Abstract
Experimental control of local spincharge interconversion is of primary interest for spintronics. Van der Waals (vdW) heterostructures combining graphene with a strongly spinorbit coupled twodimensional (2D) material enable such functionality by design. Electric spin valve experiments have thus far provided global information on such devices, while leaving the local interplay between symmetry breaking, charge flow across the heterointerface and aspects of topology unexplored. Here, we probe the gatetunable local spin polarisation in currentdriven graphene/WTe_{2} heterostructures through magnetooptical Kerr microscopy. Even for a nominal inplane transport, substantial outofplane spin accumulation is induced by a corresponding outofplane current flow. We present a theoretical model which fully explains the gate and biasdependent onset and spatial distribution of the intense Kerr signal as a result of a nonlinear anomalous Hall effect in the heterostructure, which is enabled by its reduced point group symmetry. Our findings unravel the potential of 2D heterostructure engineering for harnessing topological phenomena for spintronics, and constitute an important step toward nanoscale, electrical spin control.
Introduction
The field of spintronics has experienced a major leap forward by the recent advent of highquality devices comprised of layered twodimensional (2D) materials^{1,2}. This advancement is enabled by several unique advantages of the 2D materials platform. First, the vast library of van der Waals (vdW) materials readily provides several candidates for efficiently generating currentdriven spin polarisations, such as topological insulators with their spinmomentumlocked surface states or Weyl semimetals with their spinpolarised Fermi arc surface states^{3,4,5}. Moreover, atomically thin, layered magnets exhibit pronounced magnetic anisotropy and the possibility to control the magnetism by electric fields, thus enabling new spin generation or readout schemes^{6}. Combining such individual components into vdW heterostructures^{7} allows to further tailor the spintronic functionality through spinorbit coupling (SOC), proximity exchange, or spinorbit torques^{8,9,10,11,12}. VdW stacks also appear to be closetoideal platforms for the implementation of magnetisation switching through symmetry, in analogy to recent experiments on thin film heterostructures^{13}. Ultimately, by complementing interface design with external control via gate fields^{14}, the electronic properties can be manipulated ondemand, enabling for example switchable spin textures or topological band properties. Such type of devices are for example promising to emulate the functions of neurons and synapses, potentially paving the way for lowpower logic and data processing beyond CMOS electronics^{15,16}.
Gatetunable spincharge interconversion as a cornerstone of spinelectronics can be achieved by combining graphene and a strong SOC 2D material serving as a spin transport channel and as spin generator, respectively^{2,10}. This functionality has been demonstrated experimentally for vdW heterostructures incorporating a 3D topological insulator^{17}, a trivial or topological 2D semimetal^{18,19,20}, or a 2D semiconductor^{21,22,23,24,25}. Generally, the electrically detected spinsignals can persist up to room temperature, which is highly desirable for applications^{17,18,20,21,22,25,26}. Despite this progress, however, another relevant aspect of vdWbased heterostructures, namely their topologyrelated spintronic potential, most prominently via intrinsic Berry curvature (BC)mediated mechanisms, has remained largely unexplored. BC imparts an effective magnetic field in momentum space, while deforming the electron motion in real space, thus leading to exotic transport properties like various Hall effects^{27}. Moreover, the dipole component of the BC becomes relevant in the presence of inversion asymmetry, which can be exploited for, e.g., nonlinear optoelectronic transport^{28}. Importantly, this may be associated with substantial, local spin polarisation effects, whose investigation requires suitable readout techniques of high spatial resolution^{29}.
Here, we use Kerr rotation (KR) microscopy to detect, with submicrometre resolution, possible signatures of currentinduced spin polarisation in graphene/WTe_{2} heterostructures as a function of gate voltage. In these devices, the graphene component allows for current injection into the adjacent WTe_{2} in a manner not achievable by conventional metal contacts. Our theoretical analysis, taking into account the independently determined charge current flow in the heterostructure, reveals that the inherent symmetry breaking due to the presence of graphene at the heterointerface is crucial for explaining the observed phenomena.
Results
Basic device characterisation
The device in Fig. 1a consists of an ~20 nm thick WTe_{2} ribbon interfaced to a singlelayer graphene stripe beneath, such that the two long axes form an angle close to 90°. The long (short) axis of the WTe_{2} crystal corresponds to its aaxis (baxis), as confirmed by polarisationresolved Raman spectroscopy (Supplementary Fig. S1). The caxis points outofplane. The overlay in Fig. 1a is a currentinduced KR map, with the red and blue areas representing KR signals of opposite sign. Generally, KR spectroscopy detects the offdiagonal elements of the refractive index, i.e. the difference in the refractive indices for circularly lefthanded and righthanded photons, via a corresponding polarisation rotation of the reflected light. The polar configuration (normal incidence) used in our experiments probes the inplane Hall tensor, which is typically associated with a corresponding outofplane magnetisation (or spin polarisation) as discussed later in detail. While KR microscopy has thus far mainly been used to detect magnetic phase transitions in 2D materials under equilibrium conditions, we investigate here the KR signal generated under electrical current flow in a vdW heterostructure. For the currentinduced KR microscopy, an AC current at frequency ω (on the order of kHz) is passed along the graphene stripe between the contacts labelled 1 and 3 (i.e., parallel to the baxis of WTe_{2}), all other contacts are floating. The gate voltage V_{g} is applied to the silicon substrate with respect to contact 3, which serves as the voltage reference (ground). All measurements were conducted at a bath temperature of 4.2 K. The currentinduced outofplane spin polarisation (aligned with the caxis) is then locally resolved via the KR angle \({\theta }_{K}^{\omega }\) detected at the fundamental frequency ω of the alternating bias (Fig. 1b). The sign (or direction) of the KR is then related to the sign (or direction) of the local magnetisation. It should be noted that the present KR signals cannot be accounted for by the nonlinear anomalous Hall effect (AHE) previously reported for WTe_{2}^{30,31}. In the latter case, crystal symmetry is reduced due to the quasi2D character of the fewlayer sheets, which leads to a currentinduced outofplane magnetisation perpendicular to the charge current direction^{32}.
In Fig. 1c, transfer curves of the graphene stripe within the above device are shown for increasing AC bias up to \({V}_{{{{13}}}}^{\omega }=1.5\,{{{{{\rm{V}}}}}}\). At low AC bias amplitudes, two resistance maxima corresponding to two Dirac points are visible, pointing towards the presence of graphene regions with different doping levels^{33}. The Dirac point at gate voltage V_{g} ≈ 0 V can be assigned to the bare graphene leads from the metallic contacts to the junction. The second Dirac point at V_{g} ≈ 20 V indicates moderate pdoping and is attributable to the graphene section proximitized by WTe_{2}. With increasing AC bias amplitude, the resistance maximum associated with the Dirac point at the heterojunction progressively decreases and finally vanishes. The latter suggests a change of the current path: at large bias, the adjacent WTe_{2} opens a parallel current path and shunts the proximitized graphene, with a vertical current flow from graphene to the WTe_{2} upon entering the junction region (and analogously backwards to graphene close to the opposite junction edge).
Local heat dissipation and current flow
To further corroborate such a nontrivial current distribution in our heterostructure, we utilised our polarisation sensitive Kerr detection scheme. We applied an alternating sourcedrain voltage with a frequency of ω = 3.33 kHz and monitored the polarisation rotation of the reflected light at the second harmonic 2ω of the sourcedrain frequency by a lockin measurement. Previous experiments on metals have shown that the polarisation rotation \({\theta }_{K}^{2\omega }\) at modulation frequency 2ω can capture the effect of Joule heating on the optical reflectivity^{34} and, therefore, the spatial dependence of heat dissipation due to the local currents and resistances in the device structure. For WTe_{2}, a 2ω modulation can be understood by the temperaturedependent variation of the refractive indices along the different crystal axes, i.e., it probes the birefringence. Figure 2 shows spatial maps of \({\theta }_{K}^{2\omega }\) around the WTe_{2}/graphene heterointerface, which were obtained in four different bias configurations. For sourcedrain bias applied vertically across the junction, the maximum signal is always located along the direction of current flow, i.e., either to the right (contacts 2 and 3 are connected, Fig. 2a) or the left (contacts 2 and 1 are connected, Fig. 2b) towards the corresponding electrical contact on graphene. The signals scale approximately quadratically with the applied AC current amplitude, as expected for Joule heating (Supplementary Fig. S2). Thus, we conclude that the polarisation rotation demodulated at 2ω indeed reflects the local dissipation and hence the local charge current density. On this basis, the signal maxima in Fig. 2a, b can be explained by a local vertical current flow between the two layers. In comparison, for inplane biasing along the WTe_{2} channel (contacts 2 and 4 are connected, Fig. 2c), a much weaker signal occurs at the central interface, indicative of homogeneous Joule heating within the less resistive WTe_{2}. Finally, when the bias is applied along the proximitized graphene, which is nominally inplane, we detect an increased optical response from the edges (contacts 1 and 3 are connected, Fig. 2d). These two pronounced 2ω signals indicate the local outofplane current flow from graphene to WTe_{2} and vice versa.
Gatedependent Kerr microscopy
Figure 3 displays currentinduced KR maps of the above device for two gate voltage regimes. The bias current is applied along the graphene stripe between the contacts labelled 1 and 3 (cf. Fig. 1). Very similar behaviour has been observed on two other devices (Supplementary Figs. S3 and S4). At V_{g} = 30 V (ntype regime), strong KR of opposite sign appears around the two edges of the junction area (Fig. 3a). Changing the gate voltage to V_{g} = −30 V (ptype regime), reverses the KR polarity while its magnitude, location and spatial extent are barely affected (Fig. 3b). The location of the maximum KR coincides with the Joule heatinginduced 2ω signal, underscoring the connection between KR signal and current flow through the heterostructure. As elaborated later by our theoretical model, the sign change of the KR signals between Fig. 3a, b can be traced back to the sign reversal of current injection into WTe_{2}, depending on whether the underlying graphene is n or pdoped. Current is injected into WTe_{2} by momentum conserving tunnelling of electrons, while microscopically, the momentum of conduction (valence) electrons in graphene is antiparallel (parallel) to the current.
Tunnelling spectroscopy
To shine further light on the microscopic correlation between vertical charge currents and the Kerr signal, we performed interlayer transport spectroscopy (Fig. 4a) of a second device (Supplementary Fig. S3). With the sourcedrain bias applied vertically across the junction, the graphene and WTe_{2} can be regarded as planar tunnelling electrodes, possibly due to the weak coupling across the vdW gap^{35}. We added a small AC voltage onto the DC bias to measure the differential resistance \({V}_{23}^{\omega }/{I}_{12}^{\omega }\) across the heterointerface (for details see “Methods”). The bias and gate voltagedependent tunnelling resistance (Fig. 4a) features a prominent peak that linearly shifts along the diagonal from the upper left to the bottom right. It can be assigned to the Dirac point of the proximitized graphene. The diagonal shift arises due to the interplay of the applied gate voltage, which dopes the graphene, and the bias voltage, which compensates the difference between the WTe_{2} Fermi level and the proximitized Dirac point.
Intriguingly, this proximitized Dirac point appears also in a nominally lateral transport configuration with the bias current injected along the graphene stripe (contacts 1 and 3). This is apparent from Fig. 4b, displaying the local photocurrent \({I}_{13}^{{{{ph}}}}\) for an excitation at the junction (laser wavelength = 800 nm), and Fig. 4c which shows the differential KR signal \({\theta }_{K}^{\omega }/{V}_{{{{13}}}}^{\omega }\). In both maps, there is an onset at a bias voltage corresponding to the Dirac point of the proximitized graphene, akin to Fig. 4a. It is noteworthy that the linear, gateindependent background in the Kerr spectroscopy (Fig. 4c) is due to Joule heating. Overall, the gate and biasdependencies are consistent with the theoretical picture below, which relies on minority carriers in graphene.
Discussion
One plausible explanation for the currentinduced KR signals in Fig. 3 could be a linear spin Hall effect, driven by an electrical current within the WTe_{2} ribbon. However, this effect can be ruled out, as the electrical current direction, spin current direction, and spin direction must be mutually orthogonal^{36}, such that it is not possible to account for the observed KR signal at the left and right edge of the junction (cf. Fig. 1a), neither for vertical (along the caxis of WTe_{2}) nor horizontal charge current flow (along the baxis of WTe_{2}) within the ribbon. Consistently, our control experiments in bare WTe_{2} do not show detectable KR by any inplane currents (Supplementary Fig. S5). An alternative mechanism could be chargetospin conversion induced by lateral charge transport within the proximitized graphene with an inplane spin component due to a Rashbalike interaction, as well as an outofplane spin texture due to a valleyZeeman like interaction^{20}. Again, this scenario cannot explain our observations, as it would be expected to lead to a Kerr signal that is homogeneously distributed along the graphene/WTe_{2} interface, rather than being localised at the interface edges as observed by experiment.
While the above two mechanisms fail to account for the observed KR signals, we argue that a local, currentinduced magnetisation originating from an AHE^{37} is responsible for the observed phenomena. Generally, the current density in response to the fast optical probe field E_{j}(ν) is:
The antisymmetric components of the conductivity tensor σ_{ij}(ν) determine the Kerr response. Linear antisymmetric conductivity components in the unbiased system vanish due to time reversal symmetry. As the latter is effectively broken in our measurement configuration due to the slow bias field E_{l}(ω), we consider the nonlinear antisymmetrised current response:
From this equation, it follows that the combined actions of the fast optical probe field and the slow bias field lead to a nonlinear current response tensor λ_{lk}. Equation (2) is a generalisation of the nonlinear Hall response and circular photogalvanic effect at ν = −ω^{28,30,31,32,38,39,40,41,42}. By definition, this current is always transverse to the optical field E_{j}(ν). If the current direction is also perpendicular to the direction of light propagation, this will result in a Kerr angle in the reflected field. Figure 5a sketches the relevant electric fields in our measurement. The laser light is incident along z with polarisation along x and correspondingly the Hall current is along y. With this specific choice of coordinates we define the Hall conductivity σ_{H}(ω) = (σ_{xy}(ω) − σ_{yx}(ω))/2 = λ_{lz}E_{l}(ω) which is responsible for the Kerr angle θ_{K}(ω) ∝ −Re(σ_{H}(ω))^{43}.
According to the theory of the AHE^{37}, σ_{H} is proportional to the magnetisation 〈S_{z}〉 and thus effectively measured by the Kerr angle. Further to this, recent works have shown that λ_{ji} can be expressed in terms of the BC dipole tensor \({D}_{ji}^{({{\Omega }})}={\langle {{{\Omega }}}_{i}{v}_{j}\rangle }_{{{{{{{{\rm{FS}}}}}}}}}\), i.e., the Fermi surface average of the BC Ω_{j}(p) and velocity v_{i}^{32,39}.
Crucially, noncentrosymmetric materials allow for a finite BC dipole \({D}_{ji}^{({{\Omega }})}\)^{32} and \({\sigma }_{H}(\omega )\propto {D}_{jz}^{({{\Omega }})}{j}_{j}(\omega )\) can be thus induced by a charge current j_{j}(ω) inside the topological metal, leading to (see Supplementary Information for details):
This establishes a relationship between Kerr microscopy, spintronics, topological band theory, and nonreciprocal transport coefficients^{34,44,45}, which also determine the nonlinear AHE^{30,31,41,42} and photocurrents in topological metals^{28,38,40}. Consistently with Eq. (3), our control measurements show that the KR angle depends linearly on the amplitude of the quasiDC bias field (Supplementary Fig. S2), beyond a gatedependent onset voltage as discussed below. Moreover, the Kerr angle does not depend on the amplitude of the optical probe field (Supplementary Fig. S6), ruling out any higherorder effects^{46} as well as local photocurrents to be the origin of the Kerr response and corresponding spin accumulation.
While the currentinduced anomalous Hall response in the bulk of either graphene or bulk WTe_{2} vanishes due to crystalline symmetries, controllable net spincharge interconversion is enabled in the graphene/WTe_{2} heterostructures due to their reduced interface symmetry.
The symmetry group of T_{d}WTe_{2} is \({P}_{{mn{2}}_{1}}\), and it contains a 180° screw rotation about the caxis as well as a b → −b mirror symmetry. The latter is broken due to strain and the relative misalignment of the crystalline axes of WTe_{2} and graphene. This imposes λ_{xz} = λ_{yz} = 0, while λ_{zz} ≠ 0 becomes symmetry allowed resulting in j_{y}(ν + ω) = −λ_{zz}(ν, ω)E_{z}(ω)E_{x}(ν) (compare Eq. (2)).
To connect the above homogeneous Kerr response to the local current density, we model the diffusion currents in the heterostructure taking into account the experimentally observed interlayer current. Before that, we outline the modifications to diffusion theory in topological materials. From standard diffusion theory, the density n(x, t) and the regular current density j_{i}(x, t) obey:
For simplicity, the diffusion coefficient D is kept isotropic. For a Berrycurved material, we derive an additional differential equation for the BC density ϖ_{i}(x, t) (see Supplementary Information):
The total current \({j}_{i}^{({{{{{{{\rm{tot}}}}}}}})}\) is given by the regular current and the BC contribution:
The second term stems from the anomalous velocity contribution to the semiclassical equations of motion of Bloch electrons and E_{k} the local electric field. The local inplane Hall response is then given by \({\sigma }_{H}({{{{{{{\bf{x}}}}}}}})=\int\nolimits_{0}^{h}dz{\varpi }_{z}({{{{{{{\bf{x}}}}}}}})\).
We now address the mechanism of current injection into the WTe_{2} slab due to charge carrier hopping across the heterointerface in the presence of a current j_{0} in the graphene sheet. We consider momentum conserving tunnelling, such that the injected current comprises the imbalance current ∂_{x}[n_{e} + n_{h}] rather than a charge current ∂_{x}[n_{e} − n_{h}] where n_{e}, n_{h} are electron and hole densities in graphene. This follows from the fact that the velocity (i.e., current) of the same momentum in n and pdoped graphene is opposite (Fig. 5b, c).
Using the continuity equation, current injection thus enters effectively as a source term in Eq. (4b), \(D{\nabla }^{2}n={\partial }_{x}[\bar{D}{\partial }_{x}[{n}_{e}+{n}_{h}]]\delta (z)\), where \(\bar{D}\) is a constant. Furthermore, as the source term is given by the derivative of the imbalance current, it is dominated by its spatial dependence. As opposed to a transport current, the latter is determined by the relaxation profile of minority carriers. These are massively generated when the bias voltage across the proximitized region exceeds a threshold value set by the distance to the Dirac point and qualitatively explains the gatedependent minimal bias for the signal onset in Fig. 4c. Fitting this model to experimental data (Supplementary Fig. S7), yields a calculated KR response (Fig. 5d) within a single band approximation which reproduces both the onset and the sign change of the measured KR (Fig. 5e). We note that, in the gate voltage regime between the two Dirac points, the KR signal, although being rather weak, has nonzero spatial average and hence cannot be interpreted based on \({\varpi }_{z}=\tau {D}_{zz}^{({{\Omega }})}{\partial }_{z}n\propto {j}_{z}\), because the total current going into and out of the WTe_{2} must vanish by Kirchhoff’s law. We hypothesise that the weak KR stems from a higherorder nonlinear currentfield relation beyond Eq. (2).
The BC dipoleinduced Kerr signal in our heterostructure is surprisingly large. In general, the magnetooptical detection of currentinduced spins in simple metals is challenging due to the small ratio of optically probed to spinpolarised electrons^{47}, the short spin relaxation time^{48}, and their low optical activity compared to semiconductors. Nonetheless, this has been accomplished with the aid of currentmodulation techniques^{34,49}. The present KR angles \({\theta }_{K}^{\omega }\) in the mrad range are approximately six orders of magnitude larger than for metal wires under ac current injection^{34}, although the current densities are comparable (on the order of 1 × 7 A cm^{−2}). We assign the large KR directly to the pronounced symmetry breaking of the heterointerface in conjunction with the significant interlayer currents. It should furthermore be noted that even in a lockin detection scheme, it is difficult to completely eliminate spurious contributions of heating effects to the detected first harmonic signal, in close correspondence to previous Kerr microscopy studies of metallic systems^{34,47,48}. Nonetheless, that the currentinduced spin polarisation makes a significant contribution to the Kerr signal is underscored by angulardependent measurements of the Kerr signal (Supplementary Fig. S8).
In principle, the experimentally observed Kerr angles can be a direct measure of the BC dipole, which is a Fermi surface property of the electronic system in the low temperature limit. This requires a proper description of the optical conductivities and the carrier scattering times entering the Boltzmann equation. At optical frequencies, provided that the crystal is sufficiently clean and the bands are well resolved, extrinsic mechanisms related to disorder scattering become negligible, while the intrinsic BC related mechanisms are dominant^{39}. Indeed, for resonant optical interband excitation in 2D semiconductors, such as MoS_{2}, simple twoband models have been successfully applied to describe a straininduced BC dipole and a corresponding valley magnetisation^{50}. Here, for the particular case of semimetallic WTe_{2}, the situation at optical frequencies is more complicated, because many possible interband transitions exist^{51}. From this point of view a THz to farIR readout would be appealing. In this range, the response of the electronic system is dominated by the intraband Drude terms and for ωτ ≫ 1 the nonlinear Hall conductivity, and also the Kerr effect, becomes independent of the scattering time and a direct probe of the BC dipole^{32,39}. However, this would be achieved at the cost of sacrificing spatial resolution, for the case of an optical farfield readout.
Finally, we would like to underscore the great potential of imaging the local heat dissipation in the 2D heterostructures by applying the same polarisation sensitive detection scheme at different harmonics of the excitation frequency. Such imaging provides highly valuable insights into the local current flow and, in the present study, revealed an unexpected interlayer exchange current flow even for nominally inplane transport in the graphene/WTe_{2} heterostructure. For utilising 2D heterostructures in spintronic applications, the demonstrated knowledge of the local charge as well as spin current distribution is crucial. Considering observed spin diffusion lengths on the order of 10 μm in bare graphene^{10} and 2 μm in MoTe_{2}^{3}, farfield optical probes can indeed access physically and technologically relevant length scales via local and nonlocal optoelectronic readout schemes^{40,52}. Our generic model devised for the currentinduced spin polarisation merges classical diffusion theory with topology and it should be applicable to other 2D materials and their heterostructures where BC plays a crucial role, such as transition metal dichalcogenides or nodal line semimetals^{41,53}.
In summary, using magnetooptic Kerr microscopy we have demonstrated that a nominal inplane electrical current flowing in a graphene/WTe_{2} heterostructure induces a pronounced nonequilibrium spin density with outofplane orientation in the WTe_{2} layer. The spin polarisation profile is asymmetric along the current injection direction and depends on the dominant type of charge carriers. It is attributed to an outofplane current flowing from graphene to WTe_{2}, with the tunnelling electrons experiencing the nonzero BC dipole of the heterostructure, enabled by breaking of centrosymmetry at the heterointerface. Our theoretical model traces back the observed Kerr signals to a nonlinear Hall effect in the heterostructure, combined with a topologicallymodified diffusion theory. Overall, our measurements provide a valuable basis for implementing tunable topological electronics and local control of spin polarisation in 2D vdW heterostructures, and complement electrical detection schemes for inplane spins towards probing outofplane spins in vdW heterostructures.
Methods
Fabrication of graphene/WTe_{2} heterostructure devices
The samples were prepared using an alldry viscoelastic transfer method. Singlelayer graphene was mechanically exfoliated from natural graphite flakes (NGS Trading & Consulting GmbH, Germany) onto a Si/SiO_{2} wafer. Subsequently, bulk crystals of WTe_{2} (hq graphene, The Netherlands) were mechanically cleaved and exfoliated onto a PDMS stamp. Crystals with high aspect ratios, indicative of preferential cleavage along the a and bcrystal axes, and a thickness of 15–25 nm were identified by optical contrast and transferred from the stamp onto the graphene monolayer. All steps were performed under ambient.
Magnetooptic Kerr measurements
The magnetooptic Kerr measurements were carried out using a confocal dipstick microscope with a sample bath temperature of 4.2 K (Supplementary Fig. S9). A linearly polarised cwlaser at λ_{laser} = 800 nm was focused onto the sample with a diffractionlimited spot size of ~800 nm and a laser power of 50 μW. The reflected beam was guided through a 50:50 beamsplitter, a halfwave plate, a Wollaston beamsplitter, and detected by an amplified balanced photodetector. An alternating bias current with a frequency of ω = 3.33 kHz was applied to the sample, the polarisation change detected by the balanced photodetectors was readout using a lockin amplifier simultaneously at the fundamental (ω) and the second harmonic (2ω) frequency. Spatiallyresolved scanning was performed by moving the sample using a xypiezo scanner.
Tunnelling and local photocurrent measurements
The vertical charge transport experiments on the graphene/WTe_{2} heterojunction were carried out using a gatedependent fourprobe differential conductivity measurement at T_{bath} = 4.2 K using standard lockin detection. A DC voltage, to which a small AC amplitude (1 mV at 77 Hz) was added, was applied to the graphene/WTe_{2} junction contacts. The resulting ac voltage was measured at the opposing graphene/WTe_{2} contacts. The gate voltage was applied to the Siback gate using a source/measure unit.
Data availability
All data needed to evaluate the conclusions in the paper are present in the paper and the Supplementary Information.
References
Lin, X., Yang, W., Wang, K. L. & Zhao, W. Twodimensional spintronics for lowpower electronics. Nat. Electron. 2, 274–283 (2019).
Ahn, E. C. 2D materials for spintronic devices. Npj 2D Mater. Appl. 4, 17 (2020).
Song, P. et al. Coexistence of large conventional and planar spin Hall effect with long spin diffusion length in a lowsymmetry semimetal at room temperature. Nat. Mater. 19, 292–298 (2020).
Vaklinova, K., Hoyer, A., Burghard, M. & Kern, K. Currentinduced spin polarization in topological insulator–graphene heterostructures. Nano Lett. 16, 2595–2602 (2016).
Dankert, A., Geurs, J., Kamalakar, M. V., Charpentier, S. & Dash, S. P. Room temperature electrical detection of spin polarized currents in topological insulators. Nano Lett. 15, 7976–7981 (2015).
Huang, B. et al. Electrical control of 2D magnetism in bilayer CrI_{3}. Nat. Nanotechnol. 13, 544–548 (2018).
Novoselov, K., Mishchenko, A., Carvalho, A. & Neto, A. C. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).
Gmitra, M. & Fabian, J. Graphene on transitionmetal dichalcogenides: a platform for proximity spinorbit physics and optospintronics. Phys. Rev. B 92, 155403 (2015).
Žutić, I., MatosAbiague, A., Scharf, B., Dery, H. & Belashchenko, K. Proximitized materials. Mater. Today 22, 85–107 (2019).
Avsar, A. et al. Colloquium: spintronics in graphene and other twodimensional materials. Rev. Mod. Phys. 92, 021003 (2020).
Offidani, M., Milletarì, M., Raimondi, R. & Ferreira, A. Optimal chargetospin conversion in graphene on transitionmetal dichalcogenides. Phys. Rev. Lett. 119, 196801 (2017).
Dolui, K. et al. Proximity spinorbit torque on a twodimensional magnet within van der Waals heterostructure: currentdriven antiferromagnettoferromagnet reversible nonequilibrium phase transition in bilayer CrI_{3}. Nano Lett. 20, 2288–2295 (2020).
Liu, L. et al. Symmetrydependent fieldfree switching of perpendicular magnetization. Nat. Nanotechnol. 16, 277–282 (2021).
Island, J. O. et al. Spinorbitdriven band inversion in bilayer graphene by the van der Waals proximity effect. Nature 571, 85–89 (2019).
Grollier, J. et al. Neuromorphic spintronics. Nat. Electron. 3, 360–370 (2020).
Vedmedenko, E. Y. et al. The 2020 magnetism roadmap. J. Phys. D Appl. Phys. 53, 453001 (2020).
Khokhriakov, D., Hoque, A. M., Karpiak, B. & Dash, S. P. Gatetunable spingalvanic effect in graphenetopological insulator van der Waals heterostructures at room temperature. Nat. Commun. 11, 3657 (2020).
Zhao, B. et al. Observation of charge to spin conversion in Weyl semimetal WTe_{2} at room temperature. Phys. Rev. Res. 2, 013286 (2020).
Safeer, C. et al. Large multidirectional spintocharge conversion in lowsymmetry semimetal MoTe_{2} at room temperature. Nano Lett. 19, 8758–8766 (2019).
Hoque, A. M., Khokhriakov, D., Karpiak, B. & Dash, S. P. Chargespin conversion in layered semimetal TaTe_{2} and spin injection in van der Waals heterostructures. Phys. Rev. Res. 2, 033204 (2020).
Li, L. et al. Gatetunable reversible RashbaEdelstein effect in a fewlayer graphene/2HTaS_{2} heterostructure at room temperature. ACS Nano 14, 5251–5259 (2020).
Ghiasi, T. S., Kaverzin, A. A., Blah, P. J. & van Wees, B. J. Chargetospin conversion by the RashbaEdelstein effect in twodimensional van der Waals heterostructures up to room temperature. Nano Lett. 19, 5959–5966 (2019).
Safeer, C. et al. Roomtemperature spin Hall effect in graphene/MoS_{2} van der Waals heterostructures. Nano Lett. 19, 1074–1082 (2019).
Ghiasi, T. S., InglaAynés, J., Kaverzin, A. A. & van Wees, B. J. Large proximityinduced spin lifetime anisotropy in transitionmetal dichalcogenide/graphene heterostructures. Nano Lett. 17, 7528–7532 (2017).
KovácsKrausz, Z. et al. Electrically controlled spin injection from giant Rashba spinorbit conductor BiTeBr. Nano Lett. 20, 4782–4791 (2020).
Benítez, L. A. et al. Tunable roomtemperature spin galvanic and spin Hall effects in van der Waals heterostructures. Nat. Mater. 19, 170–175 (2020).
Sundaram, G. & Niu, Q. Wavepacket dynamics in slowly perturbed crystals: gradient corrections and Berryphase effects. Phys. Rev. B 59, 14915–14925 (1999).
Xu, S.Y. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe_{2}. Nat. Phys. 14, 900–906 (2018).
Fujita, T., Jalil, M., Tan, S. & Murakami, S. Gauge fields in spintronics. J. Appl. Phys. 110, 17 (2011).
Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in fewlayer WTe_{2}. Nat. Mater. 18, 324–328 (2019).
Ma, Q. et al. Observation of the nonlinear Hall effect under timereversalsymmetric conditions. Nature 565, 337–342 (2019).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in timereversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
SolísFernández, P., Okada, S., Sato, T., Tsuji, M. & Ago, H. Gatetunable Dirac point of molecular doped graphene. ACS Nano 10, 2930–2939 (2016).
Stamm, C. et al. Magnetooptical detection of the spin Hall effect in Pt and W thin films. Phys. Rev. Lett. 119, 087203 (2017).
Steinberg, H. et al. Tunneling in graphenetopological insulator hybrid devices. Phys. Rev. B 92, 241409 (2015).
Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. & Jungwirth, T. Spin hall effects. Rev. Mod. Phys. 87, 1213 (2015).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).
Wang, Q. et al. Robust edge photocurrent response on layered type II Weyl semimetal WTe_{2}. Nat. Commun. 10, 5736 (2019).
König, E. J., Dzero, M., Levchenko, A. & Pesin, D. A. Gyrotropic Hall effect in Berrycurved materials. Phys. Rev. B 99, 155404 (2019).
Kiemle, J., Zimmermann, P., Holleitner, A. & Kastl, C. Lightfield and spinorbitdriven currents in van der Waals materials. Nanophotonics 9, 2693–2708 (2020).
Culcer, D., Keser, A. C., Li, Y. & Tkachov, G. Transport in twodimensional topological materials: recent developments in experiment and theory. 2D Mater. 7, 022007 (2020).
Ho, S.C. et al. Hall effects in artificially corrugated bilayer graphene without breaking timereversal symmetry. Nat. Electron. 4, 116–125 (2021).
White, R. M & Geballe, T. H. Long Range Order in Solids: Solid State Physics. Chapter VIII D (Academic Press: 1979).
Tokura, Y. & Nagaosa, N. Nonreciprocal responses from noncentrosymmetric quantum materials. Nat. Commun. 9, 3740 (2018).
Lee, J., Wang, Z., Xie, H., Mak, K. F. & Shan, J. Valley magnetoelectricity in singlelayer MoS_{2}. Nat. Mater. 16, 887–891 (2017).
Choi, Y.G., Doan, M.H., Kim, Y. & Choi, G.M. Nonlinear optical Hall effect in weyl semimetal WTe_{2}. Preprint at https://doi.org/10.48550/arXiv.2103.08173 (2021).
Riego, P. et al. Absence of detectable currentinduced magnetooptical Kerr effects in Pt, Ta, and W. Appl. Phys. Lett. 109, 172402 (2016).
Su, Y. et al. Absence of detectable MOKE signals from spin Hall effect in metals. Appl. Phys. Lett. 110, 042401 (2017).
Puebla, J. et al. Direct optical observation of spin accumulation at nonmagnetic metal/oxide interface. Appl. Phys. Lett. 111, 092402 (2017).
Son, J., Kim, K.H., Ahn, Y. H., Lee, H.W. & Lee, J. Strain engineering of the berry curvature dipole and valley magnetization in monolayer MoS_{2}. Phys. Rev. Lett. 123, 036806 (2019).
Homes, C., Ali, M. & Cava, R. J. Optical properties of the perfectly compensated semimetal WTe_{2}. Phys. Rev. B 92, 161109 (2015).
Seifert, P. et al. Inplane anisotropy of the photonhelicity induced linear Hall effect in fewlayer WTe_{2}. Phys. Rev. B 99, 161403(R) (2019).
Singh, A., Ghosh, S. & Agarwal, A. Nonlinear and anisotropic polarization rotation in twodimensional Dirac materials. Phys. Rev. B 97, 205420 (2018).
Acknowledgements
Experimental work at TUM was supported by Deutsche Forschungsgemeinschaft (DFG) through the German Excellence Strategy via the Munich Center for Quantum Science and Technology (MCQST)—EXC2111390814868, SPP2244 “2D Materials—Physics of van der Waals [hetero]structures” via Grant KA 5418/11, HO 3324/121, HO 3324/131, and the excellence cluster “econversion”. C.K. acknowledges support through TUM International Graduate School of Science and Engineering (IGSSE). Experimental work at MPI was supported by Deutsche Forschungsgemeinschaft (DFG) through SPP2244 “2D Materials—Physics of van der Waals [hetero]structures” via Grant BU 1125/121 and the DFG Grant “Weyl fermionbased spin current generation” BU 1125/111. We acknowledge technical support by T. Reindl, A. Güth, U. Waizmann, M. Hagel and J. Weis from the Nanostructuring Lab of the Max Planck Institute for Solid State Research.
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J.Ki. and L.P. contributed equally and are both first authors. M.B., A.H., and C.K. conceived and designed the experiments. L.P. fabricated the heterostructures. J.Ki. and L.P. performed the optoelectronic measurements. J.Ki., L.P., and C.K. analysed the data. E.J.K. developed the theoretical analysis and wrote the theory section with input from A.P.S. and J.K. All authors cowrote and reviewed the manuscript.
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Powalla, L., Kiemle, J., König, E.J. et al. Berry curvatureinduced local spin polarisation in gated graphene/WTe_{2} heterostructures. Nat Commun 13, 3152 (2022). https://doi.org/10.1038/s41467022307443
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DOI: https://doi.org/10.1038/s41467022307443
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