This is the accepted version of the article: Benítez L.A., Savero Torres W., Sierra J.F., Timmermans M., Garcia J.H., Roche S., Costache M.V., Valenzuela S.O.. Tunable room-temperature spin galvanic and spin Hall effects in van der Waals heterostructures. Nature Materials, (2020). 19. : 170 - . 10.1038/s41563-019-0575-1. Available at: https://dx.doi.org/10.1038/s41563-019-0575-1 Tunable room-temperature spin galvanic and spin Hall effects in van der Waals heterostructures L. Antonio Benı́tez1,2 ,∗ Williams Savero Torres1 ,† Juan F. Sierra1 , Matias Timmermans1 , Jose H. Garcia1 , Stephan Roche1,3 , Marius V. Costache1 , and Sergio O. Valenzuela1,3‡ 1 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, Bellaterra, 08193 Barcelona, Spain 2 Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain and 3 Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain (Dated: August 28, 2019) Abstract Spin-orbit coupling stands as a powerful tool to interconvert charge and spin cur- rents and to manipulate the magnetization of magnetic materials through the spin torque phenomena [1–5]. However, despite the diversity of existing bulk materials and the recent advent of interfacial and low-dimensional effects [2, 3, 6], control of the interconvertion at room-temperature remains elusive. Here, we unequivocally demonstrate strongly enhanced room-temperature spin-to-charge (StC) conversion in graphene driven by the proximity of a semiconducting transition metal dichalcogenide (WS2 ). By performing spin precession experiments in properly designed Hall bars, we separate the contributions of the spin Hall and the spin galvanic effects. Remarkably, their corresponding conversion efficiencies can be tailored by electrostatic gating in magnitude and sign, peaking nearby the charge neutrality point with a magnitude that is comparable to the largest efficiencies reported to date [6, 7]. Such an unprece- dented electric-field tunability provides a new building block for spin generation free from magnetic materials and for ultra-compact magnetic memory technologies. ∗ These authors contributed equally to this work; an.benitez7@gmail.com † These authors contributed equally to this work; williams.savero@icn2.cat ‡ SOV@icrea.cat 1 While classical spintronics relies on the generation and manipulation of spin-polarized electrical currents using ferromagnetic materials, the emerging field of spin orbitronics is driven by the creation of pure spin currents in non-magnetic materials by means of the spin- orbit interaction (SOI) [1–4]. In the spin Hall effect (SHE) and the inverse spin galvanic effect (ISGE), a charge current generates a transverse spin current and a non-equilibrium spin density, respectively, that can be utilized, for example, to manipulate the magnetization of ferromagnets in non-volatile memory technologies [8]. Various categories of materials are being intensively investigated for such a purpose, including metals, oxides and topological insulators [1–5, 9]. Two-dimensional (2D) atomic crystals constitute a unique platform to en- gineer materials with novel functionalities in the limit of ultra-compact device architectures [10, 11]. Because they consist of atomically thin planes, their electrical, optical and spin properties can be enriched and tailored by proximity effects. In recent years, magnetic corre- lations and strong SOI have been successfully imprinted onto graphene and observed at room temperature [12–14]. When graphene is in direct proximity to a transition metal dichalco- genide (TMDC), it preserves its electronic properties while acquiring a complex spin texture with out-of-plane and winding in-plane components (Fig. 1a) that result in anisotropic spin dynamics [14–18]. Theoretical studies further suggest that the unique nature of this SOI can enhance the graphene StC conversion efficiency [19, 20], while the coexistence of SHE and IGSE is allowed by new SOI terms such as the valley Zeeman coupling [15, 16]. The observation of the SHE was originally reported in graphene decorated with adatoms and in contact with WS2 [21] but follow-up studies suggest that the detected signal was not spin related [22–24]. More recently, the SHE was observed in heterostructures comprising mul- tilayer graphene and MoS2 [25]. However, because MoS2 is believed to be conductive and the experiment does not allow control of the carrier density of neither graphene nor MoS2 , it is not possible to fully discriminate between StC conversion by proximity effects and in the bulk of MoS2 [25]. In this work, we demonstrate large, gate-tunable StC conversion driven by both the SHE and ISGE in monolayer graphene-WS2 heterostructures at room temperature. The SHE and ISGE are found to coexist in a narrow energy region nearby the charge neutrality point (CNP), enabling the control of both phenomena by tuning the carrier density n. The StC conversion mechanisms manifest in the presence of large spin transport anisotropy, as a consequence of the inherited spin textures of the graphene states. The observed SHE 2 conversion efficiency as a function of n and temperature is well reproduced by theoretical calculations of the spin Hall conductivity. The measurement scheme and optical image of a typical device are shown in Figs. 1b and 1c, respectively [26–28] (see Methods for fabrication details and Supplementary Fig. 1 for detailed device schematics). A carefully designed experimental protocol based on spin precession [29] allows us to isolate the proximity-induced StC conversion in the modified graphene (graphene-WS2 ) from both spurious phenomena and competing StC conversion occurring in the bulk of the TMDC [25]. The device consists of a patterned graphene Hall cross with a WS2 flake along one of the arms and ferromagnetic injector/detector electrodes (F1, F2, F3) across the other. An electric field E along the graphene-WS2 arm (and associated current I, Fig. 1b) generates a spin current and spin accumulation due to the SHE (red arrows) and a non-equilibrium spin density conveyed by the ISGE (blue arrow, see Fig. 1a). The spins, carrying information on the SHE and the ISGE, diffuse in the graphene and are detected by measuring the non-local voltage VnlF at F1. Alternatively, a spin current in graphene can be generated by applying I in F1. In this case, the spin current and non-equilibrium spin density that reach the graphene(gr)-WS2 are converted into a voltage Vnlgr−WS2 by the reciprocal effects: the inverse spin Hall effect (ISHE) and the spin galvanic effect (SGE). In the linear regime, for phenomena that are Onsager reciprocals such as the SHE and the ISHE, VnlF = Vnlgr−WS2 = Vnl . For the StC conversion experiments, F1 and F2 are equivalent and either of them can be used to investigate the SHE, the ISGE and their reciprocals. In addition, F2 and F3 (in combination with F1) are used to independently characterize the spin dynamics in both the pristine graphene and the graphene-WS2 [14] (Supplementary Section I). This allows us to determine the StC conversion efficiencies without extra fitting parameters. The out-of-plane k and in-plane spin relaxation lengths in graphene-WS2 , λ⊥ s and λs , are about one-micrometre and few-hundred nanometres, respectively [14]. Thus, the width lw of the WS2 flake is selected to be lw ∼ 1 µm to simultaneously detect the SHE and the ISGE [1]. Sufficiently large distances from the WS2 to F1 and F2 ensure large-angle spin precession at low magnetic fields, for which the magnetization of the electrodes M1,2 remain unaffected [30]. A back- gate voltage Vg is applied to the substrate to tune the carrier density of both the graphene and WS2 . For graphene-WS2 in the xy-plane and I applied along ŷ (Fig. 1b), the spins generated 3 by the SHE are polarized in the ẑ direction while those generated by the ISGE are in the x̂ direction (see Fig. 1a). Because the ISGE and SHE spins are orthogonal, their contributions to Vnl can be readily separated using spin precession [29]. Vnl is proportional to the local spin accumulation projected along the detector magnetization M1 . Due to magnetic shape anisotropy, M1 tends to be aligned with the F1 length, which is set along ŷ, orthogonal to the spins generated by both the SHE and the ISGE (Fig. 1b). Thus, at zero magnetic field, Vnl = 0 since neither the SHE nor the ISGE contribute to Vnl . For a low magnetic field Bz perpendicular to the graphene plane, Vnl solely depends on the ISGE. While the SHE spins are parallel to Bz and remain unaffected, the ISGE spins undergo precession. Because the ISGE spins are no longer perpendicular to M1 when they reach F1, Vnl 6= 0 (Fig. 1d). In contrast, for an in-plane magnetic field Bx , the ISGE spins remain unaffected so that Vnl is solely dependent on the SHE (Fig. 1e). Similar arguments can be applied to the ISHE and the SGE. For the transport to occur only in the modified graphene, it is crucial to verify the insulating character of WS2 . Otherwise, a current in WS2 could generate both out-of-plane and in-plane spins, e.g. through the SHE in WS2 [25], which can be mistaken with spins associated to the proximity effects. Figure 2a shows the current Ids versus Vg when a constant driving voltage Vds is applied between graphene and WS2 . Ids increases sharply at VgT ∼ 12 V, marking the Vg at which WS2 becomes conducting. Therefore, to avoid spin absorption (spin transfer) to (from) WS2 , all StC conversion measurements are acquired at Vg < VgT . Figure 2b shows the gate-dependent resistance R of the graphene-WS2 . In this region, the graphene is n-doped with the CNP at VgCNP = −10 V. The fact that VgCNP < VgT allows us to study the characteristic StC conversion for both electrons and holes. ↓,↑ The insets of Figs. 2c and 2d show typical Rnl = Vnl↓,↑ /I versus applied magnetic field with M1 antiparallel (Vnl↓ ) and parallel (Vnl↑ ) to ŷ (see Fig. 1b). The current I is applied at F1 and Vnl↓,↑ measured in the graphene across the graphene-WS2 arm. The orientation of M1 is prepared prior to the measurements by applying a magnetic field along ŷ with a magnitude exceeding the F1 coercive field. The inversion of the magnetic-field dependence when M1 reverses demonstrates the spin-related origin of the signal. The main panels of ↑ ↓ ↑ ↓ Figs. 2c and 2d show ∆Rnl ≡ Rnl − Rnl . By calculating the difference between Rnl and Rnl , any non-spin related component in Vnl↓,↑ is eliminated. In Fig. 2c, the magnetic field is applied in-plane in the ISHE configuration, as repre- 4 sented in Fig. 1e; therefore ∆Rnl corresponds to the ISHE signal RISHE . In Fig. 2d, the magnetic field is applied out-of-plane in the SGE configuration, as represented in Fig. 1d, and thus ∆Rnl ≡ RSGE . The experimental data in Figs. 2c and 2d exhibit an antisymmetric spin precession lineshape [29]. The spins injected by F1 are parallel to ŷ and, consequently, only when the magnetic field generates a ẑ (x̂) spin component, a nonzero RISHE (RSGE ) is detected. At low magnetic fields RISHE and RSGE are approximately linear; they reach maximum magnitude at about ±50 mT and then decrease. The extrema in RISHE and RSGE indicate an aggregate spin precession angle of π/2 when reaching the Hall cross. The asymp- totic decrease to zero at larger magnetic fields (> 50 mT) is associated to spin dephasing. The StC conversion efficiencies can be obtained from the spin precession lineshapes in Figs. 2c and 2d. To reduce the number of unknown parameters, the spin dynamics outside and inside the graphene-WS2 region is independently characterized as follows. Figure 2e shows typical non-local spin precession measurements rnl = Vnl↓↑,↑↑ /I in pristine graphene using electrodes F1 and F3. Measurements are performed for antiparallel (↓↑) and parallel (↑↑) configurations of M1,3 and magnetic fields Bz and Bx (see Supplementary Fig. 2 for Bz measurements). By fitting the results to the solution of the Bloch equations, the spin transport properties of the pristine graphene are extracted (Supplementary Fig. 2). Figure 2f shows the spin precession response in graphene-WS2 as a function of Bx using electrodes F1 and F2. The results highlight the strongly anisotropic character of the spin transport, in agreement with prior reports [14]. In particular, they show that as Bx increases, the corresponding rnl becomes much larger than its value at B = 0, which demonstrates that k that the spin lifetime of spins in the plane of graphene-WS2 , τs , is much smaller than the lifetime of spins pointing out of plane, τs⊥ . Their magnitudes are calculated by modelling the spin diffusion in the graphene and the graphene-WS2 with the parameters extracted k from Fig. 2e, yielding τs = (6 ± 1) ps and τs⊥ = (52 ± 10) ps. The anisotropy ratio, k defined as ζ = τs⊥ /τs is ζ = 8 ± 3 (Supplementary Section II). With the spin dynamics fully characterized, the spin and spin-current densities can be calculated, at any position, from the analytical solution of the Bloch diffusion equation (Supplementary Section II). At this point, the spin precession lineshapes in Figs. 2c and 2d can be readily obtained from the spin current density jsz associated to the spins projected in ẑ (ISHE) and the in- plane component of the spin density in x̂ (SGE) in the graphene-WS2 region (Fig. 1b). The only unknown parameters are the corresponding StC conversion efficiencies, which manifest 5 as scaling factors (Supplementary Section II). In the ISHE case, the efficiency is quantified with the spin Hall angle θSHE , which measures the conversion from jsz to a charge current density jcy [1]. In the case of the SGE, where a spin density is converted into jcy , several figures of merit have been proposed. In our experiments, the spin density leading to RSGE results directly from the spin current density jsx . Therefore, it is possible to adopt an SGE equivalent to θISHE , namely αSGE ≡ jcy /jsx . Because the latter conversion is from a 2D spin current into a 2D charge current, αSGE is dimensionless. This contrasts with the commonly used inverse Edelstein effect length λIEE , which quantifies the SGE conversion efficiency from a three-dimensional spin current into a 2D charge current and has the dimension of a length [6]. The solid lines in Figs. 2c and 2d represent the calculated responses from which room- temperature θSHE ≈ 0.3 %, and αSGE ≈ 0.1 % are estimated. The agreement between the model and experiment is excellent considering that only one adjustable (scaling) parameter is used. For comparison purposes, one can convert αSGE and θSHE into λIEE through λSGE IEE = k ⊥ k ⊥ αSGE λs ≈ 0.42 nm and λSHE IEE = θSHE λs ≈ 3.75 nm, where λs = 420 nm and λs = 1.25 µm are the in-plane and out-of-plane spin relaxation lengths in graphene-WS2 . Remarkably, these values compare very favourably with those estimated for heavy metals as θSHE λM M s (λs the metal spin diffusion length), yielding 0.2 nm for Pt, 0.3 nm for Ta and 0.43 for W [31]. Furthermore, λSHE IEE for graphene-WS2 is larger than the λIEE reported for any device at room temperature, being one order of magnitude larger than in Bi/Ag interfaces, λIEE = 0.2−0.33 nm [6], and almost twice λIEE = 2.1 nm in the topological insulator α-Sn [7]. The ISGE and SGE can also be investigated when M1 rotates and develops a component along x̂ with sufficiently large Bx [26, 28]. As observed in Fig. 2e, the magnetization rotation is evident for Bx > 0.2 T, with M1 (and M3 ) becoming fully aligned with Bx for |Bx | > 0.3 T. Therefore, a broad step in Rnl is expected for Bx between -0.3 and 0.3 T. Figure 3a shows Rnl versus Bx for three representative gate voltages: at the CNP (Vg = −10 V) and for electron (Vg = −3 V) and hole (Vg = −13 V) conduction. The SGE and the ISHE signals are clearly observed. The solid lines represent M1x , the projected M1 along x̂, which is independently extracted using measurements as in Fig. 2e [26]. The spin precession response associated to the ISHE, as shown in Fig. 2c, appears superimposed. The agreement between the field- dependence of M1x and the SGE step is excellent. In addition, the magnitude of the SGE extracted from these measurements coincides with the results obtained from spin precession 6 (Fig. 2d); this allows us to discard any artifacts associated with stray magnetic fields. The results in Fig. 3a suggest that the ISHE and the SGE follow distinct carrier density dependences. While the SHE signal is clearly distinguished at the CNP, the SGE signal changes sign between electrons and holes and becomes undetectable at the CNP. Figure 3b represents the room-temperature magnitude of the ISHE and SGE versus Vg . The SGE is ∗ quantified by means of the step height, RSGE ≡ Rnl (0.4 T) − Rnl (−0.4 T) and the ISHE by ∗ the substraction RISHE between the values of RISHE at its two extrema (see Fig. 3a). It is ∗ observed that n has a dramatic influence in the StC conversion efficiency. RISHE displays a sharp peak with its maximum located nearby the CNP; R vs Vg is shown in Fig. 3b for ∗ comparison (solid black line). In contrast, RSGE is asymmetric about the CNP, changing sign between electrons and holes, as concluded from Fig. 3a. ∗ The change in sign in RSGE stems from the change in the nature of the carriers, as the winding of the spin texture is symmetrical about the CNP [16, 20]. This further confirms our interpretation of the signal as originating from the SGE. Theoretical calculations for graphene-WS2 suggest that RISHE also changes sign nearby the CNP with a behaviour qual- itatively similar to that of RSGE . However, the magnitude of RISHE is expected to be much larger for holes than for electrons [19]. As a consequence, the smearing effect resulting from the presence of charge puddles and room-temperature broadening might suppress the ex- tremum in the electron side, leaving only the dominant hole peak by the CNP. The results in ∗ Fig. 4a, showing RISHE versus n as the temperature T decreases, indicate that this hypothesis ∗ is plausible. Indeed, RISHE at room temperature (300 K) presents an incipient electron-hole asymmetry, with a steeper decrease for electron conduction. At 200 K, the decrease becomes steeper as thermal broadening is reduced. At 100 K a negative minimum at n = 5 × 1011 cm−2 becomes fully developed. Figure 4b shows the computed spin Hall conductivity σxy SHE in the weak disorder limit [19] (see Supplementary Section III). The parameters used for the calculations to match the experimental trends are within a factor two of those obtained by density functional theory [16, 19]. Notably, the theoretical model describes qualitatively all of the experimentally observed features, including the relative magnitude of the positive and negative extrema, their approximate width and the temperature T ∼ 200 K at which ∗ the change in sign is observed. Although the temperature dependence of RISHE is highly ∗ non-trivial, RISHE varies roughly as 1/T nearby the extrema (Inset Fig. 4a), which is also ∗ well reproduced by the calculations (Inset Fig. 4b). The tendency for saturation in RISHE at 7 low T for hole conduction, which is not observed in the model, could indicate the presence of charge puddles or other types of impurities and defects. The observation of the SGE and ISHE within the gap of WS2 , their dependence on n and the excellent agreement with theoretical expectations prove that the phenomena originate from SOI proximity effects in graphene. However, the magnitude of the SGE and ISHE and the large spin relaxation anisotropy suggest that the theoretical understanding is still incomplete and deserves further investigation. Theoretical results, which consider only intrinsic effects [19, 20], are compatible with the experimental θSHE only for weak intervalley scattering while yielding an αSGE that is at least one order of magnitude smaller than the experimental value. Furthermore, a large SHE, as observed in Fig. 2c, has been deemed incompatible with anisotropic spin relaxation (Fig. 2f). Anisotropic spin relaxation signals the presence of intervalley scattering, which effectively reduces the mass of the carriers and leads to the suppression of the SHE [17, 19]. Such discrepancies between experimental results and purely intrinsic effects suggest additional extrinsic contributions in the observed SHE and ISGE. A larger localized SOI can be mediated by localized defects, such as sulphur vacancies in WS2 , while an effective enhancement of θSHE could arise from resonant scattering as proposed for metallic adatoms [24, 32]. Our experiments therefore provide valuable insights into the physics underpinning prox- imity effects in graphene. In addition, they offer novel strategies to manipulate spin informa- tion in ultra-compact van der Waals heterostructures, which could further impact the design and performance of advanced magnetic memory technologies [8]. Indeed, in recent years the SHE and ISGE have evolved from subtle academic phenomena to effective approaches to electrically manipulate the magnetization of a ferromagnet [1, 8]. The electric-field control of the StC conversion, both in magnitude and sign, and the unprecedented efficiency thus open the door to magnetization control with 2D materials and to novel spin-logic circuits without the use of ferromagnets. Note: After completion of the current research, a work studying the spin galvanic effect using magnetization rotation in graphene-WS2 has been reported [33]. The investigation presents results showing SGE modulation at 4.2 K and large n and shows that the SGE signal persists up to room temperature. However, the SGE modulation and the SHE are not observed at room temperature. . 8 I. METHODS Device Fabrication. van der Waals graphene-WS2 heterostructures were fabricated by dry viscoelastic stamping [14]. The transfer set-up comprises an optical microscope with large working distance optical objectives (Nikon Eclipse Eclipse LV 100ND) and a three-axis micrometer stage. Graphene is obtained by mechanical exfoliating highly-oriented pyrolytic graphite (SPI Supplies) onto a p-doped Si/SiO2 substrate. Large-area monolayer graphene is selected by optical contrast after a previous calibration with Raman spectroscopy. To fabricate the van der Waals heterostruc- ture, WS2 flakes are transferred onto a viscoelastic stamp (Gelpack), which is then transferred on top of the graphene target. After assembling, the stacks are annealed for 1 hour at 500 ◦ C in high vacuum (10−8 Torr). The heterostructure is coated with a PMMA resin mask and patterned into a Hall cross bar using electron-beam lithography followed by oxygen plasma etching [34]. The resin is then removed with acetone. The contact electrodes are defined in two electron-beam lithography steps, one for the normal metal electrodes, Ti(1nm)-Pd(50nm) and the other for the ferromagnets, TiOx /Co(30nm). The contact materials are deposited by electron-beam evaporation in a chamber with base pressure of 10−8 Torr. The TiOx barriers are fabricated by evaporating 4 Å + 4 Å of Ti and 30 min oxidation after each evaporation in an oxygen atmosphere of about 10−1 Torr. Electrical characterization. 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This research was partially supported by the European Union’s Horizon 2020 research and innovation programme Graphene Flagship CORE 2, under grant agreement No. 785219, by the European Research Council under Grant Agreement No. 306652 SPINBOUND, by the Spanish Ministry of Economy and Competi- tiveness, MINECO (under Contracts FIS2015-62641-ERC, MAT2016-75952-R, and SEV-2017-0706 Severo Ochoa), and by the CERCA Programme and the Secretariat for Universities and Research, Knowledge Department of the Generalitat de Catalunya 2017 SGR 827. M.T. acknowledges sup- port from the European Unions Horizon 2020 research and innovation programme under the Marie 12 Sklodoswa-Curie grant agreement N 665919. Author contributions L.A.B. and S.O.V. designed the device and L.A.B. and J.F.S. fabricated it. The measurements were performed by L.A.B. and W.S.T. with the participation of J.F.S. The experimental set-up was implemented by M.T. and M.V.C., who also helped with the measure- ments. J.H.G. and S.R. carried out the SHE quantum simulations. L.A.B., W.S.T. and S.O.V analyzed the data and wrote the manuscript. All authors contributed to the study, discussed the results and commented on the manuscript. S.O.V. supervised the work. 13 ek a b d ky M1 Bz TMDC ky kx kx E graphene e c E3 E1 M1 E M1 F1 I F3 z Bx F1 x - Vnl + y Vnl E4 E2 F2 FIG. 1. Spin-to-charge conversion in graphene by proximity of a TMDC and measure- ment scheme. a, Left: Spin-split bands with opposite spin helicity for graphene-TMDC (blue and purple). The black arrows represent the out-of-plane spin component. Right: Illustration of a microscopic picture of the ISGE. Spin texture for one of the bands developing a non-equilibrium spin density (blue arrow) in an applied electric field E. The opposite helical spin texture with lower Fermi wave vector, and smaller contribution to the spin density, is not drawn for clarity. b, Schematics illustrating the basic concepts of the measurement approach. The main elements of the device include a graphene Hall cross with a TMDC strip over one of the arms and a ferromagnet (F1) contacting the other. A current I generated by an electric field E in ŷ, along graphene-TMDC, induces a non-equilibrium spin density due to the ISGE with spins along x̂ (blue arrow, see a). Spin accumulation with spins out of plane (along ẑ) are generated by the SHE with opposite orientation at opposite edges of the graphene-TMDC (red arrows). The induced spins diffuse in graphene towards F1 and are detected by measuring VnlF = Vnl+ − Vnl− . At zero magnetic field VnlF = 0, as the ISGE and SHE spins are perpendicular to the F1 magnetization M1 . c, Optical image of a device with TMDC = WS2 . Besides F1 and the Hall cross, the device comprises additional ferromagnetic electrodes (F2, F3) and contacts to graphene (E1, E2) and the WS2 (E3, E4). d, ISGE detection. A magnetic field Bz induces spin precession on the ISGE generated spins (blue arrow), leading to a component along M1 and Vnl 6= 0. The SHE spins (red arrow) do not contribute to Vnl as they are parallel to Bz and do not precess. e, SHE detection. Similar to d, a magnetic field Bx induces spin precession on the SHE generated spins leading to Vnl 6= 0. The ISGE spins do not precess and do not contribute to Vnl . 14 a 6 c 8 + 1.3 V RISHE(mW) +1.2V 6 4 +1V I(nA) T 5 4 0V Vg 2 2 -1.3V 0 0 -0.1 0.0 0.1 RISHE(mW) Bx (T) -20 0 20 40 Vg(V) 0 b 15 R (kW) T Vg T = 300 K 10 -5 Vg = -10 V 5 -20 0 20 40 -0.1 0.0 0.1 Vg (V) Bx (T) e d 2 1 T = 300 K rnl(W) 0 1 Vg = -3 V -1 RSGE (mW) -0.4 -0.2 0.0 0.2 0.4 0 Bx (T) Bz (T) f 0 -0.1 0.0 0.1 -1 11 rnl (W) RSGE(mW) -5 10 -2 9 -10 -0.1 0.0 0.1 -0.1 0.0 0.1 Bx (T) Bz (T) FIG. 2. Sample characterization and spin-to-charge conversion measurements. a, Trans- fer characteristics Ids versus Vg for different bias voltage Vds in graphene-WS2 ; VgT indicates the back-gate voltage at which Ids is first observed. b, Resistance R vs. Vg along graphene-WS2 . The charge neutrality point is located at Vg ≈ −10 V, well below VgT . c, Representative room- ↓,↑ temperature non-local measurements in the ISHE configuration. Inset: Rnl vs. Bx for M1 an- ↑ ↓ tiparallel (↓, open symbols) and parallel (↑, solid symbols) to ŷ. Main panel: RISHE = (Rnl − Rnl ). d, As in c in the SGE measurement configuration. e, Spin injection and detection using F1 and F3 vs Bx (see Fig. 1c and Supplementary Fig. 1) for antiparallel (open symbols) and parallel (solid symbols) configuration of the electrodes magnetizations. f, As in e using F1 and F2. The signal becomes larger when Bx 6= 0 than at Bx = 0, indicating a large spin relaxation anisotropy in graphene-WS2 with long spin lifetimes out of the graphene plane. Solid lines in c, d and f are fittings to the solution of the anisotropic spin diffusion equations. Measurements in a, b, e and f are performed at 200 K. 15 6 a 9 Vg= -3 V b 1 M1x/M1 8 300 K 15 * 0 RSGE 4 7 -1 RISHE, RSGE(mW) RISHE+SGE(mW) 10 R (kW) 5 2 * * RISHE Vg= -10 V 0 * 2 0 2 5 M1x/M1 1 0 0 -1 -2 Vg= -13 V -2 0 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 -30 -20 -10 0 10 Bx(T) Vg(V) FIG. 3. Gate control of the inverse spin Hall and spin galvanic effects at room tem- perature. a, Nonlocal resistance Rnl vs Bx at selected Vg showing the ISHE precession response at low magnetic fields and the step feature associated to the SGE. The latter is observed when the magnetic field is large enough to rotate M1 and generate a component along x̂, M1x . The normalized M1x (sine of the rotation angle) is extracted from spin precession measurements as in Fig. 2e [26] and represented with green lines. b, Spin-to-charge conversion for the ISHE (red) and the SGE (blue) as a function of Vg . The corresponding conversion efficiencies are quantified with ∗ RISHE ∗ and RSGE as defined in a. R vs. Vg is shown for comparison (black line). 16 a 10 10 R ISHE(mW) 300 K 11 -2 -0.5 x 10 cm 200 K 100 K 0 * RISHE(mW) 11 -2 2.0 x 10 cm 5 0.005 0.010 -1 1/T (K ) * 0 -5 b sxy(10 e /h) 10 -2 5 -1.05 x 10 cm 0.04 300 K 2 200 K -2 100 K 0 z 10 -2 1.9 x 10 cm sxy (e /h) 0.02 0.005 0.010 2 -1 1/T (K ) z 0.00 -1.0 -0.5 0.0 0.5 1.0 12 -2 n (10 cm ) ∗ FIG. 4. Temperature dependence of the SHE spin-to-charge conversion. a, RISHE vs. z in the weak disorder carrier density n at the specified temperatures. b, spin Hall conductivity σxy ∗ limit using realistic parameters. The insets in a and b show the temperature dependence of RISHE z (b) for n at the extrema positions. (a) and σxy 17 View publication stats