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/s41563-021-01026-y
SyntheticRashbaspin–orbitsystemusingasilicon
metal-oxidesemiconductor
SoobeomLee1,HayatoKoike2,MinoriGoto3,ShinjiMiwa 3,5,YoshishigeSuzuki3,NaotoYamashita1,
RyoOhshima 1,EiShigematsu1,YuichiroAndo1,4andMasashiShiraishi 1 ✉
Thespin–orbitinteraction(SOI),mainlymanifestingitselfinheavyelementsandcompoundmaterials,hasbeenattracting
muchattentionasameansofmanipulatingand/,weshowthataSimetal-oxide-
semiconductor(MOS)heterostructurepossessesRashba-typeSOI,althoughSiisalightelementandhaslatticeinversion
,we
observespinlifetimeanisotropyofpropagatingspinsintheSithroughtheformationofanemergenteffectivemagneticfield
, × 10−16 eV mforagateelectric
V nm−1;thatis,
ofspin–orbitsystems.
hespin–orbitinteraction(SOI)givesrisetoawidevarietyofnanometre-thickCo25andgate-tuneableSOIresultinginthetune-
condensedmatterphysics,andithasplayedacentralpartinableinversespinHalleffectinnanometre-,whilea
awidevarietyofphysicalphenomenasuchasspinmanipula-gateelectricfieldmerelyplaysapartinmodulatingtheconductivity
T1,2
tionwithoutmagneticfields,ordinalandinversespinHalleffectsofSiinconventionalSi-basedelectronicdevices,thespindegree
enablingspinconversion3–7,thespin-galvaniceffectanditsinverseoffreedomcanbeinherentlymodulatedbyasufficientlystrong
effect8,9,giantspinsplittingataninterfaceandinbulk10,11andIsing–gateelectricfieldeveninSi,creatingasyntheticRashbaspin–orbit
,athinSimetal-oxide-semiconductor
symmetryand/orstructuralinversionsymmetryisoneofthepiv-(MOS)spinchannelwithagateinsulatorcanbeamodelsystem
,bulkinversionbecausethespinpropagationphysicsiswellunderstoodinSiMOS.
symmetrybreakinginstrainedGaAsallowscoherentspinmanipu-
lationwithoutanexternalmagneticfield1,andstructuralinversionExperimentalconceptanddevicestructure
symmetrybreakinginducesgiantspinsplittingattheBi–Aginter-WhenaRashbafield,thatis,anemergenteffectivemagneticfield,
,spinlifetimeanisot-
strongSOIisasingleheavyelement,wheretheSOImagnitudeisropyarisesbetweenthelifetimeofparallelandperpendicularspins
roughlyproportionaltothefourthpoweroftheatomicnumber13–
Becauseofthisbackground,materialswithhighinversionsymme-givesrisetoadditionalspinprecessionaroundthefielddirectionor
-lockingalongthefielddirectioninaspin-propagating-media
Single-layergraphene(SLG)withatransitionmetaldichalcogen-,toidentifywhetherthesyntheticRashba
ide(vanderWaalsheterostructure)16–19,bilayergraphene20,21andSOIisgenerated,thespinlifetimeanisotropyasafunctionofthe
22,23
asubsurfacestateofp-Ge(111)arelimitedexamples,anditisgatevoltageamplitude,Vg,andangleofanexternalmagneticfield,
noteworthythatthemagnitudeoftheSOIisnottuneableand/orBex,
,Sispinchannel,,
itwouldbesurprisingbutimportanttorealizeatuneablesyntheticapplicationofagateelectricfieldgivesrisetoanemergenteffec-
SOIsystemusingalightelementwithhighinversionsymmetrytivemagneticfieldperpendiculartothek-vectorofthepropagating
becausesuchasuccesswoulddramaticallyexpandthehorizonsspinsasγℏBeff = 2α(k × z),whereγisthegyromagneticratio,ℏisthe
,Beffistheemergenteffectivemagneticfieldandzis
SihasbeenbelievedtobeanunsuitablematerialforSOIgen-
erationbecauseofitslightnessandbulkinversionsymmetry,andprovidesanadditionalcontributiontospinprecession,thespinlife-
∥⊥
Sihasattractedattentionmainlybecauseofitsgoodspincoher-timesparallel(τs)andperpendicular(τs)tothespinchannelplane
,
,strongelectricfieldapplica-theanisotropyisthemethodestablishedfortestingthespinlifetime
tionviasolidandionicgatingmaterialsallowedpioneeringnewanisotropyinSLG27andappliedtobilayergraphene20,.
physicsincondensedmatter,suchasspinmanipulationinIII–Vestablishedtheapproach,wheretheyappliedout-of-plane(oblique)
compoundsemiconductorheterostructures1,superconductivityinmagneticfieldsandimplementedspinprecessionmeasurements
oxideinsulators24,strongmodulationoftheCurietemperatureinunderobliquemagneticfieldstogenerateanout-of-planespin
1DepartmentofElectronicScienceandEngineering,KyotoUniversity,Kyoto,Kyoto,,TDKCorporation,
Ichikawa,Chiba,,OsakaUniversity,Toyonaka,Osaka,,JapanScienceandTechnology
Agency,Honcho,Kawaguchi,Saitama,:InstituteforSolidStatePhysics,TheUniversityofTokyo,Kashiwa,Chiba,Japan.
✉e-mail:.******@kyoto-
NatureMaterials|
ArticlesNatureMaterials
ab
z4,000
y
3,000
m)
xΩ
Bex2,000
V(per
NL4Tsi
βσ
1,000
0
020406080100
Iinj
Vg(V)
c
n-Si
2
Fe()
Co()
(mV)0
Vg
MgO()NL4T
V
HighlydopedSi–
(20nm)
–
–100–50050100
Magneticfield(mT)
|,Schematicimageofa
-degenerateand100 (Iinj)
isappliedbetweenoneferromagneticcontactandonenon-magneticcontact,andNL4Tvoltages(VNL4T)aremeasuredintheseparatedcircuitincluding
aferromagneticcontactandanon-magneticcontact:non-(Bex)isappliedintheyzplanewithatiltangleof
,ConductivityoftheSiMOS(σSi)asafunctionofgatevoltage(Vg).σSiwasmeasuredusingaconventionalfour-,Typicalnon-local
in-plane(β = 0°)externalmagneticfieldwassweptupwards(redsolidline)anddownwards(blacksolidline).
reliableresultsforbothlow-andhigh-carrierdensitiesandthuscanas
beusedforgate-tuneablesystemssuchasSiMOS.
()−
VNL4Tβ=2+−121
Figure1ashowsthestructureofasyntheticRashbadevicecon-◦2
VNL4T(0)cosβcosβζsinβ
sistingofa100-nm-thickn-typeSichannel(thecarrierconcen-√()
16−3(1)
tration,n,was5 × 10 cm,thatis,theSiwasnon-degenerate)−L2(2+−12−)
exp∥cosβζsinβ1,
(Dτ)
ona200-nm-thickSiO2gateinsulator(SiMOS)andthesetupfor√s√
measurementofthenon-localfour-terminalmagnetoresistance
(NL4T-MR)andspinlifetimeanisotropyintheSiMOSunderthewhereListhecentre-to-centredistancebetweentwoferromag-
applicationofVg(Methods).Allmeasurementswereimplementedneticcontacts,Disthediffusionconstantandζisthespinlifetime
=⊥∥27
at300 ,ζτs/τs(ref.).Theratioζisafingerprint
variedfrom0to100 V;thatis,anelectricfieldwasappliedtotheSioftheanisotropy,whereζ < 1isexpectedwhenspin–orbitfields
−1
V ,σSi,ofinducingspinrelaxationarepreferentialintheSiMOSplaneand
,whichindicatesthatζ = ,ζisquan-
theback-gatevoltageswereefficientlyappliedtotheSiMOSchan-titativelycharacterizedbyplottingthenormalizedVNL4Tatβ = 0°
-MRfromtheSiMOSunderVg = 0 Vwithsweepingandβ ≠ 0°.Figure2e–hshowsthenormalizedVNL4Tasafunction
ofthein-,andclearofcos2β,wherethemagnitudesofζestimatedbyusingequation
hysteresisinspinsignalsasamanifestationofsuccessfulspintrans-(1)arealsoshown,–hwereesti-
-matedbyusingtherulesforerrorpropagationandtheseerror
ropy,Bexwasappliedwithchangingappliedangleβ,
,whereβwasvariedfrom10°to90°.andiscloseto1whenVg = 10
,andaprominentVgdependence
,ζmonotonicallyandprominentlydecreases
27
Spinprecessionsignalsforvariousβvalues(asrepresentatives,whenVg > 10 V,,ζis
10°,30°,45°,60°and90°)asafunctionofVg(asrepresentatives,afingerprintofthespin–orbitfieldsinSi,andtheobservedVg
0,10,60and100 V)––orbitfieldis
nicelyreproducedbyaconventionalone-dimensionalfittingfunc-generatedintheSiMOSandthatspinlifetimeanisotropyarises
28–30∥
tion,wherethespinlifetimeatβ = 90°,thatis,τsunderVg = 0 VfromemergenteffectivemagneticfieldsthataretuneablebyVg,
± ns,andtheprecessionalmotionofthewhiletheamplitudesofζarenotaslargeasthoseobservedina
17
spinsdephasesatBex ≅ 40 mT(SupplementaryInformation).ForsystemwithintrinsicallylargeSOI,suchasWS2/,
Bex > 40 mT,thespinvoltage,VNL4T,isdeterminedbytheremanentnotably,theexperimentalresultcounterstheconventionalunder-
non-precessionalspincomponentthatliesalongthemagneticfieldstandingthatSihasnegligiblysmallSOI,andwehavesuccessfully
NatureMaterials|
NatureMaterialsArticles
ae
Vg=0VVg=0V
10°
=
±
30°
(0°)
(µV)45°
4NL4T
/V
NL4T60°
NL4T
V
90°
0
–40–
2
Magneticfield(mT)cosβ
bf
Vg=10VVg=10V
ζ=±
8
(0°)
(µV)
NL4T
4/V
NL4T
NL4T
V
0
–4
0
–40–
2
Magneticfield(mT)cosβ
cg
Vg=60VVg=60V
12
ζ=±
8
(0°)
(µV)
NL4T
/V
NL4T4
NL4T
V
0
–40
–40–
2
Magneticfield(mT)cosβ
dh
Vg=100VVg=100V
4
ζ=±
2(0°)
(µV)
NL4T
/V
NL4T
NL4T
0V
–20
–40–
2
Magneticfield(mT)cosβ
|–d,Non-localspinsignalasafunctionoftiltangleβandgatevoltageVg.
Vgvaluesweresettobe0 V(a),10 V(b),60 V(c),and100 V(d).Solidlinesshowfittingresultsobtainedusingaconventionalspinprecessionequation.
2
e–h,Spinsignalsunderahighmagneticfield(>40 mT,thebluecircles)atvariousβnormalizedbythoseatβ = 0°
0 V(e),10 V(f),60 V(g),and100 V(h).
resultsobtainedbyusingequation(1)(ζ)isextractedbythefittingandisdepictedinthefigures,
= 1(isotropic).
NatureMaterials|
ArticlesNatureMaterials
forπ-rotationatVg = 10 , mTis
= 100 -
nalmagneticfield,Bex,neededforπrotationofthespins,helpsin
-local
-terminalschemeforspintransport,onlyspindiffusionoccurs.
)
ǁ
sHere,DisindependentofVg(SupplementalInformation),which
τ
sshowsthatmobilityμisunchangedbythegatingbecauseweexerted
-degenerateinorganicsemiconductorandthusEinstein’srela-
ζ(=τ
tion,eD = μkBT,holdsinoursystem(kBistheBoltzmannconstant
andTistemperature).Fu