University of Groningen

Spin transport in high-mobility graphene on WS2 substrate with electric-field tunable proximityspin-orbit interactionOmar, Siddharta; van Wees, Bart

Published in:Physical Review. B: Condensed Matter and Materials Physics

DOI:10.1103/PhysRevB.97.045414

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Publication date:2018

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Citation for published version (APA):Omar, S., & van Wees, B. (2018). Spin transport in high-mobility graphene on WS2 substrate with electric-field tunable proximity spin-orbit interaction. Physical Review. B: Condensed Matter and Materials Physics,97(045414), [045414]. https://doi.org/10.1103/PhysRevB.97.045414

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Spin transport in high-mobility graphene on WS2 substrate with electric-field tunableproximity spin-orbit interaction

S. Omar1, ∗ and B.J. van Wees1

1The Zernike Institute for Advanced Materials University of Groningen Nijenborgh 4 9747 AG, Groningen, The Netherlands(Dated: January 11, 2018)

Graphene supported on a transition metal dichalcogenide substrate offers a novel platform tostudy the spin transport in graphene in presence of a substrate induced spin-orbit coupling, whilepreserving its intrinsic charge transport properties. We report the first non-local spin transport mea-surements in graphene completely supported on a 3.5 nm thick tungsten disulfide (WS2) substrate,and encapsulated from the top with a 8 nm thick hexagonal boron nitride layer. For graphene,having mobility up to 16,000 cm2V−1s−1, we measure almost constant spin-signals both in elec-tron and hole-doped regimes, independent of the conducting state of the underlying WS2 substrate,which rules out the role of spin-absorption by WS2. The spin-relaxation time τs for the electrons ingraphene-on-WS2 is drastically reduced down to ∼ 10 ps than τs ∼ 800 ps in graphene-on-SiO2 onthe same chip. The strong suppression of τs along with a detectable weak anti-localization signaturein the quantum magneto-resistance measurements is a clear effect of the WS2 induced spin-orbitcoupling (SOC) in graphene. Via the top-gate voltage application in the encapsulated region, wemodulate the electric field by 1 V/nm, changing τs almost by a factor of four which suggests theelectric-field control of the in-plane Rashba SOC. Further, via carrier-density dependence of τs wealso identify the fingerprints of the D’yakonov-Perel’ type mechanism in the hole-doped regime atthe graphene-WS2 interface.

Keywords: Spintronics, Graphene, graphene-semiconductor interface, spin-orbit coupling

INTRODUCTION

Recent exploration of various two-dimensional (2D)materials and their heterostructures has provided accessto novel charge [1, 2] and spin-related phenomena [3–8]which are either missing or do not have a measurable ef-fect in intrinsic graphene. Graphene (Gr) can interactwith the neighboring material via weak van der Waalsinteractions which help to preserve its intrinsic chargetransport properties while it can still acquire some foreignproperties from the host substrate such as a sizable bandgap in Gr-on-hexagonal Boron Nitride (hBN) substrateat the Dirac point due to a sublattice dependent crys-tal potential in graphene [1, 2]. For Gr-transition metaldichalcogenide (TMD) heterostructures, an enhanced in-trinsic spin-orbit coupling (SOC) in the order of 5-15meV can be induced in graphene, along with a meV or-der valley-Zeeman splitting due to inequivalent K and K’valleys in graphene [6, 9], a Rashba SOC due to break-ing of the inversion symmetry at the graphene-TMD in-terface [3, 4] with a possibility of spin-valley coupling[10, 11]. This unique ability of the graphene-TMD in-terface makes it an attractive platform for studying thespin-related proximity induced effects in graphene.

In recent reports of spin-transport in graphene-TMDheterostructures [12, 13], a reduced spin-signal and spin-relaxation time were measured in graphene when theTMD was in conducting state. This behavior was at-tributed to the spin-absorption/enhanced SOC via theTMD. On the contrary, in weak anti-localization (WAL)magnetotransport measurements [5, 6], a reduced spin-relaxation time, independent of the carrier-type, carrier-

density in graphene and the conducting state of the TMDwas observed which was attributed to a greatly enhancedSOC in graphene via the proximity effect of the TMD.Also, the existence of the interplay between the valley-Zeeman and Rashba SOC was theoretically [11] and ex-perimentally [14, 15] demonstrated in the anisotropy ofthe spin relaxation time for the out-of-plane and in-planespin-signals in TMD-graphene heterostructures.

Surrounded by distinct conclusions, which seem to de-pend on the device geometry and experiment-type, itcalls for revisiting the problem in a different way, i.e., adirect spin-transport measurement using TMD as a sub-strate for graphene. It has multiple advantages: i) simi-lar to hBN, TMD substrates have already shown signifi-cantly improved charge transport properties of graphene[16] than graphene-on-SiO2 due to their atomically flatand dangling-bond free surface, and screening of thecharge inhomogeneities on the underlying SiO2 [17, 18].This improvement can be helpful in possibly compensat-ing for the reduced τs due to the enhanced SOC/ spin-absorption [12, 13], and improve the spin-signal magni-tude, ii) due to partial encapsulation of graphene with theTMD [13–15], the encapsulated and non-encapsulatedgraphene regions have different charge and spin-transportproperties. It requires a complex analysis for the accu-rate interpretation of the TMD induced spin-relaxationin graphene. On the other hand, spin-transport measure-ments in graphene fully supported on a TMD substratedo not have this drawback and can distinguish the possi-ble effects of spin-absorption via the TMD or a proximity-induced SOC, due to a uniform carrier density and identi-cal effect of the substrate present everywhere in graphene,

2

and iii) in contrast with the TMD-on-graphene geometry[12–15] where graphene partially shields the back-gate in-duced electric field to the TMD, and one cannot clearlycomment on the TMD’s conducting state and correlateits effect on spin-transport in graphene, the inverted Gr-on-TMD geometry does not have this drawback. Lastly,it is worth exploring the possibility of recently observedspin-relaxation anisotropy for in-plane and out-of-planespins in Gr-TMD heterostructures [11, 14, 15] in our sys-tem.

We study the charge and spin-transport properties ofgraphene, fully supported on a tungsten disulfide (WS2)substrate, and partially encapsulated with a top hBNflake, using a four-probe local and non-local geometry,respectively. We measure large values of charge mobilityup to 16,000 cm2V−1s−1. For spin-valve measurements,the obtained spin-signal ∆RNL is almost constant andindependent of the carrier type and carrier density ingraphene, ruling out the possibility of spin-absorptionvia the underlying WS2 substrate. For Hanle measure-ments, we obtain a very low spin-relaxation time τs ∼ 10ps in the electron-doped regime than τs ∼ 800 ps of areference graphene flake on the SiO2/Si substrate in thesame chip. Via the top-gate voltage application, we canaccess the hole doped regime of graphene in the encap-sulated region where τs is enhanced up to 40-80 ps forvarious carrier densities and electric fields. By changingthe electric-field in the range of 1 V/nm in the encapsu-lated region, we can change τs from 20-80 ps, almost byfactor of four, which suggests an electric-field controlledRashba SOC in our system [9, 19]. For both electron andhole regimes (stronger for the hole regime), we observethe fingerprints of the D’yakonov-Perel’ type mechanismfor spin-relaxation, similar to WAL measurements [3, 4].For Gr-on-WS2, the ratio of the out-of-plane to the in-plane ∆RNL ( therefore τs) in the electron-doped regimeis less than one, an indicative of an in-plane Rashba-typesystem [11, 20]. For the hole doped regime, we observean enhanced out-of-plane spin-signal [15] which suggestsa higher τ⊥s for the out-of-plane spins. However, in thepresence of a similar background magnetoresistance sig-nal, the anisotropic behavior can not be uniquely deter-mined and requires further measurements [14, 15].

We also confirm the signature of WS2 induced SOCin graphene-on-WS2 by measuring the WAL signature,similar to the studies performed in refs. [3–6]. Therefore,a low τs in graphene-on-WS2 substrate, with an electric-field tunable Rashba SOC and a WAL signature in thesame sample can be attributed to the WS2 induced prox-imity SOC at the graphene-WS2 interface.

DEVICE FABRICATION

The graphene-WS2 stacks are prepared on a n++-doped SiO2/Si substrate (tSiO2

∼300 nm) via a dry pick-

up transfer method [7, 21]. The WS2 flake is exfoliatedon a polydimethylsiloxane (PDMS) stamp and identifiedusing an optical microscope. The desired flake is trans-ferred onto a pre-cleaned SiO2/Si substrate (tSiO2

=300nm), using a transfer-stage. The transferred flake onSiO2 is annealed in an Ar-H2 environment at 250C for3 hours in order to achieve a clean top-WS2 surface.The graphene (Gr) flake is exfoliated from a ZYB gradeHOPG (Highly oriented pyrolytic graphite) crystal andboron nitride (BN) is exfoliated from BN crystals (size∼1 mm) onto different SiO2/Si substrates (tSiO2

=300 nm).Both crystals were obtained from HQ Graphene. Thedesired single layer graphene and hBN flakes are identi-fied using the optical microscope. In order to prepare anhBN/Gr/WS2 stack, first the hBN flake is picked up by apolycarbonate (PC) film attached to a PDMS stamp, us-ing the same transfer-stage. Next, the Gr flake is alignedwith respect to the hBN flake. When graphene is broughtin a contact with the hBN flake, the graphene region un-derneath the hBN flake is picked up by the van der Waalsforce between the two flakes. The graphene region out-side the hBN flake is picked up by the sticky PC film.Now the WS2 flake, previously transferred onto a SiO2/Sisubstrate, is aligned and brought in a contact with thePC/hBN/Gr assembly and the whole system is heated upto 150C, so that the PC/hBN/Gr assembly is releasedonto the WS2 substrate. Now, the stack is put in a chlo-roform solution for 3 hours in order to remove the PCfilm used in the stack preparation. After that, the stackis annealed again in the Ar-H2 environment for five hoursat 250C to remove the remaining polymer residues. Thethicknesses of WS2 and BN flakes were characterized bythe Atomic Force Microscopy measurements.

In order to define the contacts, a poly-methylmethacrylate (PMMA) solution is spin-coated over thestack and the contacts are defined via the electron-beamlithography (EBL). The PMMA polymer exposed via theelectron beam gets dissolved in a MIBK:IPA (1:3) solu-tion. In the next step, 0.7 nm Al is deposited in twosteps, each step of 0.35 nm followed by 12 minutes oxi-dation in an oxygen environment to form a AlOx tunnelbarrier. On top of it, 70 nm thick cobalt (Co) is depositedto form the ferromagnetic (FM) tunnel contacts with a3 nm thick Al capping layer to prevent the oxidation ofCo electrodes, followed by the lift-off process in acetonesolution at 30C.

RESULTS

We study two samples: i) stack A: a hBN/Gr/WS2

stack consisting of a single layer graphene encapsulatedbetween a bottom-WS2 (tWS2

∼ 3.5 nm) and a top-hBN(thBN ∼ 8 nm) flake , as shown in Figs. 1(a,b,d) andii) stack B: a WS2/Gr stack consisting of a single layergraphene supported on a bottom WS2 flake (tWS2 ∼ 4.2

3

FIG. 1. (a) Stack A: a hBN/Gr/WS2 stack with Co/AlOx ferromagnetic (FM) tunnel contacts and a top gate. (b) Top-viewof stack A. White region marked by C’ represents the top-gate electrode contacting the WS2 substrate. The connection schemefor measuring the I − V behavior of WS2 is also shown. (c) Stack B: graphene supported on a bottom WS2 substrate. (d)Optical image of stack A before the contact deposition. The graphene flake is outlined by a white dotted line, and the orangedotted line denotes the WS2 flake region to be contacted by the top-gate electrode after the contact deposition. On the topleft corner outlined with a black square, a graphene flake (ref A) with the developed contacts can be seen on the same SiO2/Sisubstrate. (e) Optical image of stack B, i.e., a graphene (white dashed lines)/WS2 heterostructure after the contact deposition.It also has a reference Gr flake ‘ref B’ on the same SiO2 substrate (not shown in the image).

nm), without any hBN encapsulation from the top, asshown in Figs. 1(c,e). On the same SiO2/Si chip, thereare reference graphene flakes near stack A (Fig. 1(d)) andstack B. Therefore, we can directly compare the chargeand spin-transport properties of the reference Gr flakeson SiO2 and graphene-on-WS2 substrate, prepared viaidentical steps. The reference flakes on the same SiO2,shared by stack A and stack B, are labeled as ‘ref A’and ‘ref B’ respectively. Moreover, stack A has non-encapsulated regions (region-I) and an encapsulated re-gion (region-II) both, as indicated in the device schematic

of Fig. 1(a). On the other hand, stack B only consists ofregion-I. Therefore, we will discuss the data of stack Aas a representative device.

We use a low-frequency lock-in detection method tomeasure the charge and spin transport properties of thegraphene flake. In order to measure the I-V behavior ofthe WS2 flake and for gate-voltage application, a Kieth-ley 2410 dc source meter was used. All measurementsare performed at room temperature and at 4 K underthe vacuum conditions in a cryostat.

4

Charge transport measurements

We measure the charge transport via the four-probe local measurement scheme. For measuring thegate-dependent resistance, i.e., the Dirac behavior ofgraphene-on-WS2 in region-I (II) of stack A, a fixed accurrent iac ∼ 100 nA is applied between contacts C1-C4(C1-C6) and the voltage-drop is measured between con-tacts C2-C3 (C4-C5), while the back-gate (top-gate) volt-age is swept. The maximum resistance point in the Diraccurve is denoted as the charge neutrality point (CNP).For graphene-on-WS2, it is possible to tune the Fermi en-ergy EF in graphene until EF lies within the band-gap ofWS2. After EF coincides with the conduction band edgeof WS2, it also starts conducting, and Vbg correspondingto this transition is denoted as Von. For Vbg > Von, theWS2 flake screens the electric field from the back-gatedue to a charge accumulation at the SiO2-WS2 interface[5] and the resistance of the graphene flake cannot befurther modified via Vbg.

The Dirac curves for region-I and region-II of stack Aare shown as a function of Vbg in Fig 2(a) and Fig 2(b),respectively. The same is also shown as a function oftop-gate voltage Vtg in region-II in Fig. 2(c). In or-der to extract the carrier mobility µ, we fit the charge-conductivity σ versus carrier density n plot with the fol-lowing equation:

σ =1

Rsq=

neµ+ σ0

1 +Rs(neµ+ σ0). (1)

Here Rsq is the square resistance of graphene, σ0 is theconductivity at the CNP, Rs is the residual resistancedue to short-range scattering [21–23] and e is the elec-tronic charge. We fit the σ−n data for n (both electronsand holes) in the range 0.5-2.5×1016 m−2 with Eq. 1.For the non-encapsulated region we obtain the electron-mobility µe ∼ 9,700 cm2V−1s−1 at room temperature(RT), which is enhanced up to 13,400 cm2V−1s−1 at 4K (Fig. 2(d)). For the encapsulated region, we extracta relatively lower µe ∼ 7,300 cm2V−1s−1 at RT whichis enhanced at 4 K up to 11,500 cm2V−1s−1 (Fig. 2(e)).Via the top gate voltage application, we can access thehole carrier densities up to ∼ -7×1016m−2, and extractthe hole mobility µh at different Vbg values in the range12,600-16,000 cm2V−1s−1 at 4 K (Fig. 2(f)). Via thisanalysis, we get µe ∼ 6,000-13,000 cm2V−1s−1 at differ-ent Vbg values, similar to values that were extracted fromthe back-gate sweep in Fig. 2(e).

In order to obtain the transfer characteristics of theWS2 substrate, we use a specific measurement geometry.Due to partial encapsulation of the bottom-WS2 via thetop-hBN layer, as marked by the orange dashed lines inFig. 1(d), the WS2 crystal is contacted via the top gateelectrode (white region in Fig. 1(b), labeled as C’) andone of the electrodes C1–C8 on the graphene flake. For avoltage applied between C’ and Cj (j = 1− 8), there is a

current flowing through WS2, as schematically indicatedby arrows in Fig. 1(b). The IDS − Vbg transfer curve forWS2 measured using this geometry is plotted in Fig. 2(a)(marked by blue ellipse). It is also noteworthy that thereis a negligible gating action in graphene from the top gatewhen the WS2 is conducting at Vbg=+20 V (Fig. 2(c)).

In conclusion, for graphene-on-WS2, we obtain highelectron and hole mobilities reaching up to 16,000cm2V−1s−1. We obtain similar mobilities for both encap-sulated and the non-encapsulated regions, implying thatthe observed high mobility is due to a clean Gr-WS2 in-terface in our samples, and is not significantly affected bythe lithographic process during the sample preparation.

Spin-transport measurements

A nonlocal four-probe connection scheme is usedto measure the spin-transport in graphene. In or-der to measure the spin signal ∆RNL in the non-encapsulated(encapsulated) region, iac is applied be-tween contacts C2-C1(C4-C1) and the nonlocal voltagevNL is measured between C3-C8(C5-C8), in Fig. 1(a) [24].

For spin-valve measurements, first an in-plane mag-netic field B|| ∼ 0.2 T is applied along the easy axesof the ferromagnetic (FM) electrodes, so that they havetheir magnetization aligned in the same direction. TheFM contacts are designed with different widths, there-fore they have different coercivities. Now, B|| is sweptin the opposite direction, and depending on their co-ercivities, the FM contacts reverse their magnetizationdirection along the applied field, one at a time. Thismagnetization reversal appears as a sharp transition invNL or in the nonlocal resistance RNL = vNL/iac , asshown in Figs. 3(a) and 5(a). The spin-signal is ∆RNL =RPNL−R

APNL

2 , where RP (AP )NL represents the RNL value of

the two level spin-valve signal, corresponding to the par-allel (P) and anti-parallel (AP) magnetization of the FMelectrodes.

For Hanle spin-precession measurements, first the FMelectrodes are magnetized in the parallel (P) or anti-parallel (AP) configuration. Next, for a fixed P (AP) con-figuration, an out-of-plane magnetic field B⊥ is appliedand the injected spin-accumulation precesses around theapplied field with the Larmor frequency −→ωL =

gµBh B⊥,

while diffusing towards the detector, and gets dephased.Here g is the gyromagnetic ratio(=2) for an electron, µB

is the Bohr magneton and h is the reduced Planck con-stant. The measured Hanle curves are fitted with thesteady state solution to the one-dimensional Bloch equa-tion [24]:

Ds52−→µs −−→µs

τs+−→ωL ×−→µs = 0 (2)

with the spin diffusion constant Ds, spin relaxation time

5

- 6 0 - 4 0 - 2 0 0 2 0012345

R sq (k

Ω)

V b g ( V )- 4 0 - 2 0 0 2 00

1

2

34 K R T

4 K R T 4 K

R sq

(kΩ

)

V b g ( V )

V o n

0 2 40 . 01 . 02 . 03 . 04 . 0 R T

4 K f i t 4 K

σ (mS

)

n ( 1 0 1 6 * m - 2 )- 6 - 4 - 2 0 2 4 6 8

0 . 20 . 40 . 60 . 81 . 0

( c )( a )

- 2 0 V - 3 0 V - 4 0 V f i t

σ (mS

)

n ( 1 0 1 6 * m - 2 )

( b )

( f )( e )( d )

- 3

0

3

5

8

I(µA)

- 2 0 20

2

4

6

- 2 0 V - 3 0 V - 4 0 V+ 2 0 V

R sq (k

Ω)

V t g ( V )

V b g

- 1 0 1 2 3 4 5 6

1 . 0

2 . 0

3 . 0

4 . 0

σ (mS

)

n ( 1 0 1 6 * m - 2 )

R T 4 K f i t

FIG. 2. (a) For region-I of stack A, the Rsq−Vbg dependence at RT and 4 K is shown on the left axis. The IDS−Vbg behaviorof WS2 at 4 K is shown on the right-y axis (open circle). For region-II (b) the Rsq − Vbg and (c) the Rsq − Vtg behavior of Grencapsulated between WS2 and hBN flakes. The corresponding σ − Vbg(tg) behaviors are plotted in (d), (e) and (f).

τs and spin-accumulation −→µs in the transport channel.The spin diffusion length λs is

√Dsτs.

Hanle measurements for ref A sample are shown inFig. 3(d). Since we do not observe the CNP, we couldonly measure the spin-transport only in the electron-doped regime and obtain Ds ∼ 0.02 m2s−1 and τs inthe range 730-870 ps, i.e., λs ∼ 3.6-3.8 µm.

After obtaining the spin-transport parameters for refA, we measure the spin-transport in graphene-on-WS2

substrate (region I of stack A) on the same chip. For avarying range of carrier density in graphene, from elec-tron to hole regime with the application of Vbg, we mea-sure almost a constant spin signal ∆RNL at RT via spin-valve measurements, plotted in Fig. 3(b). Here, contactresistance Rc is ∼ 2-6 kΩ, and Rc ≥ Rsq, the contacts arenot in the fully tunneling regime (Rc >> Rsq). There-fore, ∆RNL has a weak back-gate voltage dependence[25]. At 4 K, the spin signal shows a modest increasearound the CNP, and then it decreases. For Vbg < -30 V,there is a negligible in-plane charge conduction in WS2

(Fig. 2(a)). If the spin-absorption via WS2 was the dom-inant spin-relaxation mechanism, the spin-signal shouldenhance for Vbg < -30 V. Both observations cannot be ex-plained by considering the gate-tunable spin-absorptionas a dominant source of spin-relaxation at the graphene-WS2 interface within the applied Vbg range.

Now we perform spin-valve measurements in the en-capsulated region (region-II of stack A), as a function ofVbg and Vtg (Fig. 5(a)). For a wide range of carrier den-sity in the encapsulated graphene which is equivalent toapplying Vbg in the range of ±60 V, we do not see anysignificant change in the spin-signal in Fig. 5(a), simi-lar to the back-gate dependent spin-valve measurements(Fig. 3(a)). It leads to a conclusion that ∆RNL is inde-pendent of the carrier density, carrier type in grapheneand the conducting state of the TMD. Note that thisconfiguration is similar to the TMD-on-graphene config-uration with a back gate application in ref.[12, 13], exceptgraphene is uniformly covered with the WS2 flake in oursample.

In order to estimate λs from spin-valve measurementsin region-I, we measure ∆RNL at different injector-detector separation L values. Assuming equal polariza-tion p for all the contacts, we can estimate λs using therelation [24]:

∆RNL =p2Rsqλse

− Lλs

2w(3)

where w is the width of the spin-transport channel. Weobtain λs around 700-800 nm (Fig. 4), which is almostfive times lower than λs in ref A sample. For graphene-on-WS2, we obtain the charge diffusion coefficient Dc ∼

6

- 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5

0 . 0

0 . 5

1 . 0

- 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5

0 . 0

0 . 5

1 . 0 G r - S i O 2 G r - W S 2

∆R

NL(Ω

)

B⊥( T )

- 0 . 2 - 0 . 1 0 . 0 0 . 1 0 . 2- 2

- 1

0

1

2

PA P

G r - S i O 2 ( e )( d )

R NL(Ω

)

B⊥( T )

- 0 . 0 6 - 0 . 0 3 0 . 0 0 0 . 0 3 0 . 0 61 51 82 12 42 73 03 3

- 4 0 V- 3 0 V

- 1 5 V

0 V

1 5 V R NL(Ω

)

B | | ( T )

4 0 V

( a )

- 1 0 1 2 3 4 50

1

2

3 ( c )( b )

R sq(kΩ

)

n ( 1 0 1 6 * m - 2 )

- 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5- 1 0- 505

1 01 5

PA P

G r - W S 2

RNL (Ω)

R NL(Ω

)

B⊥( T )

0 . 00 . 20 . 40 . 60 . 81 . 0

4 KR T

∆RNL (Ω)

- 2

0

2

4

h

e ( f ) - 5 0 V - 4 0 V - 2 0 V 4 0 V

∆RNL

(Ω)

B⊥( T )

G r - W S 2 V b g

FIG. 3. (a) Spin-valve measurements for Gr-on-WS2 (region-I of stack A) at different Vbg for the injector-detector separationL=0.8 µm, and the corresponding (b) ∆RNL as a function of carrier density in graphene at RT and 4 K. (c) Normalized Hanlesignal ∆RNL, i.e., ∆RNL(B⊥)/∆RNL(B⊥ = 0) for graphene-on-SiO2 (green) and on-WS2 (red) at 4 K. (d) Parallel (P) andanti-parallel (AP) Hanle signals RNL for graphene-on-SiO2 and (e) for graphene-on-WS2 (region-I of stack A). A large linearbackground can also be seen in both P and AP configurations and in electron and hole-doped regimes. (f) Normalized ∆RNL

in region-I of stack A at different Vbg at 4 K.

0.05 m2s−1 using the Einstein relation: σ = e2Dcν,where ν is the density-of-states in graphene. AssumingDs = Dc [20], we estimate τs ∼ 10 ps, using λs obtainedfrom spin-valve measurements (Fig. 4). Note that thisvalue may be uncertain due to different polarization val-ues of the individual contacts, still it gives an estimateof λs [26].

In region-I of stack A, we measure broad Hanle curveswith full-width half maximum in the range of ∼ 1 T(Figs. 3(c),(e), (f)). A direct comparison between Hanlecurves of the reference sample and for graphene-on-WS2,plotted together in Fig. 3(c), clearly demonstrates theeffect of the WS2 substrate in the broadening of theHanle curve. The line shape of ∆RNL remains similarat different carrier densities (n ∼0-6×1016 m−2) in theelectron-doped regime (Fig. 3(f)). Note that the WS2

gets switched on around the CNP of the graphene andremains in the conducting-state in this regime. By us-ing the Hanle curve fitting procedure, we obtain τs ∼10-13 ps and Ds ∼ 0.03-0.04 m2s−1 which matches withDc within factor of two obtained from the charge trans-port measurements. With the obtained Ds and τs via theHanle measurements, we achieve λs ∼ 600-700 nm, usingλs =

√Dsτs, in a good-agreement with λs obtained from

the distance-dependence of spin-valve measurements. Inthe hole transport regime, we could perform the Hanlemeasurements only at Vbg = -50V (Ds ∼ 0.35 m2s−1,τs ∼ 35 ps) with Ds and Dc (∼0.03 m2s−1) differing byan order of magnitude. Therefore, we cannot comment

on the spin-transport parameters in the hole transportregime in region-I.

It should be noted that at high out-of-plane magneticfields B⊥ ∼1 T, the magnetization direction of the FMelectrodes does not fully lie in the sample-plane anda makes an angle with the plane [20]. When we cor-rect the measured data for the angular (B⊥) dependenceof the magnetization (not shown here) using the proce-dure in ref.[27], the ‘corrected’ Hanle curves become evenbroader. From these Hanle curves, we would obtain evenlower τs. Therefore, the τs values reported here representthe upper bound.

We estimate the contact polarization p∼ 15-20 % usingEq. 3 for this device which along with a reasonably goodDs ∼ 0.04 m2s−1, enables us to measure a large ∆RNL inthe order of Ohms, even with such a short τs. For stackB, we obtain a small p ∼ 1-3% and therefore a small∆RNL ∼ 7 mΩ, making it difficult to measure clear Hanlesignals at high magnetic fields in the presence of a largelinear background.

For individual Hanle curves measured in P or AP con-figuration, we also observe a large linear background sig-nal (∼ 10-20 Ω) along with the Hanle signal (Fig. 3(e)).The sign of the background-slope changes with respectto the change in the carrier-type from electrons to holes,similar to a Hall-like signal [28]. However, we do notexpect such a large Hall background because the FMelectrodes are designed across the width of the grapheneflake. The source of such background is non-trivial and

7

1 . 0 1 . 5 2 . 0 2 . 5 3 . 0 3 . 5

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

p = 1 2 %λs = 7 0 0 6 n m

∆RNL

(Ω)

L ( µm )

p = 1 8 %λs = 8 0 0 5 . 6 n m

FIG. 4. Exponentially decaying spin signal ∆RNL in stackA (region-I) for an increasing injector-detector separation L.Black square and circle data points are taken for two differentinjector electrodes. Here, we assume equal spin-polarizationfor all the contacts. The data is fitted using Eq. 3.

at the moment is not clear to us.

DISCUSSION

In graphene, there are two dominant spin-relaxationmechanisms [29–31] : 1) Elliot-Yafet (EY) mechanismwhere an electron-spin is scattered during the interactionwith the impurities. Therefore, the spin-relaxation timeis proportional to the momentum relaxation time τp, i.e.,τs ∝ τp, 2) D’yakonov-Perel’ (DP) mechanism, wherethe electron-spin precesses in a spin-orbit field betweentwo momentum scattering events, following the relationτs ∝ 1

τp.

In order to check the relative contribution of the EYand DP mechanisms in our samples, we plot the τs versusτp dependence. Here, τp is calculated from the diffusioncoefficient D, using the relation D ∼ v2

Fτp, assumingD = Ds(Dc). For reference samples on the SiO2 sub-strate, τs increases with τp in the electron doped regime(Fig. 6(a)), suggesting the dominance of the EY-type spinrelaxation in single layer graphene on the SiO2 substrate,similar to previous observations [26, 30, 31] on this sys-tem. We could not quantify the spin-orbit strength dueto unknown carrier density and the corresponding Fermienergy [32]. For stack A (region-I), processed in identi-cal conditions, we observe an opposite trend between τsand τp in the electron-doped regime (Fig. 6(b)), which

resembles the DP type mechanism. We fit the data with

the relation 1τs

=4λ2

Rh2 τp [4] and extract the Rashba SOC

strength λR ∼ 250 µeV, which is 4 to 6 times higherthan the spin orbit coupling strength in a similar mobil-ity graphene-on-hBN substrate reported in ref. [32], anddistinguishes the effect of WS2 substrate in enhancingthe SOC in graphene. The obtained magnitude of λR isof similar order as reported in refs. [4, 6, 9, 11]. However,a slight variation in τs can drastically change the τs − τpdependence and thus the value of λR. Therefore, such asmall variation of the spin-relaxation rate (τ−1

s ) from 75ns−1 to 95 ns−1 restricts us from claiming the dominanceof the DP spin-relaxation via this analysis.

Now we perform Hanle spin-precession measurementsin the encapsulated graphene (L ∼ 6.7 µm region-II ofstack A). Due to the partial encapsulation of WS2 viahBN (Fig. 1(b),(d)), we can study the effect of the top-gate on the spin-transport only when the bottom-WS2

does not conduct. For a fixed Vbg < -30V, we can accessboth electron and hole regimes via the top gating. Hanlemeasurements shown in Figs. 5(c)-(h) at Vbg=-40 V cor-respond to the CNP of the back-gated graphene, whilevarying Vtg from the hole-doped regime at Vtg=-1.5 V tothe electron-doped regime at Vtg=+1.5 V. Here, we cancontrol the carrier-density and electric field in the encap-sulated region. An out-of-plane electric field breaks thez↔-z inversion symmetry in graphene and modifies thein-plane Rashba SOC [20, 33, 34]. For the hole regimeat Vtg=-1.5 V (Figs. 5(c),(f)) and -0.5 V (Figs. 5(d),(g)),we measure a narrow Hanle shape, an indicative of ahigher τs for the hole spins. Now, at Vtg=+1.5 V, whenthe encapsulated region is in the electron-doped regime,the broad Hanle corresponding to a lower τs appears(Figs. 5(e),(h)). This feature is consistent with broadHanle curves measured in the electron-doped regime ofregion-I (Figs. 3(c),(e),(f)). We fit the Hanle data in thehole-doped regime for |B⊥|< 200 mT, while assumingDs = Dc, where Dc is obtained from the σ − Vtg depen-dence in Figs. 2(f), and obtain τs ∼ 40-80 ps. We repeatthe Hanle measurements for Vbg=-50 V,-35 V and observea similar behavior, confirming that the hole and electronspins have different τs values with τh

s > τ es (Fig. 6(c)),

where superscripts h and e refer to holes and electrons,respectively. By modulating E⊥ in the range of 1 V/nm,we can change τs almost by factor of four, which demon-strates the effective control of electric field in changingthe SOC, and therefore τs at the Gr-WS2 interface [9, 19].

A higher τhs in the encapsulated region is possibly due

to a combined effect of an intrinsically reduced spin-orbitcoupling in the hole regime [11, 19] and modification ofthe electric-field induced Rashba SOC [3, 4, 20]. Thiscan be seen in two features evident from Fig. 6(c) andFig. 6(d). First, for a similar carrier density magni-tude in the electron and hole regime, a reduced τs isobserved in the electron-doped regime. Here, the elec-

8

- 0 . 6 - 0 . 3 0 . 0 0 . 3 0 . 65 25 66 06 4

- 0 . 6 - 0 . 3 0 . 0 0 . 3 0 . 6- 1012

- 0 . 6 - 0 . 3 0 . 0 0 . 3 0 . 67 68 08 48 89 2

- 0 . 6 - 0 . 3 0 . 0 0 . 3 0 . 6- 1012

- 0 . 6 - 0 . 3 0 . 0 0 . 3 0 . 65 05 25 45 65 8

- 0 . 6 - 0 . 3 0 . 0 0 . 3 0 . 6- 10123

0 . 0 0 0 . 0 1 0 . 0 2 0 . 0 3 0 . 0 4

5 0

5 5

6 0

6 5

7 0

7 5

8 0

- 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5- 5 0- 4 0- 3 0- 2 0- 1 0

01 02 03 0

V bg(V)

V t g ( V )

6 1 3 . 01 0 8 91 5 6 42 0 4 02 5 1 62 9 9 13 4 6 73 9 4 3

( e )( d )

( a )

( c )

( b )

V t g = 1 . 5 V V t g = - 1 . 5 V V t g = - 0 . 5 V

PA P

R NL(m

Ω)

B⊥( T )

( h )( g )

∆RNL

(mΩ

)

B⊥( T )

PA P

R NL(m

Ω)

B⊥( T )

∆RNL

(mΩ

)

B⊥( T )

( f )

PA P

R NL(m

Ω)

B⊥( T )

∆RNL

(mΩ

)B

⊥( T )

V b g = - 4 0 V , V t g = - 1 . 5 V - 0 . 5 V 0 V 1 . 5 V R NL

(mΩ

)

B | | ( T )

FIG. 5. (a) Spin-valve measurements across the encapsulated region (region-II) of stack A at different top-gate voltages,changing the carrier-density of the encapsulated region from hole to electron-doped regime. (b) A contour-plot of Rsq for theencapsulated region as a function of Vbg and Vtg. The gray circles on the horizontal dotted line at Vbg=-40 V denote the Vtg

values at which spin valve and Hanle measurements are taken. Hanle measurements for the encapsulated region for the holedoped regime, at the CNP and electron-doped regime are shown in (c), (d) and (e), respectively. The corresponding Hanlesignals are shown in (f), (g) and (h).

tric field E is pointing towards WS2, i.e., E < 0 (redbox in Fig. 6(c)). Second, for the same electric field anenhanced τs is observed at lower carrier densities (bluebox in Fig. 6(d)), similar to that obtained from the WALexperiments in refs. [3, 6]. These observations supportthe presence of a DP type spin-relaxation mechanism forthe hole transport and an electric field controllable SOCat the graphene-WS2 interface.

Recently an anisotropic spin-relaxation, i.e., a higherτs for the spins oriented perpendicular to the graphene

plane than in the graphene plane (τ⊥s > τ||s ) in graphene-

TMD heterostructures was theoretically predicted byCummings et al. [11] and was subsequently experimen-tally demonstrated [14, 15]. In order to check this pos-sibility in our system, we subtract the linear background(Figs. 3(e)) from the measured Hanle data for region-I. In the electron-doped regime, the out-of-plane to in-

plane spin signal ratio is always less than one, implying

τ⊥s < τ||s . It could be due to the presence of a dominant

in-plane Rashba SOC [20] in our system. However, in thehole-doped regime of region-II, we observe an increase inRNL for a high B⊥ (Figs. 5(c),(d)), which is along thelines of a gate-tunable anisotropy in τs reported by Ben-itez et al. [15]. In order to confirm the origin of theenhanced RNL, we measure the magnetoresistance (MR)of the encapsulated region as a function of B⊥ and obtaina similar order of change in the graphene-MR. Therefore,we cannot unambiguously determine the presence of ananisotropic spin-relaxation in our system, and additionalHanle measurements as a function of in-plane [14] andoblique magnetic field [15] will be required to draw aconclusion.

According to Cummings et al. [11], the anisotropy inthe in-plane and out-of plane spin-relaxation can not al-

9

0 . 5 1 . 0 1 . 5 2 . 03 0 0

6 0 0

9 0 0

1 2 0 0

1 5 0 0

3 4 5 67 . 5

8 . 0

8 . 5

9 . 0

9 . 5

- 6 - 4 - 2 0 2 4 6 82 0

4 0

6 0

8 0

1 0 0

- 0 . 8 - 0 . 4 0 . 0 0 . 42 0

4 0

6 0

8 0

1 0 0

G r - W S 2

r e f A r e f B

τ s(ps)

τp ( 1 0 - 2 * p s )

G r - S i O 2

1 0

1 2

1 4

τs (ps)

1/τ s(1

0-2 *ps-1 )

τp ( 1 0 - 2 * p s )

V b g

( c )( a )

- 5 0 V - 4 0 V - 3 5 V

τ s(ps)

n ( 1 0 1 6 * m - 2 )

V b g

( b ) ( d )

- 5 0 V - 4 0 V - 3 5 V

τ s(ps)

E ( V / n m )

FIG. 6. (a) τs versus τp for the reference graphene on SiO2 substrate in the electron doped-regime shows an enhanced τswith the increase in τp, suggesting the EY-type spin-relaxation. (b) τs versus τp (red squares) for graphene-on-WS2 substrate(region-I of stack A) shows an enhanced τs for a reduced τp, suggesting the DP-type spin relaxation in presence of a substrateinduced SOC. Black line represents a linear fit of 1/τs − τp data (black spheres). (c) τs as a function of carrier density n and(d) Electric field E at different values of Vbg for the electron and hole transport regime in region-II of stack A. E and n in theencapsulated-region due to a combined effect of the top and bottom gates are calculated by following the procedure in ref. [20].

ways be observed. It depends on the intervalley scatter-ing rate and the relative strengths of the in-plane RashbaSOC λR induced at the graphene-WS2 interface due tobroken inversion symmetry [3, 4, 11] and the out-of-planevalley-Zeeman SOC λV induced in graphene due to theintrinsic SOC in WS2 [4, 5, 11]. In case of a weak-intervalley scattering, the dominant Rashba SOC givesrise to a faster relaxation of the out-of-plane spins andhinders us from observing a strong anisotropic effect [11].However, a direct conclusion regarding the intervalleyscattering rate cannot be drawn from the spin-transportmeasurements alone.

Our results also provide an alternative explanation tothe observations of refs.[12, 13] where an enhanced spin-signal is observed when the TMD does not conduct. Atthis point, EF in graphene is shifted to the hole dopedregime. Due to partial encapsulation of graphene viathe TMD in refs.[12, 13], the encapsulated and non-encapsulated regions have different spin-transport prop-erties, and the net spin-relaxation rate is dominated bythe spin-relaxation at the graphene-TMD interface. It isreflected in a reduced value of ∆RNL and τs, coincidingwith the conducting-state of the TMD for the electron-doped regime in graphene. Therefore, based on our re-sults, we argue that it is the modulation of the spin-orbit coupling strength than the spin-absorption whichchanges the spin-relaxation time, leading to the same re-sults.

Alternatively, in order to confirm the presence of a sub-strate induced SOC in graphene, we perform the quan-tum magnetoresistance measurements in graphene in theelectron-doped regime at 4 K, using the local four-probegeometry. Here we measure the flake resistance as afunction of an out-of plane magnetic field with severalaveraging operations, in order to suppress the univer-sal conductance fluctuations (UCF) in the sample resis-

tance at low temperatures [35]. First, we measure theMR of the reference graphene-flake on SiO2 (ref B) sub-strate at 4 K. Here we see a weak-localization (WL) sig-nature (Fig. 7(a)). A WL signature appears at low mag-netic fields due to a suppressed back-scattering of elec-trons [35]. A broad WL signal is probably due to thelow mobility of graphene-on-SiO2. [4, 6, 35]. However,for graphene-on-WS2 (region-I, stack A) under the samemeasurement conditions, we do not observe any signa-ture of the weak localization. For graphene-on-WS2 wehave even three times higher mobility than the referencesample which should help in observing a WL peak at asmall range of the magnetic field [6]. The absence of theWL signal in graphene-on-WS2 indicates the emergenceof a competing behavior, for example due to the weakanti-localization effect. In fact, when we measure theMR for a longer graphene-channel of length ∼ 8 µm, in-cluding the encapsulated region, we observe a clear WALsignature (Fig. 7(b)), which could be due to more spatialaveraging of the signal in a longer graphene-channel. Ifthe WAL effect was only due to charge carriers in theunderlying TMD substrate itself, the WAL peak wouldbe much broader ∼ 0.5-1 Tesla [36, 37]. Since, in ourcase the WAL peak is much narrower (∼ 10 mT), wecan safely exclude this possibility. The observation ofthe WAL signature in the WS2 supported single layergraphene confirms the existence of an enhanced SOC ingraphene [5, 6].

CONCLUSIONS

In conclusion, we study the effect of a TMD (WS2) sub-strate induced SOC in graphene via pure spin-transportmeasurements. In spin-valve measurements for a broadcarrier density range and independent of the conduct-

10

- 6 0 - 4 0 - 2 0 0 2 0 4 0 6 0

- 1

0

1

2

3

4

- 5 . 0 - 2 . 5 0 . 0 2 . 5 5 . 0

- 1 . 5

- 1 . 0

- 0 . 5

0 . 0

0 . 5

1 . 0

L ~ 1 . 5 µmG r - W S 2 G r - S i O 2

∆Rfla

ke(Ω

)

B⊥( m T )

L ~ 2 µm

W LL ~ 8 µm

( b )

∆Rfla

ke(Ω

)

B⊥( m T )

W A L

( a )

FIG. 7. (a) A WL signal for ref B flake on a SiO2 substrate (red) and no WL/WAL signature was detected for graphene-on-WS2

(region-I of stack A). (b) A narrow WAL signature in the encapsulated region was detected due to more spatial averaging in alonger region (region-II of stack A). All the data shown here is taken at 4 K.

ing state of WS2, we observe a constant spin-signal, andunambiguously show that the spin-absorption process isnot the dominant mechanism limiting the spin-relaxationtime in graphene on a WS2 substrate. The proximity in-duced SOC reflects in broad Hanle curves with τs ∼ 10-14ps in the electron doped regime. Via the top-gate volt-age application in the encapsulated region, we measureτs ∼ 40-80 ps in the hole-doped regime, implying a re-duced SOC strength. We also confirm the signature ofthe proximity induced SOC in graphene via WAL mea-surements. For both electron and hole regimes, we ob-serve the DP-type spin-relaxation mechanism. The pres-ence of the DP-type behavior is more (less) pronouncedfor the hole (electron) regime due to a higher (lower) τs.We also demonstrate the modification of τs as a functionof an out-of-plane electric field in the hBN-encapsulatedregion which suggests the control of in-plane Rashba SOCvia the electrical gating. In future experiments, in orderto realize more effective control of electric field on τs,the single layer graphene can be replaced by a bilayergraphene [38, 39]. To enhance the spin-signal magni-tude, a bilayer hBN tunnel barrier [8] with a high spin-injection-detection efficiency can also be used.

Summarizing our results, we for the first time, un-ambiguously demonstrate the effect of the proximity in-duced SOC in graphene on a semi-conducting WS2 sub-strate with high intrinsic SOC via pure spin-transportmeasurements, opening a new avenue for high mobilityspintronic devices with enhanced spin-orbit strength. Agate controllable SOC and thus the modulation of τs al-

most by an order of magnitude in our graphene/WS2

heterostructure paves a way for realizing the future spin-transistors.

ACKNOWLEDGEMENTS

We acknowledge J. G. Holstein, H. M. de Roosz, T.Schouten and H. Adema for their technical assistance.We are extremely thankful to M. Gurram for the scientificdiscussion and his help during the sample preparationand measurements. This research work was funded fromthe European Union’s Horizon 2020 research and innova-tion programme (grant no.696656) and supported by theZernike Institute for Advanced Materials and the Nether-lands Organization for Scientific Research (NWO).

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