The proximity effect opens ways to transfer properties from one material into another and is especially important in two-dimensional (2D) materials. In van der Waals heterostructures, transition metal dichalcogenides (TMDs) can be used to enhance the spin–orbit coupling of graphene leading to the prediction of gate controllable spin-to-charge conversion (SCC). Here, we report for the first time and quantify the spin Hall effect (SHE) in graphene proximitized with WSe2 up to room temperature. Unlike in other graphene/TMD devices, the sole SCC mechanism is the SHE and no Rashba–Edelstein effect is observed. Importantly, we are able to control the SCC by applying a gate voltage. The SCC shows a high efficiency, measured with an unprecedented SCC length larger than 20 nm. These results show the capability of 2D materials to advance toward the implementation of novel spin-based devices and future applications.

The integration of spintronic devices into an existing electronic technology will strongly depend on the all-electrical control of spin currents, with a crucial role being played by the interconversion between charge currents and spin currents. The latter can be achieved by the (inverse) spin Hall effect [(I)SHE] in bulk conductors,1–3 as well as by the (inverse) Rashba–Edelstein effect [(I)REE] in two-dimensional (2D) systems and interfaces,4 allowing ferromagnet (FM)-free electrical generation and detection of spin currents. While the experimental observations of the (I)SHE and (I)REE have been successful in different systems,3,5,6 the transition from the laboratory to industrial applications will require careful device design and material choice to achieve large enough signals for practical implementation.7–10 

Since the first mechanical exfoliation of graphene,11 the library of two-dimensional (2D) materials has grown,12,13 with a plethora of materials that possess a wide range of properties that are complementary to those of graphene. Deterministic transfer methods14 allow us to combine these properties by stacking different 2D materials into a van der Waals heterostructure.15–17 New properties such as magnetism, superconductivity, or spin–orbit coupling can also be induced in graphene by proximity,18–21 leading to new functionalities.22–24 In particular, the combination of graphene and semiconducting transition metal dichalcogenides (TMDs) with a strong spin–orbit coupling (SOC) is a promising platform to study a variety of spin-dependent phenomena. For instance, using the tunable conductivity of a graphene/TMD heterostructure, an electrical spin field-effect switch has already been realized.25,26 More interestingly, a large SOC can be imprinted by proximity from the TMD into graphene,27,28 leading to the presence of weak antilocalization,29–34 spin lifetime anisotropy,35–38 (I)SHE,31,39,40 and (I)REE.41–43 While the previous measurements claiming the SHE in graphene used a non-local Hall bar geometry,44–46 where a variety of non-spin-related effects can contribute and make an interpretation difficult,47–51 the SHE was first unambiguously reported in graphene/MoS239 and the REE later in graphene/WS2.43 Theoretical calculations show that the proximity SOC can be tuned by a gate voltage,23,52 which in the case of WSe2 could lead to larger spin Hall angles in the electron-doped regime of graphene31 and in general would lead toward an electrically controllable spin-to-charge conversion (SCC) device.

Here, we report for the first time the observation of the SHE in graphene proximitized with WSe2. In contrast to other graphene/TMD heterostructures,39,43 the IREE does not contribute to the SCC. Importantly, the SCC signal can be amplified and turned off by an applied back-gate voltage. The amplified SCC signal is up to 11 times larger than our previously reported results in devices with proximitized graphene/MoS239 due to a highly efficient conversion with a SCC length of up to 41 nm (with a lower limit of 20 nm), six (three) times larger than the largest value reported.53 The high SCC efficiency combined with the extra functionality of controlling the SCC with a gate voltage, thus, makes this van der Waals heterostructure a promising system for the creation and detection of pure spin currents in applications such as spin–orbit logic8,10 or electrical manipulation of magnetic memories.54–56 

Our device was carefully designed to measure the (I)SHE in TMD-proximitized graphene [see the sketch in Fig. 1(a)] as well as the (I)REE.39 The device was prepared by placing a multilayer WSe2 flake by dry transfer on a trilayer graphene flake and patterning it into a Hall bar structure. Metallic electrical contacts (Au/Ti) and FM electrodes (Co) with a resistive barrier (TiOx) allow for electrical spin injection and detection. The final device is shown in Fig. 1(b). Low-noise electrical measurements were performed while applying an in-plane magnetic field either along the x- or the y-axis at temperatures between 10 K and 300 K. The transport in our device is diffusive. See Note S2 for details on device fabrication and measurements.

FIG. 1.

(a) Sketch of the proximity-induced ISHE in graphene and the device used to measure it. The precession of the spins and the SCC is sketched. (b) False-colored scanning electron microscopy image of the device showing the labeling of the Co/TiOx (numbers) and Au/Ti (letters, A outside of the image) contacts used for the transport measurements. The metallic Au/Ti and the FM Co/TiOx contacts enable us to measure spin transport in a reference pristine graphene channel (LSV between electrodes 2 and 3) and spin transport and ISHE in a WSe2-proximitized graphene Hall bar (LSV between electrodes 1 and 2).

FIG. 1.

(a) Sketch of the proximity-induced ISHE in graphene and the device used to measure it. The precession of the spins and the SCC is sketched. (b) False-colored scanning electron microscopy image of the device showing the labeling of the Co/TiOx (numbers) and Au/Ti (letters, A outside of the image) contacts used for the transport measurements. The metallic Au/Ti and the FM Co/TiOx contacts enable us to measure spin transport in a reference pristine graphene channel (LSV between electrodes 2 and 3) and spin transport and ISHE in a WSe2-proximitized graphene Hall bar (LSV between electrodes 1 and 2).

Close modal

The device design enables us to study one lateral spin valve (LSV) of pristine graphene and one LSV with a graphene–WSe2 heterostructure in the center, using FM electrodes. Applying a charge current (IC) through the Co/TiOx contacts leads to a spin accumulation in the graphene beneath the electrode, which diffuses in both directions through the 2D channel and can be measured as a non-local voltage (VNL) across the interface between the second FM electrode and graphene [see Fig. 2(a)]. To study the spin injection and the spin transport properties of the pristine graphene, we measured the non-local resistance (RNL = VNL/IC) for the reference LSV by applying current between contact 3 and B and detecting the voltage between contact 2 and A. The measured RNL changes with the relative orientation of the magnetization of the different electrodes [parallel (P) and antiparallel (AP)]. This change can be measured by sweeping the magnetic field along the easy axis of the ferromagnet (By) and is defined as the spin signal.57,58 The measurement at 100 K can be seen in the inset of Fig. 2(b). The magnetizations of the electrodes switch at different coercive fields due to different shape anisotropy, which makes the P and AP states clearly visible and controllable by the proper By history.

FIG. 2.

Spin transport characterization at 100 K for pristine graphene and WSe2-proximitized graphene. (a) Measurement configuration for the Hanle precession measurement showing charge current, voltage terminals, and magnetic field direction. The precession of the spin polarization is sketched. (b) Non-local resistance RNL measured across the reference LSV (voltage 2-A and current 3-B) as a function of an in-plane magnetic field parallel to the graphene channel (Bx), while the injecting and detecting Co electrodes are in the parallel (blue) and antiparallel (red) magnetization configurations. Inset: The same measurement with the magnetic field parallel to the FM electrode (By). A positive spin signal of ∼0.55 Ω is obtained. (c) Δ R N L = ( R N L P R N L A P ) / 2 , obtained from the two curves in (b), as a function of the magnetic field Bx. The red solid line is a fit of the data to the 1D diffusion equation. The extracted parameters are shown as well. (d) Non-local resistance RNL across the graphene/WSe2 region (voltage 2-B and current 1-A) as a function of an in-plane magnetic field parallel to the graphene channel (Bx), while the injecting and detecting Co electrodes are in the parallel (blue) and antiparallel (red) magnetization configurations. Inset: Zoomed-in image of the measurement at a low magnetic field.

FIG. 2.

Spin transport characterization at 100 K for pristine graphene and WSe2-proximitized graphene. (a) Measurement configuration for the Hanle precession measurement showing charge current, voltage terminals, and magnetic field direction. The precession of the spin polarization is sketched. (b) Non-local resistance RNL measured across the reference LSV (voltage 2-A and current 3-B) as a function of an in-plane magnetic field parallel to the graphene channel (Bx), while the injecting and detecting Co electrodes are in the parallel (blue) and antiparallel (red) magnetization configurations. Inset: The same measurement with the magnetic field parallel to the FM electrode (By). A positive spin signal of ∼0.55 Ω is obtained. (c) Δ R N L = ( R N L P R N L A P ) / 2 , obtained from the two curves in (b), as a function of the magnetic field Bx. The red solid line is a fit of the data to the 1D diffusion equation. The extracted parameters are shown as well. (d) Non-local resistance RNL across the graphene/WSe2 region (voltage 2-B and current 1-A) as a function of an in-plane magnetic field parallel to the graphene channel (Bx), while the injecting and detecting Co electrodes are in the parallel (blue) and antiparallel (red) magnetization configurations. Inset: Zoomed-in image of the measurement at a low magnetic field.

Close modal

Setting the sample in one of those two states and applying a magnetic field along the hard axis of the ferromagnet (Bx) parallel to the channel leads to the precession of the injected spins around this axis. Measuring the non-local resistance for parallel ( R N L P ) and antiparallel ( R N L A P ) configurations as a function of magnetic field leads to the so-called symmetric Hanle precession curves.57 Fitting the difference between those two curves [ Δ R N L = ( R N L P R N L A P ) / 2 ] to a 1D spin diffusion equation59 enables us to extract the spin transport properties, i.e., the spin diffusion constant ( D S g r ) , the spin lifetime ( τ S g r ) , and the spin polarization of the Co/graphene interface (Pi). The measurement at 100 K is plotted in Fig. 2(b) and the corresponding fit, together with the extracted parameters, in Fig. 2(c). The oscillation and decay of the spin signal can be explained by the precession, diffusion, and relaxation of the spins in the graphene channel. As the FM electrodes have a finite width, the pulling of the magnetization into the direction of the magnetic field, which is complete for Bx > 0.3 T, has been considered for the fitting (see Note S8 for details).

The same measurement was performed across the proximitized graphene region in the second LSV, applying current from contact 1 to A and detecting the voltage between contact 2 and B. The resulting plot as a function of Bx can be seen in Fig. 2(d). As theoretically predicted37 and already experimentally observed,35,36 the enhanced SOC by the proximity effect leads not only to an enhanced spin relaxation compared to the pristine graphene but also to a large anisotropy between the in- and out-of-plane spin lifetimes ( τ g r / T M D and τ g r / T M D , respectively). This shows up in the Hanle precession curves as a suppression of the spin signal at low fields when the spins are polarized in-plane. As the magnetic field increases, the injected spins precess out of the sample plane and acquire a lifetime which is a combination of τ g r / T M D and τ g r / T M D . This leads to a sign change in ΔRNL and the observation of enhanced shoulders when compared with the zero-field value.35–37 This typically allows the determination of the two spin lifetimes from the experimental data by fitting it to the solution of the anisotropic Bloch equation.35 However, our data, while clearly showing all the other signatures of anisotropic spin transport, miss the characteristic crossing of R N L P and R N L A P at low fields [see the inset in Fig. 2(d)], preventing us from determining τ g r / T M D and τ g r / T M D . It also leads to a negative sign of the spin signal at zero field. The missing crossing is a surprising result that is not expected as the enhanced shoulders that we observe are already a consequence of the out-of-plane precession, which should lead to the reversal of the in-plane spin precession in this field range. We discuss the possible origin in Note S3. Whereas the shoulders show that the out-of-plane spin signal is enhanced (−0.2 Ω) and much larger than the in-plane one (−10 mΩ), it is still smaller than that in the pristine graphene LSV, where we obtained 0.55 Ω (half the difference between P and AP states).

The observed spin lifetime anisotropy in our symmetric Hanle curves is a fingerprint of the induced SOC in graphene by proximity with WSe2.35–37 Such a spin–orbit proximity in the graphene/WSe2 region is also expected to lead to a sizable SHE, even though the intervalley scattering leading to anisotropy has been predicted to be detrimental to the SHE.42 We used the following configuration to study the ISHE in our device: we inject the spin current into graphene by applying a charge current IC from contact 1 to A, which diffuses to both sides of the graphene channel, reaches the proximitized graphene region, and is converted into a perpendicular flowing charge current that we measure as a voltage VNL along the graphene Hall bar with the Au/Ti contacts C and D. Due to the symmetry of the ISHE, only spins that are polarized out-of-plane, perpendicular to the direction of the spin and charge currents, will be converted. It should be noted that the device can also detect SCC due to the IREE. In contrast to the SHE, the IREE will only convert spin currents that are polarized along the x-axis into a transverse charge current. To achieve an out-of-plane spin current, an in-plane magnetic field (along the x-axis) is applied that precesses the spins from the y-axis (parallel to the magnetic easy axis of the FM electrode) toward the z-axis (out-of-plane) [see Fig. 1(a)]. Reversal of the magnetic field leads to a sign change in the z-component of the spin accumulation and, therefore, in VNL across the graphene Hall bar and in the normalized signal RNL. We measure the same baseline signal for an in-plane polarized spin at zero field and, when the magnetization of the FM electrode is in the x-direction, for high fields. When the precession angle is 90° at a finite, low field, a maximum number of spins are converted, and we measure a maximum (or minimum) signal. This leads to an antisymmetric Hanle precession curve. For the two cases of initial magnetization of the Co electrode along the y-direction ( R N L for positive and R N L for negative magnetization along the easy axis), the antisymmetric Hanle curve is reversed, as expected from the precession of spins with opposite polarization.39,42,60 The measurement at 100 K can be seen in Fig. 3(a). The Onsager reciprocity, where a charge current through the graphene/WSe2 region (along the y-axis) gives rise to a transverse spin current (along the x-axis) due to the direct SHE, is also confirmed in our device (shown in Note S4). Finally, the R N L ( ) curve changes the sign with reversing the spin current direction, which further confirms the proximity-induced ISHE in graphene as the source of the SCC (see Note S5). Results in Fig. 3(a) also confirm that no IREE is present in our SCC signal, as it does not switch between positive and negative high fields, when the applied magnetic field pulls and saturates the magnetization of the FM electrode along the x-axis, and the injected spins are, thus, polarized in this direction.39 

FIG. 3.

Spin-to-charge conversion measurement at 100 K. (a) Non-local spin-to-charge conversion curves obtained by measuring across the graphene/WSe2 Hall bar (current 1-A and voltage C-D). The magnetic field is applied along the in-plane hard axis direction (Bx) for initial positive ( R N L , blue) and negative ( R N L , red) magnetization directions of the FM electrodes. (b) Net antisymmetric Hanle signal (open circles) obtained by subtracting the two curves [ R S C C = ( R N L R N L ) / 2 ] in panel (a). The red solid line is a fit of the data to the diffusion equation with the extracted parameters. The definition of ΔRSCC is shown with the black arrow.

FIG. 3.

Spin-to-charge conversion measurement at 100 K. (a) Non-local spin-to-charge conversion curves obtained by measuring across the graphene/WSe2 Hall bar (current 1-A and voltage C-D). The magnetic field is applied along the in-plane hard axis direction (Bx) for initial positive ( R N L , blue) and negative ( R N L , red) magnetization directions of the FM electrodes. (b) Net antisymmetric Hanle signal (open circles) obtained by subtracting the two curves [ R S C C = ( R N L R N L ) / 2 ] in panel (a). The red solid line is a fit of the data to the diffusion equation with the extracted parameters. The definition of ΔRSCC is shown with the black arrow.

Close modal

Similar to the symmetric Hanle curves, the difference between the two antisymmetric Hanle precession curves, R S C C = ( R N L R N L ) / 2 , gives the net signal that can be fitted to the solution of the Bloch equation,59 as shown in Fig. 3(b) for the case of 100 K alongside the fitted parameters. We extract an effective spin lifetime ( τ s e f f ), an effective spin diffusion constant ( D s e f f ), and an effective spin polarization ( P i e f f ) . As we now detect the spin current via the SCC in the proximitized graphene/WSe2 region and not with a FM electrode, Pi of the detector is replaced by the spin Hall angle θ S H e f f and, thus, P i e f f = P i θ S H e f f . Assuming the same Pi for the injector as the one obtained from the electrode pair of the reference LSV, we can calculate the value of θ S H e f f . However, because the sign of Pi is not known, the sign of θ S H e f f cannot be determined.

In our model, the spin transport for the ISHE measurements is described with a single set of effective parameters ( τ s e f f and D s e f f ). This implies that the graphene/WSe2 and the adjacent pristine graphene regions have the same spin transport parameters, which define the spin diffusion length ( λ s e f f = τ s e f f D s e f f ). This approximation was necessary to perform the quantitative analysis, as we were unable to extract the in-plane and out-of-plane spin lifetimes of the proximitized graphene/WSe2 region from the symmetric Hanle curves. Since λ s g r of the pristine graphene is expected to be larger than λ g r / T M D , the out-of-plane spin diffusion length of the graphene/WSe2 region,35,36 our approximation likely leads to λ s e f f > λ g r / T M D , which in turn leads to an underestimation of θ S H e f f . Since the product of both parameters, θ S H e f f λ s e f f (SCC length), is in fact a better quantity to estimate the conversion efficiency,9,61 we need to consider whether the two effects can compensate each other. In Note S11, we discuss this compensation in more detail and show that we are slightly overestimating the θ S H e f f λ s e f f product, by up to a factor of 2 as the upper limit.

In a next step, we measured the temperature dependence of the symmetric (spin transport) and antisymmetric (spin-to-charge conversion) Hanle curves between 10 K and 300 K. The spin transport measurements at different temperatures are shown in Note S6. The ISHE measurements at different representative temperatures with the corresponding fits are plotted in Fig. 4(a). We note that the SCC signal, ΔRSCC, defined as the difference between the minimum and the maximum of RSCC, increases with decreasing temperature [inset in Fig. 4(a)]. One contributing factor for this trend is the increasing sheet resistance of the graphene channel that increases roughly by 40% from 300 K to 10 K (see Note S2). In addition , λ s e f f and θ S H e f f are slightly increasing with decreasing temperature, which leads to more spin current reaching the proximitized area under the WSe2 flake and being converted there more efficiently at lower temperatures (see Note S12 for a list of the fitted parameters at all temperatures).

FIG. 4.

Net antisymmetric Hanle signals measured at (a) different temperatures and zero back-gate voltage, and (b) different back-gate voltages and 100 K. The scatter plots are the experimental data, and the red solid lines are fits to the data. Inset: of ΔRSCC as a function of temperature at zero gate voltage (a) and as a function of gate voltage at 100 K (b).

FIG. 4.

Net antisymmetric Hanle signals measured at (a) different temperatures and zero back-gate voltage, and (b) different back-gate voltages and 100 K. The scatter plots are the experimental data, and the red solid lines are fits to the data. Inset: of ΔRSCC as a function of temperature at zero gate voltage (a) and as a function of gate voltage at 100 K (b).

Close modal

As a final experimental characterization step, we measured the back-gate voltage, Vbg, dependence of the symmetric and antisymmetric Hanle curves at 100 K. For the ISHE measurement, the resulting data together with the fits can be seen in Fig. 4(b) and the symmetric Hanle curves in Note S6.

The back-gated measurements show that the SCC signal can be increased by 400% by applying −5 V and completely suppressed for 5 V gate voltage [see the inset in Fig. 4(b)]. This gate voltage range translates into charge carrier density values from 7.2 × 1011 cm−2 to the charge neutrality point. The strong variation of the SCC signal cannot be explained by the change in resistance of the graphene channel, as it decreases for negative gate voltages (see Note S10), or by the effective spin diffusion length, which varies only slightly when applying positive gate voltages (see Note S13 for a list of the fitted parameters at all gate voltages). However, the estimated θ S H e f f scales with the SCC signal and increases to 8.4% for −5 V gate voltage, whereas at 5 V, it decreases below 0.2%, which we estimate as an upper limit due to the noise level. Therefore, we conclude that the gate voltage directly controls the SCC.

The gate tunability of the spin Hall effect in graphene proximitized by a TMD has been theoretically predicted, where a sign change is expected around the charge neutrality point.31 Our gate voltage range limitation (due to a leakage current through the gate dielectric) prevented us from crossing the charge neutrality point to observe the sign change. Because of this, we cannot rule out that the suppression (amplification) of the SCC signal arises from an increased (decreased) spin absorption into the WSe2 flake if the applied back-gate voltage strongly modifies the resistance of WSe2 in this range.25 In this scenario, the largest estimated θ S H e f f (8.4% at −5 V) would be a lower limit. In either case, though, a large tunability of the SCC signal is achieved with a back-gate voltage, an extra functionality that opens new possibilities in spin–orbit-based logic or memory.

In agreement with other experimental studies of the proximity effect of TMDs in graphene,39,43 the measured θ S H e f f is larger than the theoretical calculation by tight-binding models31 (from which a maximum value of 1.1% is extracted in the hole-doped regime, assuming our experimental resistance), suggesting that extrinsic sources of spin-dependent scattering such as vacancies or impurities might also be relevant in these heterostructures.38,62 It should be noted that the theoretical calculation is done for ideal monolayer graphene/monolayer TMD systems, and discrepancies could, therefore, occur in thicker samples. However, as the proximity effect will strongly decay over distance, the SCC will mainly occur in the graphene layer adjacent to the TMD, and the theoretical model should be a good approximation. As we have no control of the crystallographic alignment of the graphene and TMD flake, the twist angle between the two could also lead to a deviation from the theoretical model, which assumes a quasi-commensurate structure.

In contrast to Ref. 43, the SCC signal is solely due to the ISHE, as we do not observe IREE at any temperature or gate voltage that would be visible as an “S-shaped” background in the antisymmetric Hanle measurements.39,43 From the noise level of our background, we estimate the REE efficiency αRE to be <0.05%. Our results suggest that the valley-Zeeman SOC induced in graphene, mainly responsible for the SHE, dominates over the Rashba SOC, which generates the REE. Experimentally, the same has been found in weak antilocalization measurements of graphene/WSe2 and WS2.32,33,63 The valley-Zeeman term originates in the broken sublattice symmetry of the TMD, which is imprinted into the graphene by proximity and spin-polarizes the bands out of the plane with opposite orientation in the K and K′ valleys.27,28,42 This causes an out-of-plane tilt of the spin texture and should, in principle, reduce the in-plane component induced by the Rashba term,41,42 which arises from the perpendicular electric field at the interface due to broken inversion symmetry. Additionally, theoretical calculations based on realistic values show that the spin Hall angle of graphene/MoS2 is at least one order of magnitude larger than the corresponding REE efficiency.31 

Even though the calculated spin Hall angle of 2.0% at 100 K and 1.7% at 300 K is smaller than that in transition metals as Pt64 or Ta65 that have been used for graphene-based spintronic devices66 or for spin–orbit torque magnetization switching,54 the maximum output signal ΔRSCC of 209 mΩ is an order of magnitude larger than the maximum non-local ISHE signal reported for a graphene/metal device (11 mΩ at 300 K)66 or for our recent graphene/TMD device (25 mΩ at 10 K).39 One major difference between the SCC in spin–orbit proximitized graphene and other devices is that transport of the spin current and conversion into a charge current happen in the same material, in the graphene channel itself, and no losses due to spin absorption across an interface or shunting occur.

However, ΔRSCC is not a good figure of merit if one needs to compare efficiencies in the achievable output voltage across different materials and geometries in non-local devices. We recently proposed39 an adjusted quantification of the conversion efficiency by defining the ratio Reff, which has the units of resistance and is calculated by dividing the output voltage by the input spin current at the conversion region, which actually plays a role in the conversion. The advantage is that additional factors such as the spin polarization of the injector and the properties of the spin diffusion channel do not influence Reff. In our case, it can be calculated using the following equation (see Note S9 for the calculation of the correction factor due to diffusive broadening in the precession):

R e f f = 2 θ S H e f f R s q g r / T M D λ s e f f W c r 1 e W c r / λ s e f f ,
(1)

where R s q g r / T M D is the square resistance of the proximitized region and Wcr is the width of the graphene Hall bar arm. The values for Reff at different representative temperatures and gate voltages are shown in Table I (all temperatures and gate voltages in Note S12 and S13). This normalized efficiency in our graphene/WSe2 heterostructure (160 Ω at 100 K and −5 V) is 11 times larger than those in our previously reported graphene/MoS2 heterostructures (13.4 Ω)39 and three orders of magnitude larger than those in graphene/Pt-based devices (0.27 Ω),66 using always the best case scenario.

TABLE I.

Spin-to-charge conversion parameters for selected temperatures and gate voltages. ΔRSCC is the SCC signal and θ S H e f f is the spin Hall angle. However, the output current efficiency of a material is better quantified with the SCC length (the product of θ S H e f f and λ s e f f ). To compare the output voltage efficiency across different devices, we calculate the normalized efficiency Reff with Eq. (1). The extracted parameters at other temperatures and gate voltages are listed in Notes S12 and S13, respectively.

300 K 100 K (0 V) 10 K 100 K (−5 V)
ΔRSCC (mΩ)  38 ± 2  55 ± 1  90 ± 3  209 ± 1 
θ S H e f f (%)  1.7 ± 0.2  2.0 ± 0.2  2.8 ± 0.3  8.4 ± 0.2 
λ s e f f (nm)  295 ± 14  380 ± 50  410 ± 50  480 ± 40 
θ S H e f f λ s e f f (nm)  4.9 ± 0.7  7.6 ± 0.7  12 ± 2  41 ± 3 
Reff (Ω)  21 ± 3  41 ± 4  65 ± 8  160 ± 12 
300 K 100 K (0 V) 10 K 100 K (−5 V)
ΔRSCC (mΩ)  38 ± 2  55 ± 1  90 ± 3  209 ± 1 
θ S H e f f (%)  1.7 ± 0.2  2.0 ± 0.2  2.8 ± 0.3  8.4 ± 0.2 
λ s e f f (nm)  295 ± 14  380 ± 50  410 ± 50  480 ± 40 
θ S H e f f λ s e f f (nm)  4.9 ± 0.7  7.6 ± 0.7  12 ± 2  41 ± 3 
Reff (Ω)  21 ± 3  41 ± 4  65 ± 8  160 ± 12 

If we are interested in the output current efficiency (for instance, in the case of spin–orbit torques for magnetic switching), the θ S H e f f λ s e f f product (SCC length) is the proper figure of merit,9 which has units of length and compares straightforwardly with the Edelstein length that quantifies the efficiency of the IREE.61 We obtained a SCC length up to an order of magnitude larger at room temperature (4.9 nm, or ∼2.5 nm if we correct for a maximum overestimation of a factor of 2, as discussed in Note S11) than in the best heavy metals such as Pt64 or Ta65 (0.1 nm–0.3 nm) or metallic interfaces such as Bi/Ag67 (0.2 nm–0.3 nm). MoTe2, a semimetallic TMD, shows similar high efficiencies at room temperature (>1.15 nm),68 slightly lower than the best results of topological insulators at room temperature (2.1 nm).69 Impressively, our maximum value of 41 nm at 100 K and −5 V back-gate voltage (see Table I) is six times larger than the largest value reported so far, in the LAO/STO system (6.4 nm),53 and still three times larger (∼20 nm) if we assume the overestimation of our model (see Note S11).

Finally, it is also worth noting that, even though the SCC signal at 300 K is smaller than that at low temperatures, the modulation due to the gate voltage could amplify it immensely as it is stronger than the temperature dependence of the signal (see Note S7). Applying higher negative gate voltages could also lead to giant ISHE signals at room temperature as we see from the charge transport measurements that the saturation region far away from the Dirac point is not reached yet (see Note S2).

We report for the first time the SHE due to spin–orbit proximity in a graphene/WSe2 van der Waals heterostructure. The temperature dependence of the spin transport and spin-to-charge conversion parameters are quantified, showing a robust performance up to room temperature. Interestingly, the ISHE appears as the only SCC mechanism without an accompanying IREE, suggesting the dominance of the valley-Zeeman term over the Rashba term in the proximity-induced SOC. Additionally, we are able to directly gate control the SCC signal, tuning it from an off state up to 209 mΩ, while increasing the conversion efficiency. This leads to a very large θ S H e f f λ s e f f product above 20 nm in the best scenario (at 100 K and −5 V), with a remarkable 2.5 nm at room temperature and zero gate voltage. Our results demonstrate graphene/TMD as superior SCC material systems.

Note added in proof: During the review process, we became aware of recent results that show the electrical control of the SHE and the REE (with SCC lengths of 3.75 nm and 0.42 nm, respectively, at room temperature) using WS270 and the REE using the semimetal MoTe271 and the metallic TaS272 in proximity to graphene in graphene/TMD van der Waals heterostructures. Additionally, our group published results on SHE in another graphene-based heterostructure without TMDs using the insulating Bi2O3.73 

See the supplementary material for device fabrication and characterization, discussion of the missing low field crossing, additional antisymmetric and symmetric Hanle measurements, detailed information on the fitting to the diffusion equation, determination of the parameter uncertainties due to the effective model, and tables with all extracted parameters.

The data that support the findings of this study are openly available in Zenodo at http://doi.org/10.5281/zenodo.3743388.

The authors thank Roger Llopis for drawing the sketches used in the figures. This work was supported by the Spanish MICINN under the Maria de Maeztu Units of Excellence Programme (Grant No. MDM-2016-0618), under project Grant Nos. MAT2015-65159-R, RTI2018-094861-B-100, and MAT2017-82071-ERC, and by the European Union H2020 under the Marie Curie Actions (Grant Nos. 794982-2DSTOP and 766025-QuESTech). J.I.-A. acknowledges postdoctoral fellowship support from the “Juan de la Cierva - Formación” program by the Spanish MICINN (Grant No. FJC2018-038688-I). N.O. thanks the Spanish MICINN for a Ph.D. fellowship (Grant No. BES-2017-07963).

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Supplementary Material