,describedbythe Arrhenius Ne ´ elequation:
where f0 isacharacteristictime-scalecalledtheattemptfrequency(ontheorderof 1 100GHz).Whetherornotsuperparamagnetismisimportantdependsonthetime-scale overwhichstabilityisrequired.Intherecordingindustry,datamustbepreservedfor severalyears,sotheanisotropyenergymustbeatleast40 45 kBT [3].Practically, stabilitytimesrequiredforresearchismuchshortersosampleswithanisotropyenergyof 30 kBT maybeexpectedtoretaintheirmagneticstateduringmeasurements(lasting minutestohours).
1.2Thediscoveryofgiantmagnetoresistanceandtunnelling magnetoresistance Foroverhalfacenturyafteritsdiscovery,spinwaslargelyneglectedfromelectronics applications.Thatchangedin1988,whengroupsledbyAlbertFert [4] andPeterGrunberg [5] independentlydiscoveredGMRandtriggeredthebirthofthefieldofspintronics,for whichtheywerelaterawardedthe2007NobelPrizeinPhysics.GMRisthedependenceof resistanceontherelativeorientationoftwomagneticlayersconnectedbyaconducting spacer.Theterm“giant”referstothefactthatthefirstGMRmeasurementsdemonstrated relativechangesinresistancethatwas10 100timeslargerthantheanisotropic magnetoresistance(variationofresistancewithalignmentbetweencurrentand magnetizationdirection)foundintheconstituentmaterials.AlthoughtheearliestGMR devicesweredemonstratedusingthecurrentinplanegeometry,GMRmayalsobeseenin
thecurrentperpendiculartoplane(CPP)geometry.Indeed,CPPdevicesdisplaylongerspin diffusionlengthandanevenlargerGMReffect [6].
Toprovideasimpletheoreticalundersta ndingofGMR,letusneglectresistance contributionsofthethinspacerlayerandconsideridenticalmagneticlayerssuchthat theonlydifferenceinresistanceisdueto thealignmentofthelayermagnetizations. Furthermore,letusrestrictthemagnetizationofeachmagneticlayertopointeither “up”or“down”andsplittheelectricalconductivityintotwoindependentchannels correspondingtospinspointingupanddown,withnegligiblemixingbetweenthe conductionchannels.AccordingtoMott’ss-dscatteringtheory [7] ,resistivityislow forspinsalignedwiththema gnetizationofthehostlayer( ρp )andhighforspin opposingthehostmagnetization( ρa ). Fig.1.4 showsthecircuitdiagramsofthis “two-current”modelfortheparallelandant iparallelalignmentofthemagneticlayers. Theequivalentresistancefortheparallel( Rmm )andantiparallel( Rmk )arrangements aregivenby:
Since ρp , ρa, Eq.1.7 showsthat Rmm , Rmk :greaterscatteringoccurswhenthemagnetic layersareantiparallel.Tocomparedifferentdevices,GMRisoftenexpressedasaratio:
IntheGMRstackscreatedbyFertandGru ¨ nberg,thecouplingbetweenthemagnetic layerswasantiferromagneticintheabsenceofamagneticfield.Highfieldswere neededtoovercometheantiparallelcouplingandalignthelayermagnetizationsto
Figure1.4 Schematicillustrationsandcorrespondingcircuitdiagramsoftwo-currentmodelinferromagnet (FM1)/(NM)/ferromagnet(FM2)trilayerswhentheferromagneticlayersare(A)parallel,and(B) antiparallel.Lowscatteringpathsaremarkedingreen;highscatteringpathsaremarkedinred. ρp istheresistivityofspinsalignedparallelwithhostmagnetization,and ρa istheresistivityofspins alignedantiparallelwithhostmagnetization. NM,nonmagneticspacer.
Figure1.5
Schematicdiagramofaspin-valvestructure.Alternativeconfigurationsfeaturean antiferromagneticpinninglayer.Modernspin-valvesalsoutilizeadditionalsublayerstothefree andpinnedlayerstoenhanceperformance [11]
achievethelowresistancestate.ShortlyafterthediscoveryofGMR,StuartS.P.Parkin developedanarchitecture,calledthespin-valve [8 10],whichenabledarbitrary alignmentbetweenthelayersatzero-fielda ndlow-fieldswitchingbetweenresistance states,pavingthewayforGMRtobeusedinpracticalapplications,notablyinhard diskdriveread-heads.Inspin-valves,ath irdmagnetic“pinning”layeriscoupledtothe basicGMRstructureviaathinconductingnonmagneticspacer( Fig.1.5).Duetothe thicknessofthenonmagneticspacer(labeledNM 2 in Fig.1.5 ),thepinninglayerand thebottom(“fixed”or“pinned”)layerofthebasicGMRstructurearestrongly antiferromagneticallycoupled.Thiscouplingcausesthepinnedlayertobemagnetically hard,requiringalargefieldtoinducemagneti zationreversal.Furthermore,thethickness ofthepinninglayermaybetailoredtocompensateforthemagnetizationintheother layerstogiveanegligiblemagneticmomentforthestructureasawholewheninthe lowresistancestate.Zero-fieldalignmentb etweenthepinnedandthetop(“free”)layers isdeterminedbyRKKYinteractions,enablin geitherparallel,antiparallelordecoupled remanentstatestobechosenduringfabrication,viacontrolofthespacerlayerthickness (NM1 in Fig.1.5 ).Underlowfields,themagnetizationofthemagneticallysoftfree layercanbereversedindependentlyofthepinnedlayertoswitchbetweenthehighand lowresistancestates.Figuratively,thismeansthespinofthefreelayerisusedlikea valvetoturnthecurrentthroughthedevice“on”or“off”.
TlthoughGMRiscreditedwithbeginningthespintronicsrevolution,itwasnotthefirst spin-engineeredphenomena.In1975MichelJullierereleasedabriefpaperdescribinga 14%differenceintheresistanceofatrilayerconsistingoftwoferromagnetsconnectedby an insulator (Fe/Ge/Coat4.2K) [12],whichwasalmostcompletelyoverlookedpriortothe discoveryofGMR(receivingjustthreecitations).Nowknownastunneling magnetoresistance(TMR),themagnetoresistancediscoveredbyJulliererequiresquantum tunnelinginorderforelectronstopassthroughtheinsulatinglayer.ThereforeTMR operatesthroughacompletelydifferentmechanismtoGMR,whichworksviaclassical diffusivescattering.
Figure1.6
Conceptualillustrationoftheoriginofdifferentialspinscatteringinamagnetictunneljunction, associatedwiththerelativeasymmetryintheDOSnearthe EF ofthetwoFMlayers. FM, ferromagnet; DOS,densityofstates.
Tunnelingcanonlyoccurwhenthereareavailablestatestotunnelinto,sothetunneling probabilityisdependentonthedensityofstates(DOS)neartheFermienergy,EF,ineach oftheferromagneticlayers.TheDOSisdividedbetweenthetwospin-states,leadingtoan asymmetryintheDOSofmagneticmaterials. Fig.1.6 presentsaconceptualillustrationof spintunnelingthroughtheinsulatinglayerofaTMRtrilayer(thestructure,analogousto thearchitectureoftheGMRspin-valve,isknownasamagnetictunneljunction,MTJ).Due totheasymmetryintheDOS,eachferromagneticlayerhasmorestatesavailableinone spinstatethantheother,correspondingtoitsmagnetizationdirection.Whenabiasvoltage isplacedacrosstheMTJ,theprobabilityoftunnelingthroughtheinsulatordependsonthe availabilityoffreestatesforeachspindirection.Ifthetwomagneticlayersareparallel (Fig.1.6,upperrow),theDOSforeachspin-stateissimilarinbothlayers,sotherewillbe manyavailablestates(forbothspin-channels)totunnelinto,resultinginalargetunneling currentandlowoverallresistance.Ontheotherhand,ifthelayersareantiparallel(Fig.1.6, lowerrow),thereisamismatchbetweenthesourceandsinkDOSofeachspinchannel:the majorityspin-channelinthesourcelayerhasfewerstatesavailableinthesinklayer, whereastheminorityspin-channelhasexcessofstatesavailableinthesinklayer,buttoo fewsourceelectronstofillthem.Thisbottleneckcausestheantiparallelmagnetization configurationtohaveahighresistance.
Despitethedifferencesinphysicalmechanism,thearchitectureunderlyingGMRandTMR isconceptuallysimilar,whichmaybewhyinterestinTMRgrewafterthediscoveryof GMR.Indeed,thetwo-currentmodeldescribedin Eqs.(1.7)and(1.8) mayreadilybe
appliedtoTMR.Comparingthemagnetoresistanceratios,TMRismuchstronger(with room-temperaturemagnetoresistanceratiosofupto600% [13])thanGMR(upto65%at roomtemperature [14]).Thisisaresultoftheextremesensitivityofthequantum mechanicalmechanism.Ontheotherhand,thesamesensitivitypresentsachallengefor manufacturingMTJsatindustrialscale [11],sinceminorvariationinthethicknessofthe insulatinglayercandramaticallyalterdeviceresistance.
BothGMRandTMRtechnologyhavebeencommerciallyexploitedintoharddiskdrive read-heads,andthisremainstheirpredominantrealization [15].Whenusedinfieldsensing, thefreelayerismadetolieorthogonaltothepinnedlayeratremanence,usingeithershape anisotropy,alocalizedbiasingfieldorweakpinning [11].Theorthogonalconfiguration enablesthesensorstooperatewithinalinearregime,sincethemagnetoresistanceis proportionaltotheprojectionofthefreelayermagnetizationalongthedirectionofthe pinnedlayermagnetization.
Beyondfieldsensinganddataread-outapplications,thebi-stablenatureofspinvalvesand MTJshasledtoGMRandTMRbeingimplementedformemorytechnologies.Sincethe magneticstateofGMRandTMRcellsisnonvolatile(thememorystateisretainedeven whenthepoweristurnedoff),iselectricallyaddressableandcanbeaccessedon nanosecondtimescales,therehasbeengreatresearcheffortinthedevelopmentofdevices capableofperformingasmagneticrandomaccessmemory(MRAM).Ifthepotentialof MRAMcouldberealized,itwouldproduceanewtypeofmemorythatcombinedfeatures ofmagneticharddiskdrives(nonvolatile,lowpower)withthoseofsemiconductingrandom accessmemory(fastread/writetimes,nomechanicalfailure).Howevercommercial realizationsofMRAMhavelaggedbehindsemiconductormemory,withtheleading producer,EverspinTechnologies,onlyannouncingpilotproductionof1GbMRAMinJune 2019.ThemainchallengestoincreasingMRAMdatadensityareswitchingindividualcells astheirfootprintdecreasesandthespacetakenupbyarchitecturesupportingtheMRAM cells,sincetransistorsareneededtocontrolcurrentpathsthroughthecells.Currently, MRAMdesignsmakeuseofspin-transfertorque(STT),acurrent-basedmechanismthat makesuseofthetransferofangularmomentumwhenspin-polarizedelectronsmovingfrom thepinnedlayer.FurtherprogressinMRAMtechnologywillrequireimprovementsinthe switchingcurrentorefficiencyofspintransferordiscoveryofalternativemechanismsthat canretaintheabilitytoswitchsmallercells.
1.3Semiconductorspintronics:dilutemagneticsemiconductorandspin field-effecttransistor
ThesuccessofGMRandTMRdevices(oftenclassifiedasthefirstgenerationofspintronic devices)hasinspiredahugeresearcheffortintospin-basedphenomena,reachingintofields
previouslyconsideredunrelatedtomagnetism.Oneofthemostfascinatingareasthathave developedhasfocussedoninducingandcontrollingspinpolarizationinnonmagneticor paramagneticsemiconductors.Semiconductorsdisplayenhancedspin-propertiescompared tometallicspintronicmaterials.Forexample,semiconductorelectronspinrelaxationtimes areseveralordersofmagnitudelongerthantheelectronmomentumandenergyrelaxation times [16],enablingelectronstopropagateupto100 μmwithoutlosingtheirspin coherence [17].Thisdemonstratesthatsemiconductorshavethepotentialtoefficiently transportspininformationoverlongchannellengths.Furthermore,carrierprofilesin semiconductorscanbemodifiedwithdopants,indicatingthatdevicepropertiescouldbe tailoredtowardspecificspintronicapplications.Dopingalsoopensupopportunitiesfor realizingnovelphysicalphenomena,suchasthegenerationofadissipationlessspincurrent intheabsenceofanetchargecurrent(thespinHalleffect) [18 20].Thesepromising properties,combinedwiththealreadyestablisheddominanceofnonspintronic semiconductorsinsignalprocessingandthecomputinghierarchy,indicatethatdevelopment ofspintronicsemiconductingtechnologycouldwellleadthenextgenerationofspintronic devices.
Broadly,therearethreestrategiesemployedtoinducespinpolarizationinsemiconductors. Firstly,hybridstructures,consistingofaferromagnetincontactwiththesemiconductor, provideamechanismofdirectspininjectionsincethespinpolarizationfromthe ferromagnetisretainedwhentheelectronsenterintothesemiconductor [21 23].Secondly, opticalpumpingbyirradiationwithcircularlypolarizedlighttakesadvantageofmagnetoopticaleffectstopreferentiallyexcitespinpolarizationwithinthesemiconductor [16,24]. Whereasbothofthesestrategiesmanipulatenonequilibriumelectrons,inthefinalstrategy generatesspinpolarizationbydopingwithmagneticionstocreateanewclassof semiconductorthathasamagneticmoment,theDMS [25].
Muchworkonhybridspintronicshasbeenstimulatedbytheideaofthespinfield-effect transistor(FET),firstproposedbySupriyoDattaandBiswajitDasin1990 [26].Similarly toaconventionalFET(suchasthemetal-oxide-semiconductorFET,MOSFET),thespin FETinjectselectronsfromasourceelectrodethroughatwo-dimensionalelectrongas (2DEG)channelthatcanbeelectricallygatedandintoasinkelectrode(Fig.1.7A). HoweverspinFETsfunctionthougharemarkablydifferentmechanismbecauseboththe sourceandsinkelectrodesareferromagnetic,providingadditionalcontrolbasedonthe electronicspin.Transportoftheelectronspinsisconfinedinthehighmobility2DEG channel,soisdependentontheappliedgatevoltage [27].Withoutbiasfromthegate,the relativemagnetizationdirectionsinthesourceanddraindominatetheconductivityinthe device(Fig.1.7B).Whenagatevoltageisappliedacrossthechannel,thespin-polarized electronsexperienceaneffectivemagneticfieldduetotheRashbaspin orbitinteraction, leadingtoaprecessionofspinandconsequentlyachangeinthespinpolarizationofthe current(Fig.1.7C).Thereforethegatevoltagemodulatestheamountofspin-scatteringat
Not-to-scaleschematicdiagramsof(A)thespinFETproposedbyDattaandDas [26],together withthespinpolarizationinthe2DEGchannelwith(B)nogatevoltageapplied,and(C)whena gatevoltageisusedtoinduceprecessionofthespinpolarizationinthe2DEG. FET,field-effect transistor; 2DEG,two-dimensionalelectrongas.
thesinkelectrodeandthereforethecurrentpassingthoughthetransistor.Sinceonlyasmall amountofenergyandashorttimeperiodsareneededtoswitchthecurrentthroughthe device(comparedtothatrequiredinaMOSFETwherethechannelneedstobeunder inversion),spinFETsareexpectedtocombinehighcomputingspeedwithlowpower consumption [27 30].
OneofthemajoradvantagesofthespinFETdesignisthatithasanall-electricaldevice design(allcontrolofspinexistswithinelectroniccircuits),soisintrinsicallycompatible withexistingcircuitarchitecture.Analternativemechanismofincorporatingall-electrical controlintoaspintronicdeviceistoutilize“nonlocal”devicegeometries. Fig.1.8 shows anexampleofanonlocaldevicewithdown-spin-polarizedcurrentinjectedatmagnetic electrodeM1andflowingthroughasemiconductorbetweenM1,andnonmagnetic electrodeNM1 [31,32].Sincethesemiconductorisnonmagnetic,theaccumulationofthe down-spinpolarizationaroundthemagneticinjectioncontactcausestheup-spin polarizationtodiffuseuniformlyawayfromthecontact(withoutchargeflow),both towardsNM1andtowardsthesecondnonmagneticelectrode,NM2.Crucially,theflowof up-spinpolarization(duetothediffusion)towardsNM2createsapotentialdifference, eventhoughnochargecurrentisflowing.Measurementofthevoltageacrossthesecond magneticelectrode,M2,andNM2is“nonlocal”becauseitisoutsideofthechargecurrent circuit(betweenM1andNM1).Sincespinpolarizationdiminisheswithdistancefromthe injectionpoint,andisnegligiblearoundNM2,thelackofmagnetizationinNM2doesnot
Figure1.7
