Bias induced up to 100% spin-injection and detection polarizations in ferromagnet/bilayer-hBN/graphene/hBN heterostructures

We study spin transport in a fully hBN encapsulated monolayer-graphene van der Waals heterostructure at room temperature. A top-layer of bilayer-hBN is used as a tunnel barrier for spin-injection and detection in graphene with ferromagnetic cobalt electrodes. We report surprisingly large and bias-induced (differential) spin-injection (detection) polarizations up to 50% (135%) at a positive voltage bias of + 0.6 V, as well as sign inverted polarizations up to −70% (−60%) at a reverse bias of −0.4 V. This demonstrates the potential of bilayer-hBN tunnel barriers for practical graphene spintronics applications. With such enhanced spin-injection and detection polarizations, we report a record two-terminal (inverted) spin-valve signals up to 800 Ω with a magnetoresistance ratio of 2.7%, and achieve spin accumulations up to 4.1 meV. We propose how these numbers can be increased further, for future technologically relevant graphene based spintronic devices.

1 arXiv:1704.01328v1[cond-mat.mes-hall]5 Apr 2017 Recent progress in the exploration of various two-dimensional materials has led to special attention for van der Waals (vdW) heterostructures for advanced graphene spintronics devices.For graphene spin-valve devices, an effective injection and detection of spin-polarized currents with a ferromagnetic (FM) metal via efficient tunnel barriers is crucial 1,2 .The promising nature of crystalline hBN layers as pin-hole free tunnel barriers 3 for spin injection into graphene [4][5][6][7][8] has been recently demonstrated.However, due to the relatively low interface resistance-area product of monolayer-hBN barriers, there is a need to use a higher number of hBN layers for non-invasive spin injection and detection 9 .Theoretically, large spin-injection polarizations have been predicted in FM/hBN/graphene systems as a function of bias with increasing number of hBN layers 10 .Kamalakar et al. 11 reported an inversion of the spin-injection polarization for different thicknesses of chemical vapour deposited (CVD)-hBN tunnel barriers, as well as an asymmetric bias dependence of the polarization using multilayer CVD-hBN/FM tunnel contacts.The observed behaviour was attributed to spin-filtering processes across the multilayer-hBN/FM tunnel contacts.
Here we explicitly show the unique role of current/voltage bias for spin-injection and detection through bilayer(2L)-hBN tunnel barriers with ferromagnetic cobalt (Co) electrodes.
Application of a bias across the FM/hBN/graphene tunneling contacts a) allows to widen the energy window up to ∼ 1 eV for an additional spin polarized states in the FM and graphene to participate in the tunneling spin-injection and detection processes, b) induces a large electric-field between the FM and graphene which can modify the tunneling processes, c) provides electrostatic gating for the graphene which could change the carrier density between electrons and holes, and d) is predicted to induce magnetic proximity exchange splitting in graphene of up to 20 meV 12,13 .We show that bilayer-hBN tunnel barriers are unique for spin-injection and detection in graphene, with (differential) polarizations unexpectedly reaching values close to ± 100% as a function of the applied DC bias at room temperature.Furthermore, we demonstrate a two-terminal (inverted) spin-valve with a record magnitude of the spin signal reaching 800 Ω with magnetoresistance ratio of 2.7%.
We study the spin transport in fully hBN encapsulated graphene, prepared via dry pickup and transfer method 14 to obtain clean and polymer free graphene-hBN interfaces 4 (see Methods for device fabrication details).We use a four-terminal non-local measurement geometry to separate the spin current path from the charge current path (Fig. 1a).An AC current (i) is applied between two Co/2L-hBN/graphene contacts to inject a spin-polarized current in graphene.The injected spin accumulation in graphene diffuses and is detected non-locally (v) between the detector contacts using a low frequency (f=10-20 Hz) lockin technique.For the spin-valve measurements, the magnetization of all the contacts is first aligned by applying a magnetic field B y along their easy axes.Then B y is swept in the opposite direction.The magnetization reversal of each electrode at their respective coercive fields appears as an abrupt change in the non-local differential resistance R nl (= v/i).Along with a fixed amplitude i of 1-3 µA, we source a DC current (I in ) to vary the bias applied across the injector contacts.In this way, we can obtain the differential spininjection polarization of a contact, defined as p in = is i = dIs dI where I s (i s ) are the DC (AC) spin currents, and study in detail how p in of the contacts depends on the applied bias.
We observe that the magnitude of the differential spin signal ∆R nl at a fixed AC injection current increases with the DC bias applied across the injector (Fig. 2a, 2c).Moreover, a continuous change in the magnitude of ∆R nl between -4.5 Ω and 2.5 Ω as a function of DC current bias across the injector, and its sign reversal close to zero bias can be clearly observed (Fig. 3a).A similar behaviour is also observed for different injection contacts.
In Hanle spin-precession measurements, where the magnetic field B z is swept perpendicular to the plane of spin injection, the injected spins precess around the applied field and dephase while diffusing towards the detectors.We obtain the spin transport parameters such as spin-relaxation time τ s and spin-diffusion constant D s by fitting the non-local Hanle signal ∆R nl (B z ) with the stationary solutions to the steady state Bloch equation in the Here, the net spin accumulation µ s is the splitting of spin chemical potentials spin-up µ ↑ and spin-down µ ↓ , i.e., (µ and γ is the gyromagnetic ratio.In order to obtain reliable fitting parameters, we probe the Hanle signals for a long spin transport channel of length L = 6.5 µm.We measure the Hanle signals for different DC current bias and see that the signals cross zero at the same values of B z (Fig. 2d).This implies that τ s and D s in the channel are not affected by the bias across the injector.We obtain τ s ∼ 0.9 ns, D s ∼ 0.04 m 2 /s, and λ s ∼ 5.8 µm.We estimate the carrier density n 5 × 10 12 cm −2 from the Einstein relation by assuming D s = D c 15 , where D c is the charge diffusion constant (see supplementary information section-VIII (SI-VIII)).

II. SPIN-INJECTION POLARIZATION
Since λ s does not change due to the bias applied between the injector contacts, the bias dependence of the non-local differential spin signal ∆R nl in Fig. 2 and Fig. 3a is due to the change in spin-injection polarization.From ∆R nl in Fig. 3a, we can obtain the differential spin-injection polarization of the injector contact 8, p 8 in from 16 using a known unbiased detection polarization of detector 9, p 9 d (see SI-III for the analysis and calculation of p 9 d ), the length between contacts 8 and 9, L 8−9 = 1 µm, the square resistance R sq ∼ 400 Ω, and the width W = 3 µm of graphene.The non-local spin signal as a function of bias due to the spin injection through 8 is obtained from ∆R [8][9] nl , where R ↑↑↑ nl (I in ) is the non-local signal measured as a function of I in when the magnetization of contacts 7, 8, and 9 are aligned in ↑ , ↑ , and ↑ configuration, respectively.We find that p 8 in changes from -1.2% at zero bias to +40% at +25 µA and -70% at -25 µA (Fig. 3b).It shows a sign inversion which occurs close to zero bias.The absolute sign of p cannot be obtained from the spin transport measurements and we define it to be positive for the majority of the unbiased contacts (SI-III).
The observed behaviour of the (differential) polarization is dramatically different from what has been observed so far for spin-injection in graphene, or in any other non-magnetic material.For spin-injection/detection with conventional ferromagnetic tunnel contacts, the polarization does not change its sign close to zero bias.It can be modified at high bias 17 .However, in our case we start with a very low polarization at zero bias which can be enhanced dramatically in positive and negative directions.
The above analysis is repeated for other bilayer-hBN tunnel barrier contacts with different interface resistances.Figure 4a shows p in for four contacts plotted as a function of the voltage bias obtained from the respective ∆R nl (I in ).All contacts show similar behaviour, where the magnitude of p in increases with bias and changes sign close to zero bias.For the same range of the applied voltage bias, contacts with either 1L-hBN or TiO 2 tunnel barriers do not show a significant change in the spin polarization (SI-VI and SI-X).This behaviour implies that the observed tunneling spin-injection polarization as a function of the bias is unique to bilayer-hBN tunneling contacts.

III. SPIN-DETECTION POLARIZATION
We now study the effect of the bias on spin-detection.The (differential) spin detection polarization p d of a contact is defined as the voltage change (∆V ) measured at the detector due to a change in the spin accumulation underneath (∆µ s ) (see SI-II for the derivation and details), where ∆V = i ∆R in−d nl (I d ) is measured as a function of the detector bias I d , and ∆µ s /e = iRsqλs 2W p in e −L/λs .In a linear response regime at low bias, p d should resemble p in because of reciprocity.However in the non-linear regime at higher bias, they can be different.A comparison between Fig. 4a and 4b shows that the bias dependence of p i and p d is similar.
However, we find that p d of contact 9 can reach more than 100% above +0.4V. We note that the presence of a non-zero DC current in the graphene spin transport channel between injector and detector could modify λ s due to carrier drift, and consequently the calculated polarizations have a typical uncertainty of about 10% (SI-IX).Although there is no fundamental reason that the biased detection polarizations p d cannot exceed 100% 18 , it could be that our observation of over 100% polarization is due to effect of the drift which is expected to have a bigger effect on the accurate determination of p d (I) as compared to p i (I) (Fig. 1a).
Concluding, we have obtained a dramatic bias induced increase in both the differential spin-injection and detection polarizations, reaching values close to ±100% as a function of applied bias across the cobalt/bilayer-hBN/graphene contacts.

IV. TWO-TERMINAL LOCAL SPIN TRANSPORT
A four-terminal non-local spin-valve scheme is ideal for proof of concept studies, but it is not suitable for practical applications where a two-terminal local geometry is technolog-ically more relevant.In a typical two-terminal spin-valve measurement configuration, the spin signal is superimposed on a (large) spin-independent background.Since we have found that the injection and detection polarizations of the contacts can be enhanced with DC bias, the two-terminal spin signal can now be large enough to be of practical use.For the two-terminal spin-valve measurements, a current bias (i + I) is sourced between contacts 8 and 9, and a spin signal (differential, v and DC, V ) is measured across the same pair of contacts as a function of B y (inset, Fig. 5a).Figures 5a and 5c show the two-terminal differential resistance R 2t (=v/i) and the two-terminal DC voltage V 2t , respectively, measured as a function of B y .As a result of the two-terminal circuit, both the contacts are biased with same I but with opposite polarity, resulting in opposite sign for the injection and detection polarizations.Therefore we measure an inverted two-terminal differential spin-valve signal R 2t with minimum resistance in anti-parallel configuration.We observe a maximum magnitude of change in the two-terminal differential (DC) signal ∆R 2t (∆V 2t ) of about 800 I) represent the difference in the two-terminal signals when the magnetization configuration of contacts 8 and 9 changes between parallel(↑↑) and anti-parallel(↓↑).A continuous change in ∆R 2t and ∆V 2t can be observed as a function of DC current bias (Fig. 5b and 5d).
The magnetoresistance (MR) ratio of the two-terminal differential spin signal is a measure of the local spin-valve effect, and is defined as ) is the two-terminal differential resistance measured in the anti-parallel (parallel) magnetization orientation of the contacts.From the spin-valve signal, we calculate the maximum MR ratio of -2.7% at I = +20 µA.
Since we have already obtained the differential spin-injection and detection polarizations of both the contacts 8 and 9 as a function of bias (Fig. 4), we can calculate the two-terminal differential spin signal from The calculated differential signal R 2t (I) is plotted in Fig. 5b.A similar analysis can be done for the two-terminal DC spin signal V 2t (I) (SI-II) and is plotted in Furthermore, we can now calculate the total spin accumulation in graphene, underneath each contact in the two-terminal biased scheme, due to spin-valve effect.The results are summarized in Table I.The maximum spin accumulation, beneath contact 9, due to spininjection/extraction from contacts 8 and 9 reaches up to 4.1 meV for an applied bias of I = 20 µA.It is noteworthy that such a large magnitude of spin accumulation in graphene at room temperature has not been reported before.
We will not speculate here on possible explanations of our fully unconventional observations.We note however that further research will require the detailed study of the injection/detection processes as a function of graphene carrier density, in particular the interaction between contact bias induced and backgate induced carrier density. 19Via these measurements one could also search for possible signatures of the recently proposed magnetic proximity exchange splitting in graphene with an insulator spacer, hBN 12,13 .

V. CONCLUSIONS
In conclusion, by employing bilayer-hBN as a tunnel barrier in a fully hBN encapsulated graphene vdW heterostructure, we observe a unique sign inversion and bias induced spininjection (detection) polarizations between 50% (135%) at +0.6 V and -70% (-60%) at -0.4 V at room temperature.This resulted in a large change in the magnitude of the nonlocal differential spin signal with the applied DC bias across the Co/2L-hBN/graphene contacts and the inversion of its sign around zero bias.Such a large injection and detection polarizations of the contacts at high bias made it possible to observe the two-terminal differential and DC spin signals reaching up to 800 Ω, and magnetoresistance ratio up to 2.7% even at room temperature.Moreover, we obtain a very large spin accumulation of about 4.1 meV underneath the contacts in a two-terminal spin-valve measurement.
Note that we have been conservative in biasing the contacts to prevent breakdown of the 2L-hBN barriers.By increasing the bias to the maximum theoretical limit of ∼ ±0.8 V 20 , we expect that we can increase the polarizations even further.Also one can increase the  channel, corresponding to the spin injector contact 8 (7) and measured with the detector contact 9(11).The measured data is represented in circles and the solid lines represent the fits to the data.
Hanle signals in b at different injection bias values ∆R [8][9] nl  nl (I in ) corresponding to the spin current injected through contact 8 and detected via contact 9, as a function of the DC current bias (I in ) applied across the injector.The solid line represents the spin signal ∆R [8][9] nl (I in ) for a continuous sweeping of the I in bias, while the dots are extracted from the Hanle signals ∆R [8][9] nl (B z ) at B z =0, measured at different bias (from Fig. 2b).(b) Differential spin-injection polarization of the injector contact 8, p 8 in as a function of I in , calculated from the ∆R [8][9] nl (I in ) (Eq. 3) data plotted in a.

XI. DEVICE CHARACTERIZATION
An optical microscopy image of the 2L-hBN flake and its AFM thickness measurement is shown in Fig. S1.Charge and spin transport measurements in graphene are performed using low-frequency (21 Hz) lock-in measurements.All measurements are performed in vacuum (∼ 1 × 10 −7 mbar) at room temperature.In order to eliminate the effect of the contact resistances, the graphene resistivity was characterized using a four-terminal local geometry by applying an AC current between contacts 1-13 and measuring the voltage drop across a pair of contacts in between 1 and 13 (see Fig. 1b of the main text).The square resistance R sq of graphene is consistently found to be ∼ 400 Ω for different regions, suggesting that the background doping profile is uniform in the fully encapsulated graphene flake.The differential contact resistances R c (=dV /dI) of the cobalt/2L-hBN/graphene interface were characterized using a three-terminal connection scheme.For example, to determine the differential resistance of contact 9, a small and fixed AC current (i) along with a DC current bias (I) is applied between contacts 9-1, and a differential (AC) voltage is measured between 9-13 (Fig. S2a) while sweeping the DC bias I.The resulting data is plotted in the Fig. S2b.
The non-linear behaviour of the high resistive contacts is an indication of the tunneling nature of the 2L-hBN tunnel barrier, whereas the nearly constant differential resistance in the applied bias range, is a characteristic of a transparent (ohmic) contact.For our sample, the differential contact resistances are in the range of 4 -130 kΩ, and the data is summarized in a table XI.We derive an analytical expression for a DC/AC spin injection and detection polarizations.In our measurements, we observe that the measured polarization depends on the applied DC current bias (I) across the contact.For the DC current injection, the DC polarization of an injector contact P in is defined as: where I s is the DC spin current and I is the injected DC charge current.Similarly, the AC (differential) polarization of the injection contact p in , in the presence of a DC bias current I, is defined as:  S1.A summary of all the used contacts.Here R λ = R sq λ s /W = 773 Ω is the spin resistance of the graphene flake with the width W = 3 µm, spin-relaxation length λ s = 5.8 µm, and R sq ∼ 400 Ω.The number of hBN layers is determined from the optical contrast analysis of the optical microscopic images and the AFM measurements.
where i s is the AC spin current and i is the injected AC charge current.
In our experiment, we apply a DC current at the injector contact along with a small and fixed magnitude of the AC current.The total injected spin current can be represented as: Eq. S3 can be expanded in to a Taylor series.For a small and fixed AC current i, the second order terms can be neglected and the expression can be rewritten as: The AC (differential) polarization can then be written as: Eq. S5 can be used for a consistency check between the measured p in and P in (I) (Fig. S6).
In our case, we observe that p in approximately scales linearly with bias I, implying that dP in dI ∼ constant.Eq.S5 then gives P in ≈ 1 2 p in (I).

B. Detection polarization
The spin-detection polarization is defined as a voltage measured at the detector due to the spin accumulation underneath the detector contact.A charge current I will flow in the ferromagnet via a spin-charge coupling due to a change in the spin accumulation µ s underneath the detector: where the net spin accumulation µ s is the splitting of spin chemical potentials spin-up µ ↑ and spin-down µ ↓ , i.e., (µ ↑ − µ ↓ )/2.Note that Eq.S6 holds under the condition of independent spin channels.For a fixed current bias I at the detector, to compensate for I, the change in the voltage V at the detector will give rise to a change in the charge current I in the opposite direction: Solving Eq.S6 and Eq.S7 leads to: Since the spin accumulations underneath the detector contacts are generally small, this equation is valid for both the DC detector polarization P d and the differential detector polarization p d , i.e., Note that electrons can only inject one spin h/2 (up or down), which implies that P in (I) is restricted below ± 100%.However, this does not hold for the differential injection polarization p in as well as detection polarizations p d (I) and P d (I) which can in principle exceed ±100% in case of applied bias.Note however that when a detector is biased, it will also where R sq is the square resistance of graphene, λ s is the spin relaxation length in graphene and W is the width of the graphene flake.Consider a group of five contacts 7, 8, 9, 10, and 13 in Fig. S3a, where the current (I + i) is injected through a ferromagnet in contact 8 and extracted through 7, and the total differential spin accumulation is detected as a non-local differential voltage, using a low-frequency lock-in detection scheme, between the contacts 9 and 13 v is used to determine the DC spin-injection polarization of contact 8 P 8 in (I) from the DC spin transport measurements where a non-local spin signal is measured via a DC voltmeter.
Figure S6 shows p 8 in (I) determined both from the measurements and from the analytical expression Eq.S5.The measured and the calculated differential polarization (p in (I)) are in a good agreement, supporting the consistency of our approach.) is the non-local signal from spin-valve data when the injection bias V applied across the injector(in) and measured via detector(d), p in (V ) is the differential injection polarization of injector contact at bias V, calculated from the analysis explained in section-IV, and V max(min) is the maximum(minimum) bias applied across the injector.Here, the detector polarization p d at zero bias obtained from following the analysis described in the section-XIII.

XVI. LOW INTERFACE RESISTANCE CONTACTS
As indicated in the optical microscope picture in Fig. 1b of the main text and Fig. S1a, a part of the hBN tunnel barrier flake consists of a monolayer(1L)-hBN region.The contacts from 2 to 5, either fully or partially deposited on top of the monolayer region of the tunnel barrier flake, show low interface resistance of ≈ 4-5 kΩ, whose differential interface resistance R c (= dV /dI) is constant as a function of bias (Fig. S2b).
Figure S7 shows the non-local spin-signal corresponding to the spin injection through the where Q is the heat transport rate i.e., heating at the interface.We obtain T ∼ 3 K on SiO 2 /Si substrate.
The high value of the DC current will heat up the tunnel junction and could mimic a spin accumulation due to temperature gradient and the spin dependent Seebeck coefficient of the interface 22 .In our experiments, however, we also demonstrate the modification of the spin-detection polarization along with the spin-injection polarization, which cannot be explained via these effects.Therefore, the effect of heating on the spin transport can be disregarded in our case.

XVIII. CARRIER DENSITY ESTIMATION UNDERNEATH THE CONTACT
In graphene, the carrier density can be estimated from the Einstein relation: where D c is the charge diffusion coefficient, ν(E F ) is the density of states at the Fermi energy E F , which given by the following equation: where g s = 2 and g v =2, are the spin degeneracy and the valley degeneracy of the electron, respectively, and v F = 10 6 m/s, is the Fermi velocity of the electron.The density of the carriers n can be estimated by integrating Eq.S22 from zero to E F : Using Eq.S22, Eq.S23, and Eq.S21, n can be obtained from 23 : When a bias is applied across a cobalt/2L-hBN tunnel barrier, it modifies the carrier density underneath the contact 24 .In order to estimate this, we assume that initially, the graphene is undoped (E F = 0) underneath the contact.However, the actual doping is unknown.On applying the bias V , the Fermi level is changed by E F : which can be related with the external bias V with the following relation: Here, C o is the geometrical capacitance of the 2L-hBN tunnel barrier, 0 is the dielectric permittivity (= 8.85 × 10 −12 F/m), r is the relative dielectric permittivity of the hBN (∼ 4), e is the electronic charge, and d is the thickness of the tunnel barrier (= 7 A).Now, we can obtain E F by combining Eq.S25 and S26: where c = (4πde 2 )/(h 2 v 2 F 0 r ) We obtain E F and n from the equations S27 and S25.For the applied bias V ∼ ± 0.6 V across the tunnel barrier, n can be modified up to ± 8*10 12 cm −2 , implying that it is possible to tune the carrier density underneath the contact from p-to n-type or vice versa around the charge neutrality point.

XIX. DRIFT EFFECTS ON SPIN INJECTION/DETECTION POLARIZATION AND SPIN TRANSPORT
Jozsa et al. 25 reported an enhanced differential spin-injection polarization using the pinhole Al 2 O 3 barriers from 18% at zero DC current bias upto 31% at +5 µA bias, while it approaches zero at reverse bias due to a strong local carrier drift near the low resistive regions beneath the contact.On the contrary, we observe an increase in the magnitude of the differential polarization and a change in the sign on reversing the bias.This indicates that the observed behaviour in our device is not due to the carrier drift.
The presence of a non-zero electric-field in the graphene spin transport channel could also modify λ s .The spin relaxation length due to the positive drift field (upstream of spins)λ + , Fig. 5d.Even though there is an uncertainty in the calculation of p d due to the a possible effect of carrier drift between the injector and detector, we get a close agreement between the measured and calculated signals in different (local and non-local) geometries.This confirms the accurate determination of the individual spin-injection and detection polarizations of the contacts.
FIG. 1. Device layout and measurement scheme.(a) A layer by layer schematic of the vdW heterostructure of the 2L-hBN/graphene/thick-hBN stack with FM cobalt electrodes.A measurement scheme is shown for the non-local spin transport measurements with a DC current bias I in and AC current i, applied across the injector contacts and a non-local differential (AC) spin signal v is measured using a lock-in detection technique.A DC current bias I d can also be applied in order to bias the detector contact.(b) An optical microscopic picture of the vdW heterostructure.The black-dashed line outlines the hBN tunnel barrier flake.The red-dashed line outlines the monolayer region of the hBN tunnel barrier flake (see SI-I for the optical microscopic picture of the tunnel barrier).A schematic of the deposited cobalt electrodes is shown as orange bars and the Co/hBN/graphene contacts are denoted by numbers 1, 2,.., and 13.The orange-dashed lines represent the unused contacts.Cobalt electrodes from 2 to 5 are either fully or partially deposited on top of the monolayer region of the tunnel barrier flake while the electrodes from 6 to 12 are exclusively deposited on the bilayer region.The width of the cobalt electrodes (2 to 12) is varied between 0.15 and 0.4 µm.

FIG. 2 .
FIG. 2. Non-local spin-valve and Hanle measurements at different DC bias across the injector.(a,c): Non-local differential spin-valve signal R nl (= v/i) as a function of the magnetic field B y applied along the easy axes of the Co electrodes, for a short (L = 1 µm) (a), and a long (L = 6.5 µm) (c) spin transport channel.An offset at zero field is subtracted from each curve for a clear representation of the data.The vertical dashed lines correspond to the switching of the electrodes at their respective coercive fields.The switch of the outer detector 13 is not detectable as it is located far (> 2λ s ) from the nearest injector.The legend shows the applied injection DC current bias I in values.The up(↑) and down(↓) arrows represent the relative orientation of the electrode magnetizations.The three arrows in (a) correspond to the contacts 7, 8, and 9, and the two arrows in (c) correspond to the contacts 7 and 11, from left to right.The insets show the measurements schematics, injection AC current (i) and the DC current bias (I in ), the respective contacts used for the spin current injection, and non-local differential voltage (v) detection.The differential spin signal in a due to spin injection through 8 is ∆R 8-9 nl = (R ↑↑↑ nl −R ↑↓↑ nl )/2, and in c due to spin injection through 7 is ∆R 7-11 nl = (R ↑↑ nl − R ↑↓ nl )/2.(b,d): Non-local (differential) Hanle signal ∆R nl (B z ) as a function of the magnetic field B z .b(d) shows ∆R nl measured for the short(long) . The two vertical dashed lines in d correspond to the fields where the Hanle signals cross zero.

FIG. 3 .
FIG.3.Bias enhanced non-local differential spin signal and large differential spininjection polarization at room temperature.(a) Non-local spin signal ∆R[8][9] nl (I in ) corresponding to the spin current injected through contact 8 and detected via contact 9, as a function

FIG. 4 .FIG. 5 .
FIG. 4. Differential spin-injection (p in ) and detection (p d ) polarizations of the cobalt/bilayer-hBN/graphene contacts.(a) Differential spin-injection polarization p in of four contacts with 2L-hBN tunnel barrier, as a function of the DC voltage bias V .Top axis represents the corresponding electric-field (=V /t hBN , t hBN ≈ 7 Å, the thickness of 2L-hBN barrier) induced across the Co/2L-hBN/graphene contacts.Note that the ∆R nl used to calculate p 8 in in Fig. 3b is obtained from a different data set.(b) Differential spin-detection polarization p d of contacts 8 and 9 as a function of DC voltage bias V applied across the detector while the injector bias is fixed at I in = +20 µA.The insets in a and b show p in and p d of contacts at zero bias, respectively.
attached to it in a transfer stage arrangement.When the sticky PC film comes in a contact with a 2L-hBN flake, the flake is picked up by the PC film.A single layer graphene (Gr) flake, exfoliated onto a different SiO 2 /Si substrate is aligned with respect to the already picked up 2L-hBN flake in the transfer stage.When the graphene flake is brought in contact with the 2L-hBN flake on the PC film, it is picked up by the 2L-hBN flake due to van der Waals force between the flakes.In the last step, the 2L-hBN/Gr assembly is aligned on top of a 10 nm thick-hBN flake on another SiO 2 /Si substrate and brought in contact with the flake.The whole assembly is heated at an elevated temperature ∼ 150 • C and the PC film with the 2L-hBN/Gr is released onto the thick-hBN flake.The PC film is dissolved by putting the stack in a chloroform solution for three hours at room temperature.Then the stack is annealed at 350 • C for 5 hours in an Ar-H 2 environment for removing the polymer residues.The electrodes are patterned via the electron beam lithography on the PMMA (poly(methyl methacrylate)) coated 2L-hBN/Gr/hBN stack.Following the development procedure, which selectively removes the PMMA exposed to the electron beam, 65 nm thick ferromagnetic (FM) cobalt electrodes are deposited on top of the 2L-hBN tunnel barrier for the spin polarized electrodes via electron-beam evaporation.Vacuum pressure is maintained at 1 × 10 −7 mbar during the deposition.To prevent the oxidation of the cobalt, the ferromagnetic electrodes are covered with a 3 nm thick aluminum layer.The material on top of the unexposed polymer is removed via the lift-off process in hot acetone solution at 50 • C, leaving only the contacts in the desired area.* corresponding author; m.gurram@rug.nl† corresponding author; s.omar@rug.nl 1 Roche, S. et al.Graphene spintronics: the European Flagship perspective.2D Materials 2, 030202 (2015).
FIG. S1.(a) An optical microscopic image of the hBN tunnel barrier flake on a Si/SiO 2 substrate (t SiO 2 = 90 nm) where the lighter contrast regions indicate the single-layer hBN.(b) An AFM height profile of the 2L-hBN corresponding to the red line drawn in a, showing a thickness value ∼ 0.7 nm.
FIG. S2.Electrical characterization of the contacts (see section-II).
XIII.DETERMINING THE BIAS DEPENDENT SPIN-INJECTION POLARIZA-TIONS FROM NON-LOCAL SPIN SIGNALSIn a typical non-local spin-valve measurement, a differential voltage signal v nl , measured by a detector contact 'd' with differential detection polarization p d , located at a distance L from an injector contact 'in' with differential injection polarization p in , is given by FIG. S3.Schematics of the measurement configurations for determining the spin-injection polarization of the contact 8. (a) Measuring non-local spin signals as a function of bias on injector contact.(b) Measuring unbiased non-local spin signal with the two detector contacts 9 and 10.
FIG. S4.Differential spin-injection polarization for different injector contacts as a function of DC voltage bias across the injector.The spin injection into graphene from the FM cobalt is facilitated via a 2L-hBN tunnel barrier, clearly demonstrating the change in the magnitude and the sign of the injector polarization as a function of the bias current I .The injection polarizations of contact 7 p 7 in (a), contact 8 p 8 in (b), contact 9 p 9 in (c), and contact 10 p 10 in (d) are shown.
FIG. S5.Measurement geometry for biasing the detector to measure the spin-detection polarization FIG. S8.(a) DC contact resistance R c (= V /I) of a Co/TiO 2 /graphene tunnel barrier shows a nonlinear behaviour as a function of DC current bias I, implying a tunneling behaviour of contacts.(b) A spin-valve measurement for graphene with TiO 2 tunnel barriers.An offset at zero field is subtracted from the non-local resistance.(c) Non-local spin signal R nl for the spin injection through an injector electrode with TiO 2 tunnel barrier a function of DC current bias.Arrows indicate the direction of the bias sweep.In contrast to the contacts with 2L-hBN tunnel barriers (Fig. S7), the contacts with TiO 2 barriers show no change in the magnitude and the sign of the injection polarization as a function of I.

TABLE I .
Spin accumulation µ s in graphene, beneath the contacts, in the two-terminal spin-valve geometry at bias I = +20 µA.The arrows ↑↑ (↓↑) represent the parallel (anti-parallel) orientation of the magnetization of contacts 8 and 9 respectively, from left to right.
VII. METHODS: DEVICE PREPARATIONA fully encapsulated hBN/graphene/hBN heterostructure is prepared via a dry pickup transfer method developed in our group 14 .The graphene flake is exfoliated from a bulk HOPG (highly oriented pyrolytic graphite) ZYA grade crystal (supplier: SPI) onto a precleaned SiO 2 /Si substrate (t SiO 2 =300 nm).A single layer is identified via the optical contrast analysis.Boron nitride flakes (supplier: HQ Graphene) are exfoliated onto a different SiO 2 /Si substrate (t SiO 2 =90 nm) from small hBN crystals (∼ 1 mm).The thickness of the desired hBN flake is characterized via the Atomic Force Microscopy (AFM).For the stack preparation, a bilayer-hBN (2L-hBN) flake on a SiO 2 /Si is brought in contact with a viscoelastic PDMS (polydimethylsiloxane) stamp which has a polycarbonate (PC) film