Observation of Spin Hall Effect in Weyl Semimetal WTe2 at Room Temperature

Discovery of topological Weyl semimetals has revealed the opportunities to realize several extraordinary physical phenomena in condensed matter physics. Specifically, these semimetals with strong spin-orbit coupling, broken inversion symmetry and novel spin texture are predicted to exhibit a large spin Hall effect that can efficiently convert the charge current to a spin current. Here we report the direct experimental observation of a large spin Hall and inverse spin Hall effects in Weyl semimetal WTe2 at room temperature obeying Onsager reciprocity relation. We demonstrate the detection of the pure spin current generated by spin Hall phenomenon in WTe2 by making van der Waals heterostructures with graphene, taking advantage of its long spin coherence length and spin transmission at the heterostructure interface. These experimental findings well supported by ab initio calculations show a large charge-spin conversion efficiency in WTe2; which can pave the way for utilization of spin-orbit induced phenomena in spintronic memory and logic circuit architectures.


Main
A strong resurgence of interest in two-dimensional (2D) transition metal dichalcogenide (TMD) is sparked with the successful preparation of materials with different properties that have the potential to revolutionize the future of electronics 1,2 . While semiconducting TMDs brings enormous interest in transistors [3][4][5][6] and optoelectronic applications 7 ; the semimetals are predicted to host novel topological electronic states [8][9][10] . The recently predicted type-II Weyl semimetals [10][11][12] such as WTe2 shows extraordinary electronic phenomena, likea giant magnetoresistance 13 , high mobilities 14 , chiral anomaly 15 and anomalous Hall effect 16 . These novel transport features indicate the existence of Weyl fermionic states, which are characterized by a tilted linear dispersion of Weyl cones and Fermi arc surface states. Due to the monopole-like Berry curvature in the momentum space, strong spin-orbit interaction, a unique spin texture in Weyl cones and Fermi arc surface states are predicted to exist [17][18][19] . In addition to the topological Weyl features in these semimetals, trivial spin-polarized Fermi arc surface states are also shown to exists at the Fermi level between the electron and the hole pockets at room temperature [20][21][22][23][24][25][26] . Taking advantage of these properties, recent experiments with WTe2/ferromagnet bilayers showed a control of spin-orbit torque arising from its crystal symmetry 27,28 .
Therefore, these 2D semimetals are considered to have a huge potential for ultra-low power spintronic devices 29 with an efficient conversion of charge-to-spin current, i.e. a large spin Hall effect (SHE) and (or) Rashba Edelstein effect (REE) at room temperature 30 , however, it has not been yet experimentally measured.
Here, we report an observation of a large spin Hall effect (SHE) in semimetal WTe2 devices at room temperature. We electrically detect the SHE signals by employing a van der Waals heterostructure device of WTe2 and graphene, taking advantage of 2D layered structures of both classes of the materials. In these experiments, we exploit the best of both the worlds, such as a large spin Hall angle of WTe2, along with a long spin coherence length in graphene and an efficient spin transfer at the WTe2-graphene interface. The large charge-spin conversion signal stems mainly from bulk SHE of WTe2 and possibly REE from the WT2 surface states. Our detailed spin sensitive electronic measurements both in the in-plane and perpendicular geometries, its angle and gate dependent studies, and theoretical calculations manifest the existence of the large spin Hall phenomena in WTe2 devices at room temperature.   The left and right parts of the Fermi surface and spin texture can be transformed into each other by a mirror reflection (kx to -kx). Such as strong spin-momentum locking feature indicates that the charge current comes together with a spin current, like SHE and REE. We experimentally investigated the influence of the spin degree of freedom on the charge currents and vice versa due to the presence of strong SOC, broken inversion symmetry and the novel spin textures in WTe2. The SHE in WTe2 is expected to cause a transverse spin current induced by a charge current, whereas, the inverse SHE (ISHE) produces a transverse charge current that is caused by a pure spin current 31,32 . Figure  1c,d show the nanofabricated devices consisting of van der Waals heterostructures of WTe2 with fewlayer graphene having ferromagnetic tunnel contacts to detect the SHE and ISHE in a spin sensitive potentiometric measurement (see Methods for details about the fabrication process). The heterostructure of graphene with WTe2 flakes of 11-30 nm in thickness was used (from Hq Graphene), as measured by the atomic force microscope (AFM) (Supplementary Fig. S1). The quality of the WTe2 was characterized by Raman spectrometer, showing peaks corresponding to the Td-phase ( Supplementary Fig. S2).   Supplementary Fig. S3a). The application of longitudinal charge current (I) in WTe2 produces a pure transverse spin current due to SHE, which is injected into the graphene at the interface and subsequently detected as a voltage signal (VSHE) by the non-local ferromagnetic Co tunnel contacts. The direction of the injected spins is in the plane of the graphene and perpendicular to the ferromagnet electrodes. The magnetic field Bx is applied perpendicular to the electrodes for changing the magnetization direction of Co from 90˚ to 0˚ with respect to the injected spins. Figure 2b shows the measured SHE data of RSHE=VSHE/I for I=60 µA at room temperature for a Bx sweep for Dev 1 with graphene channel length LSHE=2.6μm. As expected, RSHE follows a linear dependence at low B field, due to sin(θ) dependence of the ferromagnetic moments rotation angle θ with the Co electrodes, whereas at large enough B field, the magnetization of Co rotates 90˚ and become parallel to B field and also the injected spin directions, resulting in the saturation of RSHE.

Figure 2. Electrical detection of spin Hall effect and Inverse spin Hall effect in
Next, we performed the ISHE experiment, where a pure spin current is injected from the ferromagnet and absorbed by the WTe2. The spin current at the WTe2-graphene interface should give rise to a transversal charge voltage (VISHE) due to the ISHE (Fig. 2a). Figure 2b shows the measured ISHE data of RISHE=VISHE/I for I=60 µA at room temperature with sin(θ) behavior for a Bx field sweep. These observed features confirm that the measured signal arises from spin to charge conversion in WTe2.
According to our measurement geometry and the SHE signal ( Fig.2a and 2b), the spin hall angle is positive based on Is ∝ s× Ic 33 . This is confirmed by a bias current polarity dependence of the (I)SHE signals ( Supplementary Fig. S5). Both the signals RSHE and RISHE saturate with the magnetization of the injector/detector ferromagnetic Co electrode, as verified from the spin precession Hanle measurements with Bx field in graphene channels (see Supplementary Fig. S7). The observed comparable SHE and ISHE signal magnitudes, their line shapes with magnetic field sweeps are in agreement with the Onsager reciprocity relation 34 and demonstrate the generation and detection of pure spin currents in WTe2.
To further verify the charge-spin conversion, out-of-plane BZ field sweep measurements were also performed in the ISHE configuration in Dev 3. This Dev 3 consists of monolayer graphene, 11 nm WTe2 with 1 µm width and 25 Ω•µm 2 graphene-WTe2 interface resistance (see Supplementary Table   1 for details about the device). The spin current injected from the FM electrode experience a spin precession in the graphene channel (L=3.5µm) as the BZ field is perpendicular to the graphene plane.
Subsequently, the spin current gets absorbed ~100 % at the graphene/WTe2 interface for the monolayer graphene device used here (see Supplementary   The angle-dependent measurements of the ISHE signal 33 were performed in Dev 2 to verify the relation between the direction of the injected spins and the induced charge accumulation in WTe2.
The measurements were carried out at different in-plane B field along the tilting angle φ respecting to the x-axis (Fig. 3a). As shown in Fig. 3b, the measured RISHE decreases with the transverse magnetic (x-direction) component and vanishes when the magnetization is aligned with the y-axis. The sign change of RISHE is observed between φ=0° and 180° (π) due to switching of the Co magnetization direction and associated reversal of polarization of the spin current. A null RISHE signal is observed for φ = 90° (π/2) when the magnetization Co is aligned with the y-axis, as the injected spins are parallel to the WTe2 long axis and no ISHE voltage is generated in the measured geometry of WTe2 electrode. The magnitude of the measured ISHE signals ∆RISHE as a function of the measurement angle φ is shown in Figure 3c. As expected, charge current IC is proportional to s×IS (s is the spin and Is is spin current), the angular dependence of the ∆RISHE is expected to vary with cos(φ Gate dependence of ISHE measurement was performed in WTe2-graphene heterostructure (Dev 2) by using the Si/SiO2 as a back gate (Fig. 4a). The gate voltage dependence of the graphene channel resistance across the heterostructure shows the Dirac point at VD= 35 V (Fig. 4b), while WTe2 channel resistance does not show much change due to its semi-metallic character (Fig. S3e). The gate dependence of the graphene-WTe2 interface resistance shows some modulation due to change in the

Discussion
The SHE signals observed in our experiment can be rationalized by the conventional bulk SHE and the REE in WTe2. In an ideal type-I Weyl semimetal (or an ideal topological insulator), in which the bulk Fermi surface vanishes, the bulk SHE is purely contributed by the topological effect 44  To be noted, one cannot extract spin Hall angle and spin diffusion length 2 at the same time by fitting the out-of-plane (I)SHE signal 36 or solving the in-plane case equation 38

Conclusion and Outlook
The emergent Weyl semimetal WTe2 is shown here to be a promising material for charge-spin conversion at room temperature due to its unique electronic band structure giving rise to huge spin-orbit coupling and spin-polarized bulk and surface states. Particularly, the strong spin Hall signal in the WTe2-graphene hybrid devices and the gate tunability of the spin absorption process provide a new tool for potential application in future spintronic device architectures. Furthermore, as predicted in theoretical calculations, the spin Hall conductivity can be controlled by using Weyl semimetals with tunable Fermi-level 10 and alloys with tunable-resistivity 37,49 . This will allow achieving systematic control over the charge-spin conversion via electrical and optical means and a better understanding of the Weyl physics. Such measures providing large charge-spin conversion efficiency in Weyl semimetals at room temperature can be used to switch or oscillate the magnetization of nanomagnets with a very low current density. These developments will have a huge potential for emergent spin-orbit induced phenomena and applications in ultralow power magnetic random-access memory and spin logic circuits 29,50 .

Methods
Device Fabrication -The exfoliated few layers graphene was mechanically exfoliated onto the n-doped Si substrate with 300 nm SiO2. The CVD graphene was transferred on the substrate Si/SiO2 substrate by wet transfer method and followed by EBL and Ar patterning. The WTe2 flakes were exfoliated on PDMS and drytransferred on to the graphene flake under a microscope using a home-built micromanipulator transfer stage.
The CVD graphene-WTe2 devices were made by exfoliation of WTe2 and dry transfer process inside the glove box. Contacts to graphene and WTe2 were defined by standard electron beam lithography and lift-off process.
For the preparation of ferromagnetic tunnel contacts to graphene, a two-step deposition of 0.3 nm of Ti and oxidation process was carried out, followed by a 100 nm of Co deposition. The ferromagnetic tunnel contact (TiO2/Co) resistances on graphene channel were in the range of few kΩs.

Measurements -
The measurements are performed in a vacuum system equipped with a variable angular rotation facility and with an electromagnet with a magnetic field up to 0.

Data availability
The data that support the findings of this study are available from the corresponding authors on reasonable request.    For the sake of clarity, the linear background is subtracted from the (I)SHE signals.

Note 1. Spin absorption effect at the WTe2-graphene interface
The spin current in the graphene channel can be absorbed by WTe2 due to its high SOC 2 , highly depending on the contact resistance of the graphene-WTe2 interface 3,4 . We observed that the van der Waals interface contact resistance of graphene-WTe2 usually evolved during the measurements (Fig. S3a and  Due to the decrease of the resistance and the ultimate formation of low stable interface resistance between graphene and WTe 2, the oxidation of WTe2 at the interface can be ruled out. Such a contact behaviour is believed to be caused by a gap or air bubble at the interface introduced in the WTe2 flake dry transfer process. During the fabrication, the use of a vacuum treatment of the heterostructure before spin coating with e-beam resist, resulted in a faster evolution of the interface resistance. Moreover, the graphene channel covered by WTe2 is found to be very stable with an almost unchanged Dirac Point and other parameters (see Table 1), which shows a harmonious van der Waals bonding nature of graphene and WTe2.
With the evolution of graphene-WTe2 interface resistance, the spin current in the graphene channel gets increasingly absorbed by the WTe2 at the interface. Direct evidence for this is the obvious decrease of the spin valve signal by 81.3% from 106 mΩ to 20 mΩ as the contact resistance changes from stage I=70 kΩ to stage III= 310 Ω (Fig. S9c). Similar behavior is also observed in Dev 1 (about a 50% decrease, see Fig.   S9b). Moreover, the TiO2/Co contact resistances and graphene channel resistance at stage-I and -III remain comparable. Therefore, we can conclude that the strong spin absorption effect is the origin for the reduction of the spin valve signal from the state I to stage III 3,4 , which allowed us to measure the ISHE signals in our devices. As expected, no (I)SHE signals could be measured for higher graphene-WTe2 contact resistances in stage I, because of very-low spin absorption at the interface.
However, in the Dev 3, the heterostructure of CVD monolayer graphene and 11 nm WTe2 devices, a much lower interface resistance 25 Ωµm 2 is obtained (see Table 1 for Dev 3), which guarantees the transparent interface between WTe2 and graphene. In this device, no spin valve signal could be observed across the heterostructure channel (Fig. S9d), which suggests about 100% spin absorption at the WTe2-graphene interface. To verify the spin injection and detection of the ferromagnetic contacts of Co/TiO2 in the Dev 3, the spin valve and Hanle measurement of the only area graphene channel outside the WTe2 were also performed. The standard spin valve and Hanle signal can be observed. Furthermore, the use of a narrow WTe2 (1µm), less than spin diffusion length in graphene, makes sure that the 1D model can be used in the analysis.

Note 2. Estimation of the Spin Hall Angle and Spin Diffusion Length in WTe2
The calculation of shunting factor x is very crucial 2,5 for (I)SHE measurement and for the verification of the possible SHE origins. The shunting factor is defined as the relative value under the assumption that all the charge current flows within WTe2, while (1-x) means the corresponding current shunted by graphene. We use the 3D COMSOL AC/DC module to calculate current distribution in our WTe2-graphene heterostructure with all the parameters taken from the devices. Our calculation result shows that the shunting effect is highly suppressed due to the relatively higher interface resistance of WTe2-graphene and the comparable conductivity of the two materials. Therefore, the shunting factor x≈1. Therefore, all the shunting related origins can be ruled out, such as proximity-induced SHE in graphene and proximity induced Rashba-Edelstein effect in graphene 6,7 .
To estimate the spin Hall angle θSH and spin diffusion length λWTe2 in WTe2, usually one should obtain the spin diffusion length from spin absorption experiments 2,8 , in which one can estimate the spin diffusion length from the reduction of spin signal due to the presence of WTe2 in the graphene channel. However, experimentally it is challenging to compare different graphene spintronic devices with and without WTe2, as FM contact spin polarization, tunnel resistances and graphene spin transport parameters and channel doping level are not always comparable in the device with and without the WTe2 layer. These factors can affect the magnitude of the spin signals and spin lifetime in the channels. So, it is not reliable to obtain the λWTe2 by the spin absorption experiments. Therefore, here we use both the in-plane ISHE 2,8 and out-ofplane ISHE 9 method in the same device (Dev 3) for estimation of spin parameters. By comparing the results from these two methods, we can check the self-consistency and reliability of the calculations. Out-of-plane ISHE -For the out-of-plane ISHE, we adopt the formula as below 9 , Where , , , and 2 are resistivity, width, thickness, spin Hall angle and spin diffusion length of WTe2, respectively. LSH is graphene channel length, =0.32 and Ds=0.032m 2 /s are the effective spin polarization of Co/TiO2 and spin diffusion constant which are extracted from the standard Hanle fitting of the spin valve nearby the WTe2. Here we assume the Ds does not change in all the graphene area.
is the spin diffusion time in graphene. 0 = gμ B /ħ is the Larmor precession frequency, where g=2 is Lande gfactor, μ B and ħ are the Bohr magneton and reduced Planck constant. If the θSH=0.013 is taken from the literature 10 , one can extract that the λWTe2 =8±0.9nm and =185±9ps (main text Fig.2c) from the Eq. S1 fitting. The spin resistance R s,WTe2 = 2 ℎ( / 2 ) ≈ 80 Ω ≪ R s,gr = , ≈1.2kΩ which is vital to guarantee the accurate extraction for the shunting effect can be highly suppressed 9 .
In-plane ISHE -In order to quantitatively understand the in-plane ISHE data from the same device, we use a model based on one-dimensional spin diffusion equations. The detected ΔRISHE can be expressed as 2,11,12 : , with i=1, 2, Rci corresponding to injector and detector contact resistance, respectively. = ∎ , RcM, wgr, ∎ are WTe2-graphene interface resistance, graphene channel width and square resistance, respectively. By analyzing the Eq. S2 and substituting all the device parameters from Dev 3 ( Table 1 and Fig. S6), one can obtain the plot of the relation between the spin Hall angle θ(I)SHE and spin diffusion length λWTe2 (Fig.S10). As expected, by substituting λWTe2=8±0.9nm from the out-of-plane ISHE result, one obtains =0.014, which is comparable to the value in the literature 10 and proves the self-consistency in the calculations.