Strongly anisotropic spin relaxation in graphene–transition metal dichalcogenide heterostructures at room temperature

A large enhancement in the spin–orbit coupling of graphene has been predicted when interfacing it with semiconducting transition metal dichalcogenides. Signatures of such an enhancement have been reported, but the nature of the spin relaxation in these systems remains unknown. Here, we unambiguously demonstrate anisotropic spin dynamics in bilayer heterostructures comprising graphene and tungsten or molybdenum disulphide (WS2, MoS2). We observe that the spin lifetime varies over one order of magnitude depending on the spin orientation, being largest when the spins point out of the graphene plane. This indicates that the strong spin–valley coupling in the transition metal dichalcogenide is imprinted in the bilayer and felt by the propagating spins. These findings provide a rich platform to explore coupled spin–valley phenomena and offer novel spin manipulation strategies based on spin relaxation anisotropy in two-dimensional materials. Large spin–orbit coupling can be induced when graphene interfaces with semiconducting transition metal dichalcogenides, leading to strongly anisotropic spin dynamics. As a result, orientation-dependent spin relaxation is observed.

G raphene has emerged as the foremost material for future two-dimensional spintronics due to its tuneable electronic properties [1][2][3][4] . Spin information can be transported over long distances 5,6 , and in principle can be manipulated by using magnetic correlations or large spin-orbit coupling (SOC) induced by proximity effects 4,[7][8][9][10][11][12][13][14][15][16][17][18][19][20] . First-principle calculations have shown that semiconducting transition metal dichalcogenides (TMDCs) can induce an SOC in graphene in the milli-electron volt range while preserving its linear Dirac band structure 10,11 . Enhancement of the SOC has been demonstrated using non-local charge transport and weak (anti-)localization measurements 9,[12][13][14][15] , the most salient signature being a drastic reduction of the spin lifetime to the picosecond range. In recent spin transport experiments, the spin sink effect in TMDCs was used to modulate the transmission of pure spin currents. This enabled the realization of a spin field-effect switch that changes between "on" and "off " by gate tuning 21,22 .
A further consequence of the SOC induced by the proximity of a TMDC, which has not been addressed experimentally, is the imprint of the strong spin-valley coupling [23][24][25][26][27] . As depicted in Fig. 1a, a bandgap should open in the graphene Dirac cone due to the breaking of pseudospin symmetry, while the SOC, combined with broken space inversion symmetry, removes the spin degeneracy 10,11 . The spins in these bands tilt out of the graphene plane, with the out-of-plane component alternating from up to down as the energy of the bands increases, in a sequence that inverts between the K and K′ points of the Brillouin zone.
The spin splitting and texture in graphene-TMDC imply that the spin dynamics would probably differ for spins pointing in (||) and out of (⊥ ) the graphene plane, leading to distinct spin lifetimes, τ || s and τ ⊥ s , and associated spin relaxation lengths, λ || s and λ ⊥ s . Indeed, realistic modelling indicates that the spin lifetime anisotropy ratio Quantification of ζ can therefore provide unique insight into spinvalley coupling mechanisms and help elucidate the nature of the induced SOC in graphene 1,29 .
Recent experiments have demonstrated that ζ can be determined combining in-plane and out-of plane spin precession measurements 29,30 . In order to reveal the nature of the spin dynamics in graphene-TMDC, we implement such a technique using the device depicted in Fig. 1b, with TMDC being either WS 2 or MoS 2 . The experiments are based on the standard non-local spin injection and detection approach [31][32][33] . A multilayer TMDC flake is placed over graphene between the ferromagnetic injector (F1) and detector (F2) electrodes, creating a graphene-TMDC van der Waals heterostructure (see Methods and Fig. 1c). The TMDC modifies the graphene band structure by the proximity effect and, as a consequence, the spin relaxation. Considering that τ || s in the modified graphene region is expected to be in the range of a few picoseconds 22,28 , the spin relaxation length should be in the submicrometre range. The width w of the TMDC flake is thus selected to be about 1 μ m so as not to completely suppress the spin population when spins are in plane. The spin channel length L, which is defined as the distance between F1 and F2, is much longer than w (about 10 μ m) to ensure that the spin precession can be studied at moderate magnetic fields 29,30 . A backgate voltage is applied to the substrate to tune the spin absorption in the TMDC 21,22 while all the measurements are acquired at room temperature.
Owing to magnetic shape anisotropy, the magnetizations of F1 and F2 tend to be in plane. A perpendicular magnetic field B causes spins to precess exclusively in plane and senses τ || s only. In order to obtain τ ⊥ s , the strategies represented in Fig. 1d,e are followed. These strategies are described in refs 29,30 and rely on the application of an oblique B characterized by an angle β (Fig. 1d) or an in-plane B perpendicular to the easy magnetization axes of F1/F2 (Fig. 1e). As represented by the red arrows, such magnetic fields force the spins to precess out of the plane as they diffuse towards the detector. When a spin reaches the graphene-TMDC region, its orientation relative to the graphene plane is characterized by the angle β * , which depends on the magnitude of B (Fig. 1b). The spin precession dynamics therefore becomes sensitive to both τ || s and τ ⊥ s , and τ ⊥ s can be determined. Figure 2 demonstrates the changes in the spin precession lineshape, R nl versus B, induced by the TMDC. The non-local spin resistance R nl = V nl /I is determined from the voltage V nl at the detector F2, which is generated by a current I flowing at the injector F1 (Fig. 1b). Figure 2a-c shows measurements for a typical graphene-WS 2 device (Device 1). The data are acquired for parallel and antiparallel configurations of the F1/F2 magnetizations. Figure 2d-f shows equivalent measurements for a reference device (without WS 2 ), which was fabricated in the same graphene flake (Fig. 1c).

Strongly anisotropic spin relaxation in graphene-
The spin precession response in the two devices is strikingly different. Figure 2a,d presents conventional spin precession measurements with an out-of-plane magnetic field. Even though spin precession is observed in both cases, R nl is two orders of magnitude smaller in the graphene-WS 2 device (Fig. 2a) than in the reference (Fig. 2d). The decrease in R nl indicates a large reduction of λ || s in the graphene-WS 2 region, as observed previously for MoS 2 (ref. 22 ). The value of λ || s can be determined by solving the diffusive equations at B = 0 (Supplementary Information). From the change in R nl,0 = R nl (B = 0) between the graphene-WS 2 and the reference devices, λ || s is estimated to be about 0.2-0.4 μ m, which is significantly smaller than the typical λ s,gr ~ 3-5 μ m in our pristine graphene. Figure 2b,e presents spin precession measurements for in-plane B, as shown in Fig. 1e. While the change in the B orientation results in no significant variation in the reference device, the changes observed in the graphene-WS 2 device are remarkable (compare Fig. 2a,b). Figure 2b shows that, as B increases, R nl becomes much larger than its value at B = 0. The anomalous enhancement of R nl is a clear indication of anisotropic spin relaxation, with λ ⊥ s larger than λ || s and thus ζ > 1. Similar results for three other devices are shown in Supplementary Fig. 1, one of them with MoS 2 , which demonstrates that the anisotropic relaxation is not limited to graphene-WS 2 .
The difference between Fig. 2d and Fig. 2e is due to the tilting of the F1/F2 magnetizations with B. The tilting angle γ, which is calculated from the fittings to the spin precession in ref. 29 , is more pronounced for in-plane B, for which the shape anisotropy is smaller. In an isotropic system, the non-local resistance has the form nl,0 for initially parallel (+ ) and antiparallel (− ) magnetization configurations, with g(B) a function that captures the precession response 30,32,33 .
nl , it is evident that, for an isotropic system and small γ, Δ R nl ≈ 2 g(B)R nl,0 is independent of the B orientation. The obtained Δ R nl for B in plane (red) and out of plane (blue) are shown in Fig. 2c,f for the graphene-WS 2 and the reference device, respectively. The nearly perfect overlap of the two curves in Fig. 2f is a consequence of the isotropic spin relaxation in graphene 29,30 , while the disparity of the curves in Fig. 2c further demonstrates the highly anisotropic nature of the spin transport in graphene-WS 2 . The extrema in R nl are reached when the aggregate orientation of the diffusing spins has rotated by about π/2 at the WS 2 location. Because the diffusing spins pass by WS 2 before F2, this occurs at magnetic fields that are slightly larger than those at which R nl = 0 in the conventional spin precession measurements (dashed vertical lines in Fig. 2c).
Having determined λ || s , ζ can be obtained using out-of-plane precession with oblique B. Because the spins diffuse towards WS 2 , they are characterized by a broad distribution of inclination angles β * (Fig. 1b). As B increases, the spin component that is perpendicular to the magnetic field dephases and only the component parallel to B contributes to R nl (ref. 29 ). In the case depicted in Fig. 1d, this component is non-zero and the spin orientation is univocally determined by β * = β, which greatly simplifies the analysis to obtain λ ⊥ s and ζ. Indeed, the effective spin relaxation length in graphene-WS 2 for arbitrary β, λ β s , can be calculated using the same procedure as is used to find λ || s (Supplementary Information). Note that, to achieve full dephasing at moderate B, the WS 2 flake is close to the ferromagnetic electrode that typically plays the role of detector (F2 in Fig. 1b). Figure 3a shows spin precession measurements for a representative set of β values for Device 2, with F2 as detector. A back-gate voltage V g = − 15 V is applied to suppress the spin absorption in WS 2 (see later). It is observed that diffusive broadening dephases the precessional motion at the response is similar to that in Fig. 2a. However, as soon as B is tilted from the perpendicular orientation, β R nl increases anomalously, and a few degrees tilt results in > β R R nl nl,0 even at small B (e.g. for β = 85.5°). This is in stark contrast to the case of pristine graphene. Equivalent measurements for a reference device are shown in Supplementary Fig. 2; there, ζ ≈ 1 and R nl,0 is an upper limit for R nl (ref. 29 ). As a comparison, Fig. 3b shows measurements with the role of F1 and F2 reversed. Because the injector (F2) is now close to WS 2 , the aggregate spin precession angle at the WS 2 location for any given B is smaller than in the case where the injector is far away (Fig. 3a). Full dephasing at graphene-WS 2 is not achieved, while R nl does not reach the largest values observed in Fig. 3a, which implies that there the spins do not fully rotate out of plane.
For a generic anisotropic spin channel, β R nl can be written as , where β R nl is the non-local resistance that would be measured if the magnetization of the injector and detector were parallel to B. The factor cos 2 (β − γ) thus accounts for the projection of the injected spins along B and the subsequent projection along the detector magnetization 29 . For ζ = 1, = β R R nl nl,0 regardless of the value of β; therefore, plotting β R nl versus cos 2 (β − γ) results in a straight line. For ζ ≠ 1, β R nl lies above or below the straight line depending whether ζ > 1 or ζ < 1 (ref. 29 ). The magnitude of β R nl normalized to R nl,0 is shown in Fig. 4a both for the graphene-WS 2 and the reference devices (full and open symbols, respectively), as extracted from Fig. 3a and Supplementary Fig. 2. Consistent with the results in Fig. 2, ζ ≈ 1 for the reference, while ζ ≫ 1 for graphene-WS 2 .
In order to find the origin of the anisotropy, the spin transport is studied as a function of V g , which tunes the carrier density of both graphene and WS 2 . Figure 4b shows the obtained β R nl versus β for different V g . Below a threshold back-gate voltage ~− T a rapid reduction of β R nl is observed for all values of β. For V g > 10 V, no spin signal can be detected when the spins are oriented in-plane; the spin signal is recovered as soon as the out-of-plane spin component is non-zero, indicating that ζ ≫ 1 for all values of V g . A vanishing R nl for positive V g has been recently reported in graphene-MoS 2 heterostructures and was attributed to the change of the MoS 2 channel conductivity and associated modulation of the Schottky barrier at the MoS 2graphene interface 21,22 . As proposed in refs 21,22 , the carrier diffusion into the MoS 2 leads to an additional relaxation channel that suppresses the spin signal. In agreement with this interpretation, the decrease of β R nl correlates with the increase of the WS 2 conductivity with V g . The inset of Fig. 4b shows the current I ds versus V g when a  Fig. 4 | Spin lifetime anisotropy ratio, ζ. a, β R nl normalized by R nl,0 as a function of cos 2 (β − γ), with γ = γ(β, B). The data represented by filled symbols are extracted from Fig. 3a at B = 0.16 T. The solid green line represents the modelled response for ζ = 10. The data represented by open symbols are extracted from Supplementary Fig. 2 and correspond to a reference device. The error bars reflect the propagation of the uncertainties in R nl and R nl,0 deriving from the measurement noise in Fig. 3a and Supplementary Fig. 2. In this case, ζ ≈ 1, as shown by the straight black line. b, β R nl as a function of β for the indicated back-gate voltages Inset, transfer characteristics I ds versus V g for different bias voltages V ds in graphene-WS 2 ; V g T coincides with the back-gate voltage at which I ds is observed.
constant driving voltage V ds is applied between graphene and WS 2 . It is observed that I ds increases sharply nearby V g T , suggesting that only for > V V g g T can spins enter WS 2 , as proposed for MoS 2 (see also Supplementary Fig. 3). Since for < V V g g T the carriers cannot enter WS 2 and β R nl is independent of V g , the anisotropic spin relaxation for < V V g g T must be due to proximity-induced SOC. The spin anisotropy ratio ζ can readily be obtained from nl Ω for β ~ 90° (Fig. 4b) implies that λ⊥ 1 s μ m, which combined with λ~. 0 3 s μ m results in ζ ≈ 10. Using these parameters, it is possible to calculate β R nl versus cos 2 (β − γ) (Fig. 4a, solid green line), which shows very good agreement with the experimental results considering that no adjustable parameters are used. Furthermore, β R nl versus B can be found by solving the diffusive Bloch equation 30 . Supplementary Figs. 4,5 show the calculated β R nl for a homogeneous graphene-WS 2 system for oblique and in-plane B, respectively. The general agreement between Fig. 2c and Supplementary Fig. 4a and between Fig. 3a and Supplementary  Fig. 5 gives further confidence in the interpretation of our results.
Because the WS 2 flake is significantly narrower than the distance between F1 and F2, most of the precession occurs in graphene. This renders the precession response rather insensitive to the spin diffusion constant D and the spin lifetimes within graphene-WS 2 , as long as their product, which determines λ ⊥ s and λ s , is kept constant (see Supplementary Information and Supplementary Fig. 6). Assuming that D in graphene-WS 2 is of similar magnitude to that in graphene, D ~ 0.03 m 2 s −1 , then τ| | 3 s ps and τ⊥ 30 s ps. Here, τ s is of the same order as that reported in graphene-MoS 2 with conventional spin precession measurements, τ s ~ 5 ps (ref. 22 ). It is also very close to the values extracted from weak anti-localization experiments in graphene-WS 2 , τ s ~ 2.5-5 ps (refs 12,13 ).
Spin dynamics modelling and numerical simulations have been used to compute ζ in graphene interfaced with several TMDCs 28 . In the case of graphene-WS 2 with strong intervalley scattering, ζ is calculated to lie between 20 and 200, with τ| | 1 s ps and τ ⊥ s ~ 20-200 ps. In the absence of intervalley scattering ζ decreases all the way down to 1/2, as expected for Rashba SOC, with τ τ ≈ || ⊥ 2 s s ~ 10 ps near the charge neutrality point. Therefore, the large ζ in our devices is not only a fingerprint of proximity-induced SOC but also indicates that intervalley scattering is important. The somewhat smaller ζ found in the experiments can originate from a number of factors, the most straightforward being that the intervalley scattering is stronger or the SOC weaker in our devices than assumed in the model 28 . The adopted parameters can also be sensitive to the number of layers in the TMDC or the specific supercells in the calculations 10,11 . The model is developed for monolayer TMDCs; nevertheless, since the proximity effects are due to the TMDC layer that is adjacent to graphene, no dependence on the number of layers is expected, as long as the transport in graphene occurs in states within the TMDC bandgap. There are other possibilities to explain the differences from the calculations, including the characteristics of the interface with graphene, and strain or twisting between the layers, which are currently not controlled in the experiments. Because the obtained λ ⊥ s is similar to the width w of graphene-WS 2 , our approach could also become insensitive for large values of ζ. However, Supplementary  Fig. 7 demonstrates that this limit has not been reached, in particular when B is tilted slightly from the perpendicular orientation. Another aspect to be considered is the relevance of intravalley scattering and how it compares with intervalley scattering. Our measurements are all carried out at room temperature; phonon scattering can increase the weight of intravalley scattering and effectively reduce the anisotropy.
The spin lifetime anisotropy therefore provides insight into the physics underpinning spin and valley dynamics. Our results show that the large SOC and spin-valley coupling in a semiconducting TMDC can be imprinted in graphene. In addition, they open the door for novel approaches to control spin and valley information. The out-of-plane spin component propagates through graphene-TMDC much more efficiently than the in-plane component. Thus, graphene-TMDC acts as a filter with a transmission that depends on the effective orientation of the spins that reach it and that can vary over orders of magnitude. Such a filter represents a new tool in spintronics to detect small variations in the orientation of spins arriving at it. Interfacing graphene with TMDCs can also be utilized for direct electric-field tuning of the propagation of spins and for implementing spin-valleytronic and optospintronic 10,34,35 devices in which charge, spin and valley degrees of freedom can be simultaneously used 36 , as previously proposed for TMDCs 26 . This is thus an important milestone for next-generation graphene-based electronics and computing.
Note. Since submission of the present manuscript, a related work studying the spin relaxation anisotropy in graphene-MoSe 2 has been reported 37 . Measurements are carried out with in-plane magnetic fields at 75 K, where a spin lifetime anisotropy ratio ζ ≈ 11 was found.