1

Nanosecondspinrelaxationtimesinsinglelayergraphenespin

valveswithhexagonalboronnitridetunnelbarriers

SimranjeetSingh1,JyotiKatoch1,JinsongXu1,ChengTan2,TiancongZhu1,Walid

Amamou3,JamesHone2andRolandKawakami1,3*

1DepartmentofPhysics,TheOhioStateUniversity,Columbus,Ohio,UnitedStates43210

2MechanicalEngineeringDepartment,ColumbiaUniversity,NewYork,NY,UnitedStates10027

3Program ofMaterials Science and Engineering, University of California, Riverside, CA, United

States92521

Abstract:

We present an experimental study of spin transport in single layer graphene using atomic sheets of

hexagonal boron nitride (h-BN) as a tunnel barrier for spin injection. While h-BN is expected to be

favorableforspininjection,previousexperimentalstudieshavebeenunabletoachievespinrelaxation

timesinthenanosecondregime,suggestingpotentialproblemsoriginatingfromthecontacts.Here,we

investigate spin relaxation in graphene spin valveswithh-BNbarriers andobserve room temperature

spinlifetimesinexcessofananosecond,whichprovidesexperimentalconfirmationthath-BNisindeed

agoodbarriermaterial for spin injection intographene.Bycarryingoutmeasurementswithdifferent

thicknessesofh-BN,weshowthatfewlayerh-BNisabetterchoicethanmonolayerforachievinghigh

non-localspinsignalsandlongerspinrelaxationtimesingraphene.

*Authortowhomcorrespondenceshouldbeaddressed:kawakami.15@osu.edu

2

Grapheneisapromisingspinchannelmaterialfornextgenerationspintronicdevicesduetothe

experimental demonstration of long spin diffusion lengths at room temperature1-3 and theoretical

predictionsoflongspinrelaxationtimes4,5arisingfromtheweakspin-orbitandhyperfinecouplings5,6.

However, experimentally measured spin relaxation times1-3,7,8 in graphene are orders of magnitude

shorterthantheoreticallypredicted4,5.Ingraphenespinvalves,thetunnelbarrierplaysacrucialrolefor

spin injection by circumventing the problem of impedance mismatch9 between graphene and the

ferromagneticelectrodes.AsdemonstratedbyHanet. al.8, highquality tunnelbarriersare critical for

obtaininghigherspinrelaxationtimes(τs) ingraphenebecausebarrierswithpinholesorroughsurface

morphology can cause additional contact-induced spin relaxation,which has received a great deal of

interest recently.10-14Asopposed togrowingoxide tunnelbarriersongraphene,a thin insulating two-

dimensional (2D)vanderWaalsmaterialcanalsobeusedasa tunnelbarrier.Aparticularmaterialof

interestissingle(orfew)layerh-BNbecauseofitsvarioussuitableproperties15:largeenergybandgap

~5.97eV,highcrystallinity,spinfiltering16,absenceofpinholesanddanglingbonds,atomiclatticesimilar

to graphene, and chemical stability at ambient conditions. In addition, atomically clean vertical

heterostructures of h-BN/graphene can be mechanically assembled using polymer-based transfer

techniques17,18. The first experimental report demonstrating spin injection into graphene using a

monolayerh-BNtunnelbarriershowedτslessthan100ps19.ThiswasfollowedbytheworkofKamalakar

et. al.20,21 and Fu et. al.22, which used chemically grown h-BN barriers, yielding τs ~ 500 ps. Another

recent study using an encapsulated geometry23 with graphene sandwiched between a thick bottom

layer of h-BN and a monolayer of h-BN on top showed τs less than 200 ps. As evident from these

studies,graphenespinvalvedeviceswithh-BNtunnelbarriershaveyieldedrelativelysmallvaluesforτs

(< 1 ns) that are comparable to or lower than the values obtained using oxide barriers. Thus, it is

worthwhiletoask:areh-BNtunnelbarrierscompatiblewithlongerspinlifetimesingraphene?

3

In this letter,weperformspin transport insingle layergraphenespinvalvedeviceswithh-BN

tunnel barriers and observe spin relaxation times exceeding a nanosecond at room temperature, the

highest valuesachieved so far fordevicesemployingh-BN tunnelbarriers. Inaddition,we investigate

thethicknessdependentcharacteristicsoftheh-BNtunnelbarriersandfindthatfewlayerh-BN,rather

thanmonolayer, is requiredtoobserve largenon-localspinsignalsand longerspinrelaxationtimes in

graphene.Ourworkestablishestheeffectivenessofultrathinh-BNasahighquality tunnelbarrier for

spin injection into graphene, which is a crucial step towards realizing high performance spintronic

devicesbasedcompletelyonultrathinvanderWaalsmaterials.

For making h-BN/graphene interfaces, thin h-BN flakes are exfoliated from bulk crystals (HQ

graphene)ona90nmSiO2/Siwafer,andthethicknessofh-BNisconfirmedbyatomicforcemicroscopy

(AFM). On a separate 300 nm SiO2/Si substrate, Kish graphite is exfoliated to obtain single layer

graphene,confirmedbyRamanspectroscopy.Figure1ashowstheRamanspectraofthegrapheneused

in the h-BN/graphene heterostructures. Thin h-BN is transferred onto single layer graphene using a

process similar to Zomer et. al.24 In short, a polydimethylsiloxane (PDMS) stamp coated with

polycarbonate(PC)polymerisattachedtoaglassslideandisbroughtincontactwithanexfoliatedh-BN

flake.Next,thePCfilmisheatedto70°Ctopick-uptheh-BNflakefromtheSiO2surface.Oncetheh-BN

isonthePCfilm,itisopticallyalignedtothedesiredgrapheneflakeandthenthePCfilmismeltedonto

thegraphene flake’s substrateat150 °C.ThePC film is removedbydissolving it in chloroform for30

minutes.Afterward,theh-BN/grapheneheterostructureiscleanedbyannealinginH2/Arforminggasat

350 °C for 3 hours. Figure 1c shows the surface topography of the measured h-BN/graphene stack,

where the toph-BNand thegrapheneareoutlinedby yellowand reddashed lines, respectively. The

measuredthicknessoftheh-BNis0.85nm,asshownbythestepheightintheinsetofFigure1b,which

corresponds to 2-3 layers of h-BN25 (monolayer thickness is ~0.34 nm). Although there are few small

bubblestrappedbetweenthegrapheneandh-BN,therearestill largebubble-freeregionsthatcanbe

4

usedforthecobaltcontacts.Figure1cshowstheopticalmicroscopeimageofthemeasuredspinvalve

device, in which yellow dotted lines highlight the boundary of the h-BN tunnel barrier. In order to

electrically characterize the graphene sheet, we measure the four-probe resistance (at room

temperature)ofgrapheneasafunctionofbackgatevoltage(VG)appliedtothedegeneratelydopedSi

substrate(Figure1d).Anelectronmobilityof4000cm2/Vsisextractedfromtheslopeofthegraphene

conductivity versus gate voltage scan26. The contact resistance of the electrodeswith h-BN barrier is

measured using a three-probe measurement configuration8. The zero bias contact resistance of the

electrodesvariesfromafewkilo-Ohms(kΩ)tohundredsofkΩdependingonthethicknessoftheh-BN.

Thiswillbediscussedindetaillater.

Webeginbydiscussingthespintransportmeasurementscarriedoutatroomtemperature.For

the data presented here, the graphene channel length is 1.5microns (µm) andwidth is 2.5µm. The

contactresistancesoftheinjector(E2;Fig.1c)anddetector(E3;Fig.1c)electrodesare42kΩand6kΩ,

respectively. The temperature dependence and bias dependence of the contact resistances indicate

tunneling behavior (see supplementary material). Tomeasure the non-local magnetoresistance (MR)

signal,weperformlowfrequencyacmeasurementsusingacurrentexcitationof1µΑrms.Asshownby

theschematicintheinsettoFigure2a,spininjectioncurrentisappliedbetweentheelectrodeslabeled

E1 and E2, and a non-local voltage signal is measured using the electrodes labeled E3 and E4. An

externalmagneticfieldissweptintheplaneofthegraphenedevice(alongtheelectrode’slength),anda

non-localvoltagesignalisrecordedasafunctionoftheappliedmagneticfield.Toobtainthenon-local

resistance(RNL),thevoltagesignalisdividedbythemagnitudeofappliedcurrent(1µA).Figure2ashows

the observed non-local MR signal at room temperature, where black circles are data recorded by a

sweep in increasing magnetic field. At ~20 mT, we see an abrupt change in RNL when one of the

magnetizationsreversestocreateanantiparallelalignmentoftheinjectoranddetectormagnetizations

(arrows indicate the relative alignmentof themagnetizations throughout themagnetic field sweeps).

5

This is thehallmarkofspin transport from injector todetector.With further increaseof themagnetic

field,theresistancesignalagainchangesbacktotheoriginalvalueduetothealignmentoftheinjector

anddetectormagnetizationsbacktoaparallelconfiguration.AlsoshowninFigure2a istheMRsignal

when sweepingwith a decreasingmagnetic field (blue circles). Themagnitude of themeasuredMR

signal(ΔRNL)isdefinedasthedifferenceofRNLbetweentheparallelandantiparallelconfigurations,and

isapproximately4ΩforthemeasureddeviceatVG=+10V.Wealsomeasurethegatedependenceof

thenon-localMRontheappliedgatevoltage,whichtunesthepolarityanddensityofthechargecarriers

and observe ΔRNL as large as 5 Ω over the measured gate voltage range (data shown in the

supplementaryFigureS2b).

To study the spin relaxation times in the graphene channel,weperformnon-localHanle spin

precessionmeasurementsatroomtemperature.InatypicalHanlemeasurement,thein-planepolarized

spinsprecessinthegrapheneplanebyanexternallyappliedoutofplanemagneticfield.Afteraligning

the magnetization of the injector and detector, either in a parallel or antiparallel configuration, a

magnetic field is swept perpendicular to the plane of the graphene device tomeasure the non-local

resistancesignalasafunctionofappliedmagneticfield.Figure2bshowstheHanlecurvesobtainedfor

the graphene spin valve device measured in parallel (blue circles) and antiparallel (black circles)

configuration.Themeasuredsweepsforparallelandantiparallelconfigurationsaresubtractedtoobtain

the curve as shown in Figure 2c (black circles). In general, once the spins are injected from the

ferromagneticelectrode,thespintransportingraphenecanbedescribedbymajorityandminorityspin

channels. The voltage signal measured at the detector electrode is proportional to net spin

accumulation (μS), where |μS| is the difference of the electrochemical potentials of majority and

minority spins and the vector points along the polarization axis. This spin accumulation in an applied

magneticfieldcanbedescribedbysolvingthesteadystateBlochequation:

6

𝐷∇!𝝁𝒔 −𝝁𝒔!!+ 𝝎𝑳 × 𝝁𝒔 = 0, (1)

where𝐷 isthediffusionconstantinthegraphenechannel, 𝜏! isthespinrelaxationtime,𝛚𝐋 =𝑔µ!𝐁/ℏ

is the Larmor frequency,g = 2 is the gyromagnetic factor, μBis the Bohrmagneton,ℏis the reduced

Planck’s constant, andB is theexternally appliedmagnetic field. To fit themeasurednon-localHanle

dataweuseananalyticalexpressiondevelopedbySosenkoet.al.27whichisthesolutiontothesteady

stateBlochequation(eq.1)inthepresenceofboundaryconditionsfortheinjectionandabsorptionof

spincurrentattheferromagneticelectrodes:

𝑅!"± = ±𝑝!𝑝!𝑅!𝑓(2)

wherethe±correspondstotherelativealignmentofinjector/detectormagnetizations,p1andp2are

theelectrodespinpolarizations,𝑅! = !! ! !!

isthespinresistanceofgraphene,λisthespindiffusion

lengthingraphene(relatedtoτsby𝜆 = 𝐷𝜏!),Wisthewidthofthegraphene,σNistheconductivityof

grapheneand

𝑓 = 𝑅𝑒 2 1 + 𝑖𝜔!𝜏! +!!

!!!+ !

!! 𝑒

!! !!!!!!! + !!

!!!! !"#$ !

! !!!!!!!!!!!!!!

!!

(3)

Inthefunctionf,𝑟! =!!!!!

!

!!"𝑊with𝑖 = 𝑠,𝑑fortheinjectoranddetector,respectively,RCisthecontact

resistance,RSQ isthegraphenesheetresistance,RF=ρFλF/Aisthespinresistanceoftheferromagnetic

electrode material, ρF is the resistivity of the ferromagnet, λF is the spin diffusion length in the

ferromagnet,andAistheareaofthegraphene/electrodejunction.

Using Equation 2, the experimentally obtained Hanle curves can be fit using τs, λ, and the

product p1p2 as fitting parameters. The fit for the Hanle curve at zero gate voltage (solid red line in

Figure 2c) yields values of τs = 1.86 ns, λ = 5.78 μm, 𝑝!𝑝! = 0.053, and D = 0.018 m2/s. The

7

corresponding spin injection efficiency is found to be 0.052 (see supplementary material). We also

investigated the gate dependence of the spin lifetimes by measuring Hanle precession curves at

different VG and fitting each of these curves with Equation 2. Figure 2d shows the extracted τsas a

function ofapplied gate voltages,where, formost of the applied gate voltages, τs exceeds 1 ns. This

experimental demonstration of nanosecond spin lifetimes in graphene on SiO2 substrates at room

temperature, employing h-BN tunnel barriers, is the central result of this work. These observed

nanosecondspin lifetimesarethehighestvaluesreported inthe literature forasingle layergraphene

channel employing an h-BN tunnel barrier19-23. It is important to note that for van der Waals

heterostructures, it isnon-trivialtoachievecleaninterfaces17,28,andtheimpurities(orresidues)atthe

interfacecanaffecttheelectricalandspinrelatedpropertiesacrossthevanderWaalsheterostructures.

One possible explanation for the high quality spin transport observed in our studies may be the

relatively clean h-BN/graphene interface, evidenced by the flat surface topography of the

heterostructure,inareaswherewedepositedferromagneticelectrodesforspininjection.

Wehavealsospintransportingraphenespinvalvesusingmonolayerh-BN19,25(~0.50nmthick)

tunnelbarriers, incontrasttothefewlayer(2-3)h-BNbarriersdiscussedsofar.Herewepresentdata

using a pair of electrodes with injector and detector contact resistance of 7.7 kΩ and 3.7 kΩ

respectively.Thedetailedtemperaturedependenceofthecontactresistanceisshowninsupplementary

material.Thegraphenechannellengthis5µmandwidthis4.9µm.Thechargecarriermobilityofthe

graphenechannelis8000cm2/Vs.AsshowninFigure3c,thenon-localMRsignalmeasuredat11Kand

VG=+10Vexhibitsamagnitudeof170mΩ.Wepresentdatatakenatlowtemperaturesbecauseweare

unable to resolve clear MR switching at RT beyond the noise, but can observe clear MR at low

temperatures.ThemagnitudeoftheMR(ΔRNL)asafunctionofgatevoltagevariesfrom100mΩto350

mΩ (data shown in the supplementary material). Figure 3b shows the Hanle curve (black circles)

obtained by carrying out non-local Hanle measurements at a VG = +10 V. By fitting the data with

8

Equation2weextractτs=490ps,λ=3.8μm, 𝑝!𝑝! = 0.023,andD=0.03m2/s. Figure3cshowsthe

extractedτsasafunctionofappliedgatevoltage,wheretheinsetshowsthegatedependentresistance

of themeasured graphene channel. The spin relaxation times extracted from theHanle curves range

from300ps-600ps,whicharesimilarto(orslightlyhigherthan)previousstudiesemployingmonolayer

h-BN tunnel barriers19,23. Our measurements suggest that monolayer h-BN may not be the optimal

choice for efficient spin injection, while thicker h-BN allows the realization of largerMR signals and

longer spin relaxation times in graphene spin valves. One of the possible reasons for higher spin

relaxationtimesingrapheneusingmultilayerh-BNtunnelbarrierscouldberelatedtothefactthatfew

layerh-BN(onSiO2substrate)isflatter17,i.e.lessripplesinsurfacemorphology,thansinglelayerh-BN.

This could lead to smoother growth of cobalt electrodes on multilayer h-BN and thus reducing the

contact-inducedspindephasingmechanismduetothemagnetostaticfringefield29oftheferromagnetic

material. Apart from this, we also speculate that single layer h-BN is more prone to surface

contaminantssuchasorganicresiduesorwrinklesduringthetransferprocessandcancauseadditional

spindephasingundertheferromagnetcontactresultinginshorterspinrelaxationtimesingraphene.

In order to investigate the range of h-BN thickness required to observe largeMR signals and

higherspinrelaxationtimesingraphenespinvalves,wehaveprepareddifferenth-BN/graphenestacks

with h-BN thicknesses varying from ~ 0.50 nm to 3.20 nm. The thicknesses of the h-BN flakes were

characterizedbyAFM. In total,wemeasuredsixdifferentdeviceswithh-BNtunnelbarriers.Foreach

devicewithmultipleferromagneticelectrodes,theinterfacialcontactresistancewasmeasuredusinga

3-probeconfiguration8,whereinthedifferentialcontactresistance(dV/dI)wasmeasuredasfunctionof

dcbiascurrentat lowtemperature.ThedV/dIcurvesshowazerobiaspeak,asexpectedforatunnel

barrier.ThevaluesofzerobiasdV/dIasfunctionoftheh-BNthicknessareplottedinFigure4forallthe

measuredelectrodes.Thegraydottedcircledenotestheregion,correspondingtoh-BNthicknesses,for

whichwewereabletoobserveMRsignals.Wedidnotobserveanynon-localMRsignalindeviceswith

9

h-BN thickness larger than 1.50 nm (~4monolayers of h-BN). Note that onewould expect to have a

smalldistributionofcontactresistancesforagivenh-BNthickness,buttheinterfacialinhomogeneities

(e.g.,bubblesororganicresidues)attheh-BN/grapheneinterfaceovermesoscopicsizeareascouldgive

risetotheobservedcontactresistancedistributions.

In conclusion, our experimentalwork demonstrates that h-BN is a high quality tunnel barrier

material forspin injection intographene,asevidentfromourdatashowinglargenon-localMRsignals

and nanosecond spin relaxation times at room temperature. Our experimental observations indicate

that few layer h-BN leads in better characteristics, as opposed tomonolayer h-BN, for tunnel barrier

applicationstoachievehigherqualityspintransportingraphene.Moreexperimentalstudiesareneeded

tofurtherimprovetheinterfacequalityofh-BN/grapheneinordertoexploitthefullpotentialofvander

Waalsheterostructuresforspinrelatedphysicsingrapheneandother2Dmaterials.

Acknowledgements:

The authors acknowledge Elizabeth Bushong for carefully reading themanuscript. S.S., J.K., J.X., T.Z.,

W.A. andR.K. acknowledge support fromONR (No.N00014-14-1-0350),NRI-NSF (No.DMR-1124601),

NSF (No.DMR-1310661), andC-SPIN, oneof the six SRC STARnet Centers, sponsoredbyMARCOand

DARPA.C.Twas supportedby aDOD-AFOSR,NDSEG fellowshipunder contract FA9550-11-C-0028, 32

CFR168a.C.T.andJ.H.acknowledgesupportfromtheNanoelectronicsResearchInitiative(NRI)through

theInstituteforNanoelectronicsDiscoveryandExploration(INDEX).

See supplementary material for detailed discussion and data for: temperature dependence of the

interfacialcontactresistances,gatedependentMRsignalsandh-BNthicknessdependenceofthespin

injectionefficiency.

10

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12

FigureCaptions:Figure1:(a)Ramanspectraconfirmingsinglelayergraphene.(b)Atomicforcemicroscopyoftheh-BN/graphenestack(beforedefiningtheferromagneticelectrodes)showingthetopographyofgrapheneandthinh-BN.Theboundariesofthegrapheneandtoph-BNarehighlightedbyredandyellowdottedline,respectively.Thethicknessoftheh-BNis~0.85nm(2-3monolayers)andthestepheightofh-BNisshownintheinset.(c)Theopticalimageofthecompleteddevice,withdifferentelectrodesusedforthemeasurementslabeledforconvenience.Theh-BNflakeboundaryisdepictedbyyellowdottedlines.(d)Thegatedependentresistanceofthegraphenechannelmeasuredatroomtemperature.

Figure 2:Spintransportinsinglelayergrapheneusingfewlayerh-BNtunnelbarriers,measuredatroom temperature. (a) Non-local magneto-resistance (MR) signal measured in a graphene spin valvewith h-BN tunnel barriers using E2 and E3 as injector and detector electrodes, respectively, at roomtemperature.Theblueandblackarrowsrepresenttherelativemagnetizationdirectionof injectoranddetector electrodes. ΔRNL is the magnitude of the MR signal. Inset: schematic of the non-localmeasurement configuration. (b) Non-local Hanle spin precession signal measured in parallel (bluecircles)andantiparallel(blackcircles)configurationbyapplyinganoutofplanemagneticfield.Theblueandblackarrowsrepresentstherelativemagnetizationdirectionofinjectoranddetector.(c)Non-localHanlespinprecessioncurve(blackcircles)obtainedbysubtractingparallelandantiparallelHanlecurvesfromFigure2b.Thethickred line is the fit to thedatatoextract thespinrelaxationtime(τs). (d)Thegatedependenceofthefittedspinrelaxationtimesoverarangeofappliedbackgatevoltages.

Figure3:Spintransportinsinglelayergrapheneusingmonolayerh-BNtunnelbarriers,measuredat11K.(a)Non-localmagnetoresistance(MR)signalmeasuredinagraphenespinvalveusingmonolayerh-BN at VG = +10 V. (b) Non-local Hanle signal (black circles) measured by applying an out of planemagneticfieldatVG=+10V.Theredlineisthefittingtothedatatoextractspinrelaxationtime(τs).(c)Thefittedspinrelaxationtimesasfunctionofappliedbackgate.Inset:graphenechannelresistanceasafunctionofgatevoltage.

Figure4:Lowtemperaturetunnelingcharacteristicsofdifferentthicknessh-BNbarriers.Differentialcontact resistanceof theelectrodes (for6differentdevices) is shownasa functionofAFMmeasuredthicknessoftheh-BNlayer.ThegraycircleshowstheregionforwhichwehaveobservedMRsignals.

-40 -20 0 200.0

0.4

0.8

1.2

1.6

R (k

:)

VG (V)

1500 2000 2500 3000

Inte

nsity

(a.u

.)

Wave number (cm-1)

(a) (b)

(c) (d)10 μm

E1

E2

E3

E4

Fig. 1

-60 -40 -20 0 20 40 60

14

16

18

20

22

RN

L (:)

B (mT)

(a) (b)

(c) (d)

ΔRNL

-150 -100 -50 0 50 100 150

15

16

17

18

19

RN

L (:)

BA (mT)

VG=+10 V

-40 -20 0 200.0

0.5

1.0

1.5

2.0

W s�(ns

)

VG (V)-150 -100 -50 0 50 100 150

0

1

2

RN

L (:)

BA (mT)

Ws= 1.86 ns

D=0.018 m2/s

Fig. 2

(a) (c)(b)

-60 -40 -20 0 20 40 600.15

0.20

0.25

0.30

0.35

0.40

RN

L (:

)

B (mT)-150 -100 -50 0 50 100 150

-0.05

0.00

0.05

0.10

VG= +10 V Ws= 490 ps

D=0.031 m2/s

RN

L (:)

BA (mT)

-40 -30 -20 -10 0 10 200.0

0.4

0.8

1.2

1.6

W s�(ns

)

VG (V)

-40 -30 -20 -10 0 10 200

1

2

3

4

R (k

:)

VG (V)

Fig. 3

0 1 2 30

20

40

250500750

1000

dV/d

I (k:

)

h-BN thickness (nm)

Fig. 4

1

SupplementalMaterial

Nanosecondspinrelaxationtimesinsinglelayergraphenespin

valveswithhexagonalboronnitridetunnelbarriers

SimranjeetSingh1,JyotiKatoch1,JinsongXu1,ChengTan2,TiancongZhu1,Walid

Amamou3,JamesHone2andRolandKawakami1,3

1DepartmentofPhysics,TheOhioStateUniversity,Columbus,Ohio,UnitedStates43210

2MechanicalEngineeringDepartment,ColumbiaUniversity,NewYork,NY,UnitedStates10027

3Program ofMaterials Science and Engineering, University of California, Riverside, CA, United

States92521

2

I.Temperaturedependenceofcontactresistances

Wepresent the temperature dependence of the contact resistances of the injector and detector

electrodes.Forthe0.85nmthickh-BNtunnelbarrier,theinsettotheFigureS1ashowsthemeasured

dV/dIcurveasafunctionofdcbiascurrentforboththeinjectoranddetectorelectrodes.Thezerobias

contact resistanceof injectoranddetectorelectrodes, forwhichwehavepresenteddata in themain

text,showsveryweaktemperaturedependencefrom11Kto300K.Thisindicatestunnelingcontacts,in

contrast to pinhole barriers which display a sharp increase in contact resistance with increasing

temperature. Similarly, the temperature dependenceof contact resistanceof the 0.50nm thick h-BN

tunnelbarrierisshowninFigureS1b.Thedcbiasdependenceofthecontactresistanceisshowninthe

insettotheFigureS1b.

FigureS1:Thetemperaturedependenceofthezerobiascontactresistanceoftheinjector(blackfilledcircles) and the detector (red filled circles) electrode. Inset: the differential contact resistance of theinjector (black filled circles) and detector (red filled circles) electrodes as a function of bias currentmeasuredat11K.(a)Contactresistancesforthe0.85nmthickh-BN.(b)Contactresistancesforthe0.50nmthickh-BNtunnelbarrier.

50 100 150 200 250 300

0

40

80

120

Injec torD etec tor

dV/dI(kΩ

)

T empera ture (K )

-4 -2 0 2 40

2

4

6

2428323640

dV/dI(kΩ

)

IDC(µA)

11K

50 100 150 200 250 300

0

10

20

dV/dI(kΩ

)

T empera ture (K )

Injec torD etec tor

-4 -2 0 2 40

2

4

6

8

dV/dI(kΩ

)

IDC(µΑ)

11K

(a) (b)0.85nmh-BN 0.50nmh-BN

3

II.Gatedependenceofnon-localMRsignals

Weshowthegatedependenceofthenon-localMRsignalsmeasuredusingdifferentthicknessesof

theh-BNtunnelbarrier.FigureS2ashowstheMRsignals,measuredusing0.85nmh-BNtunnelbarrier,

at room temperature for the applied back gate voltages ranging from -40V to +30V. TheMR signal

varies from2Ωto5Ω.The insetofFigureS2ashowsthegatedependentresistanceof thegraphene

channelwheretheDiracpoint,maximumresistance,isat-30V.FigureS2bshowsthegatedependence

oftheMRsignalmeasuredusing0.50nmthickh-BNtunnelbarrier.TheMRsignals,whichvaryfrom100

mΩto350mΩ,aremeasuredat11K.Thegraphenechannelresistanceasafunctionofgatevoltageis

shownintheinsettoFigureS2b.

FigureS2:(a)Thegatedependenceofthemagnitudeofthenon-localMRsignalfor0.85nmthickh-BNtunnelbarrieratroomtemperature.Insetshowstheresistanceofthegraphenechannelasafunctionofapplied back gate voltage. (b) Low temperature gate dependence of themagnitude of theMR signalusing0.50nm thickh-BN tunnelbarrier. Inset shows thegraphene resistance vs applied gate voltagescan.

-40 -30 -20 -10 0 10 200.0

0.2

0.4

0.6

ΔR

NL(Ω

)

VG(V )

-40 -30 -20 -10 0 10 20

1

2

3

4

R(kΩ

)

VG(V)

-40 -30 -20 -10 0 10 200

2

4

6

8

10

12

ΔR

NL(Ω

)

VG(V )

-40 -30 -20 -10 0 10 200.0

0.4

0.8

1.2

1.6

R(kΩ

)

VG(V)

(a) (b)0.85nmh-BN 0.50nmh-BN

4

III.Spininjectionefficiency

The spin injection efficiency 𝛾 is defined as the polarization of the injected current,

𝛾 =!!"#↑ !!!"#

↓

!!"#↑ !!!"#

↓ .Thisisanimportantquantitythatdependsnotonlyonthebulkandinterfacialspin

polarizationsof the injector,butalsoonvariousquantities suchas resistances, spindiffusion

lengths, etc. It is valuable to understand the factors which determine the spin injection

efficiency for h-BN tunnel barriers, especially considering that the spin lifetime depends

stronglyonthebarrierthickness(Fig.2and3ofmaintext).Tothisend,wederivetherelation

between𝛾andtheparametersextractedfromtheHanlefitinthemaintext( 𝑝!𝑝!,𝜏!,𝜆,𝐷)

and quantities determined experimentally (e.g. resistances, geometry, etc.). Because we are

interested in the spin injection efficiency in zero applied field, we consider the Takahashi-

Maekawamodel1 which is the zero field limit of the Aji model2 used in themain text. The

parameters 𝜏! (spin lifetime), 𝜆 (spin diffusion length), and𝐷 (diffusion constant) are used

similarlyinbothmodels,butthepolarizationsaredefinedslightlydifferently.IntheTakahashi-

Maekawa model, the spin polarization of the ferromagnet is the asymmetry of the bulk

conductivity 𝑝!,! =!!,!↑ !!!,!

↓

!!,!↑ !!!,!

↓ , where i = 1 for injector and 2 for detector, and the spin

polarization of the junction is the asymmetry of the interfacial conductance 𝑃!,! =!!↑!!!

↓

!!↑!!!

↓ .

However,theAjipolarization𝑝! isaweightedaverageof𝑝!,! and𝑃!,! givenby𝑝! =!!,!!!!!!,!!!,!

!!,!!!!,

where 𝑅! are the contact resistances and 𝑅!,! = 𝜌!,!𝜆!,!/𝐴! are the spin resistances of the

injector (i=1)anddetector (i=2) ferromagnets,𝐴! are the junctionareasand𝜌!,! and𝜆!,! are

theconductivityandspindiffusionlengthsoftheferromagnets,respectively.

5

UsingtheapproachofTakahashiandMaekawa1,wecalculatethespininjectionefficiencyto

be

𝛾 =!

!!,! !!,!!!!!,!

! !! !

!!,! !!!!!!,!

! !! ! !

!!!,!!!!!,!

! !! ! !!!

!!!!,!! !!

! ! !!!,!

!!!!,!! !!

! !!!!!!!,!

! !! ! !

!!!,!!!!!,!

! !! ! !!!

!!!!,!! !!

! !!!!

!

(S1)

where𝐿 is the spacing between injector and detector,𝑅! = 𝑅!"!! is the spin resistance of

graphene,𝑤 is thewidth of the graphene channel, and𝑅!"(=!!

) is the sheet resistance of

graphene.

Inthelimitwhencontactresistanceoftheinjectoranddetectorelectrodesaremuchlarger

thanthespinresistanceoftheferromagnet(i.e.𝑅! ≫ 𝑅!,!),thespininjectioncanbewrittenas:

𝛾 =!

!!,! !!!!!!,!

! !! ! ! !!!

!!!!,!! !!

! ! !!!!!!!,!

! !! ! ! !!!

!!!!,!! !!

! !!!!

!

(S2)

In addition, the Aji polarization becomes equal to the junction polarization (𝑝! = 𝑃!,! ). This

limitissatisfiedfortheh-BNbarriersduetothelowresistivityoftheferromagnet.Becausethis

doesnotassume𝑅! ≫ 𝑅!, thespin injectionefficiencycouldstillbe reducedbyconductivity

mismatch (between graphene and ferromagnet) if the barrier resistance is comparable to or

lowerthanthegraphenespinresistance.

Forcalculating𝛾,weuseassume𝑃!,!=𝑝!=𝑝!= 𝑝! 𝑝!,whichisafitparameterfromEq.

2 in the main text. Using Eq. S2, we extract 𝛾 = 0.022 and 𝛾 = 0.052 in graphene for

monolayer and multilayer h-BN tunnel barrier, respectively, for measurement conditions

6

describedinthemaintext(e.g.gatevoltage,temperature,etc.).Wenotethatcalculatedvalues

of spin injection efficiencies are similar to the fitted values of 𝑝! 𝑝! = 0.023 and 𝑝! 𝑝! =

0.053formonolayerandmultilayerh-BN,respectively,fromthemaintext.Thisillustratesthat

thespininjectionefficiencyisdeterminedbythejunctionpolarizationandisnotsubstantially

reducedbytheconductivitymismatchbetweentheferromagnetandthegraphenechannel.For

both monolayer and multilayer h-BN tunnel barriers, we are in the limit where interfacial

contact resistance is much higher than both the ferromagnetic spin resistance and the spin

resistanceofthegraphene.Aninterestingquestioniswhetherthehigherjunctionpolarization

for the thicker h-BN is due to spin filtering effects3,4 predicted for h-BN tunnel barriers. To

address this, further studieswould be needed to determine if there is a systematic trendof

enhancedspininjectionefficiencywithincreasedh-BNthickness.

References

1. S.TakahashiandS.Maekawa,Phys.Rev.B.67,052409(2003).

2. E.Sosenko,H.Wei,andV.Aji,PhysicalReviewB89,245436(2014).

3. M.V.Kamalakar,A.Dankert,P.J.Kelly,andS.P.Dash,ScientificReports6,21168(2016).

4. Q.Wu,L.Shen,Z.Bai,M.Zeng,M.Yang,Z.Huang,andY.P.Feng,PhysicalReviewApplied2,044008(2014).