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Graphene10 is an ideal two-dimensional (2D) system with large Young’s modulus11 and low bending rigidity12. Its extraordinary in-plane mechanical strength allows for large out-of-plane deformations, even at the atomic scale. This enables a broad class of chemical reactions/functionalizations, that are not practical with other 2D materials13,14,15. The out-of-plane distortion of the planar carbon bonds is unique to graphene and may allow for a strong enhancement in its otherwise weak intrinsic SO coupling strength1. This enhancement is unlike the SO enhancement in metals16 and semiconductors17, and is even distinct from the curvature-induced SO coupling in carbon nanotubes18,19. As the sp3-bond angle depends strongly on the graphene–substrate interaction, the hydrogenation of graphene allows for a controllable SO strength ranging from a few tens of microelectronvolts up to 7 meV (ref. 1). This allows the manipulation of electron/hole spins in graphene through SHE (refs 17, 20, 21, 22, 23, 24), thus eliminating the need for any magnetic elements or externally applied (local) magnetic fields in the device architecture.

We introduce small amounts of covalently bonded hydrogen atoms to the graphene lattice by the dissociation of a hydrogen silsesquioxane (HSQ) resist25. The extent of hydrogenation for our samples is determined by Raman spectroscopy measurements26,27 (see Supplementary Information) and gives ∼ 0.01–0.05% hydrogenation for a HSQ dose in the range 0.4–5 mC cm−2 (Fig. 1c). Our studies focus on samples that are only weakly hydrogenated, because hydrogen atoms are predicted to cluster at higher densities28. In such samples, our spin-transport measurements both at room temperature and low temperatures show a large non-local signal in the absence of any externally applied magnetic fields. By studying the length, width, adatom density and in-plane magnetic field dependence of the spin signal, we estimate the SO coupling strength (ΔSO), the spin relaxation length (λs)and the spin relaxation time (τs).

Figure 1: Device characterization.
figure 1

a, Scanning electron micrograph of a hydrogenated graphene sample showing multiple Hall bar junctions. Scale bar, 5 μm. b, Measurement schematics for the non-local spin Hall measurement. Inset: schematics showing the deformation of the graphene hexagonal lattice due to hydrogenation. c, Evolution of the percentage of hydrogenation with increasing irradiation dose for HSQ (0–5 mC cm−2) calculated from the ID/IG ratio of Raman peaks.

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Charge and spin transport measurements are characterized in graphene Hall bar devices (Fig. 1 and see Supplementary Information). The scanning electron micrograph of one such device with multiple Hall bar junctions is shown in Fig. 1a. The room-temperature local resistivity (ρ) and the non-local resistance (RNL) measurements for the exfoliated pristine graphene device S1 with length L = 2 μm and width W = 1 μm are shown in Fig. 2a. The presence of a finite RNL at zero fields is not intriguing, because it is comparable to the estimated ohmic contribution (ROhmic; refs 29, 30),

Figure 2: Room-temperature measurements of non-local signal.
figure 2

a, RNL versus n for pristine graphene and hydrogenated graphene at room temperature. The dark grey dashed lines show the ohmic contribution to the measured signal. Inset: ρ versus n for pristine and hydrogenated graphene. b, Dependence of the RNL on the percentage of hydrogenation. The dark grey dashed lines show the calculated ROhmic contribution for this sample.

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However, already after very weak hydrogenation ∼ 0.02%, we observe a significant (∼ 400%) increase in RNL (Fig. 2a), well above what can be accounted for by ROhmic. With increasing hydrogenation the measured RNLshows a steep increase, reaching 170 Ω at 0.05% hydrogenation (Fig. 2b). A strong increase of the RNLis observed even at charge densities >1×1012 cm−2. These results are reproduced consistently in 18 junctions in 5 samples. As the ohmic contribution to RNL remains negligible over the entire hydrogenation rate (Fig. 2b), the only plausible explanation for the observed physical phenomenon (in the absence of an applied field and at room temperature) is the SHE.

The most direct way to confirm the SHE is to study the in-plane magnetic field sweeps, where only the presence of spin-polarized current can lead to an oscillating signal29. For this geometry the non-local signal has been predicted to oscillate in a magnetic field range given by the Larmor frequency ωB = Γ B≤ (Ds/W2) (ref. 29), where Γ is the gyromagnetic ratio, Bis the applied magnetic field, Ds is the spin diffusion coefficient and W is the width of the sample. For this, devices with higher mobility (higher D) and smaller W are selected so that the condition W<λs is satisfied and the variation in the spin polarization across the strip is negligible29. Figure 3 shows the in-plane field dependence of RNL for the device with 0.01% hydrogenation at T = 4 K (μ∼20,000 cm2 V−1 s−1, L/W = 5). A fit to this oscillating non-local signal using29

where γ is the spin Hall coefficient, gives λs(B)∼1.6 μm and γ∼0.18. It should be noted that such an oscillatory behaviour is absent for pristine graphene samples. Thus, the oscillatory behaviour of RNL is a direct signature of both the SHE arising from the hydrogenation of the graphene lattice and the enhancement of an otherwise weak SO coupling strength on hydrogenation.

Figure 3: Magnetic field dependence of RNL.
figure 3

Parallel-field precession data for the sample S2 with L/W = 5 and mobility ∼20,000 cm2 V−1 s−1. A smooth background has been subtracted from the raw data (see Supplementary Information). The red dotted line is the fit for the experimental curves. The fitting gives λs∼1.6 μm.

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Further to the magnetic field dependence, we also employed the length and the width dependence to confirm that the origin of the non-local signal in weakly hydrogenated graphene samples is due to the SHE. We first discuss the length dependence by keeping W = 1 μm constant. Figure 4a,b shows the length dependence of RNL/ρ, both at the charge neutrality point (CNP) and at n = 1×1012 cm−2, for the same sample (S3) hydrogenated first to 0.02% and then at 0.05%. The sample has mobilities of 1600 cm2 V−1 s−1 and 900 cm2 V−1 s−1 for 0.02% and 0.05% hydrogenation respectively. At zero applied field the equation (1) for the non-local signal, for a device with length L and width W, becomes29,30

Figure 4: Length and width dependence of RNL at room temperature.
figure 4

a,b, At the CNP (a) and at n = 1×1012 cm−2 (b) for samples with 0.02% (red solid circles) and 0.05% (blue solid circles) hydrogenation. Here the length is the centre–centre distance between the injector and detector electrodes. The solid lines are the fit for the data and the dark grey dashed line is the calculated ohmic contribution at these charge carrier densities. c, RNL (red circles) as a function of width W (W = 400 nm–1.8 μm) for a fixed length L (2 μm). The solid red line is the fit for the data and the dark grey dashed line is the calculated ohmic contribution (inset: R versus W on a linear scale).

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By fitting the RNL/ρ versus L curve using equation (2), we determine λs∼(0.95±0.02) μm and γ∼0.58 at CNP and λs∼(1.12±0.06) μm and γ = 0.45 at n = 1×1012 cm−2. These results are consistent and in good agreement with the results from conventional lateral spin-valve31,32,33,34 devices for hydrogenated graphene with ferromagnetic contacts35 (see Supplementary Information for further data).

Next we study the width dependence of the non-local signal at a fixed length L = 2 μm (Fig. 4c, sample S2). After 0.01% hydrogenation S2 still shows a mobility of 14,000 cm−2 V−1 s−1 at room temperature. In such higher mobility samples, the width dependence of the SHE signal shows a power-law dependence. The ROhmic, on the other hand, depends on the width as exp(−πL/W) and is orders of magnitude smaller. The distinction between RNL and ROhmic is most apparent at the smallest width (400 nm). This is in good agreement with the theoretical prediction of ref. 29, for narrow channels. The observed width dependence can also be well explained by the theoretical model for clean wires36,37, that is, for high-mobility devices in the limit W<λso, where λso is the spin-precession length. For most of our width range (0.4–1.8 μm) this condition is easily fulfilled, because for S2 λso∼8 μm (see Supplementary Information).

We next evaluate other key spin parameters such as the τs and the ΔSO. In hydrogenated graphene, the dominant spin relaxation is predicted to be the spin dephasing due to Elliott–Yafet scattering1. In the Elliott–Yafet mechanism, τs = (ɛF/ΔSO)2τp, where ɛF is the Fermi energy and τp is the momentum relaxation time38,39. By substituting the value for τp,τs = λs2/D = 90 ps (D is the diffusion coefficient from the R versus n curve) and the ɛF at n = 1×1012 cm−2, we estimate for hydrogenated samples. Remarkably this is three orders of magnitude higher than the value predicted for pristine graphene. In such an undistorted graphene lattice, all of the bonds are sp2 with the σ and π bands orthogonal and separated by energy of the order of . Hence, SO coupling can occur only as a second-order process with energy , explaining the small SO strength in flat graphene40. On the other hand, an adatom locally breaks the reflection symmetry across the graphene plane leading to an out-of-plane distortion by an angle φ relative to the plane (it varies from φ = 0° for sp2, to φ≈19.5° for a full sp3). For φ≠0 ° the distortion mixes σ and π orbitals that are no longer orthogonal (for full sp3 these states are degenerate). Hence, the SO interaction becomes a first-order effect leading to a large enhancement of SO coupling for covalently bonded hydrogen impurities in graphene. Following ref. 1, we can show that the strength of the SO coupling can be written as: or equivalently, φ = Arctan{[1/4−(9−8rSO2)1/2/12]1/2}. Our experimental results give , which implies φ≈5°. This value is of the same order of magnitude as the value predicted theoretically, φDFT≈16°, by ab initio calculations for suspended graphene41. We assign the difference between the measured value and the one obtained by density function theory (DFT) to the interaction between graphene and its substrate40, which is not taken into account in ab initio methods.

In the presence of this local SO coupling two new terms can be added to the Hamiltonian , where σ are Pauli matrices that act on the subspace of the sublattices A and B, vF is the Fermi–Dirac velocity (∼106 m s−1) and is the gradient operator: a Dresselhaus term, HD = λDσzszτzδ(r)a2, where τz = ±1 represents either the K or K′ points (a is the lattice spacing); and a Rashba term, HR = 2λR (σxsyτz−σxsy) δ(r)a2. Note that HD is invariant under time-reversal symmetry, T (T: σ→σ, T: s→−s, T: τ→−τ) and parity, P (P: σ→−σ, P: s→s, P: τ→−τ). For a uniform system, it opens a gap in the spectrum of size λD. HR is allowed in this case because reflection symmetry is broken. In a uniform system, this term does not open a gap but it splits the up and down spin bands into four hyperbolic bands of energy ER(k) = ±λR±[λR2+vF2]1/2 that are parabolic at low energies with an effective mass given by m* = λR/vF2. These two terms are allowed by symmetry and, in a scattering process, lead to a spin precession and hence to SHE.

Finally, we identify the dominant microscopic mechanism for the observed spin Hall scattering42. For the side-jump mechanism the spin Hall resistivity ρSHE is independent of nimp, whereas for the skew-scattering mechanism ρSHEnimp (ref. 42). The spin Hall resistivity ρSHE is estimated from γ = (σSHE/σG) = (ρG/ρSHE) and gives a value of ρSHE = 12.9 kΩ and 14.2 kΩ for 0.02% and 0.05% hydrogenation, respectively. The value of ρSHE, thus, depends only weakly on nimp (nimp∼0.9×1012 cm−2 for 0.02% and 1.6×1012 cm−2 for 0.05% hydrogenation) and hence suggests the dominance of the side-jump mechanism in hydrogenated graphene samples42.

We have demonstrated that the SO interaction in graphene can be markedly enhanced by introducing a small concentration of covalently bonded adatoms, without a significant suppression of the conductivity. Hydrogenated graphene has been used as a model system to demonstrate that this leads to a strong SHE. The SHE is confirmed by the non-monotonic oscillatory behaviour of the non-local signal in an applied in-plane magnetic field and also by the length, width and adatom density dependence of the non-local signal. From the length dependence of the non-local signal, we extract a spin relaxation length of ∼1 μm, a spin relaxation time of ∼ 90 ps and a SO interaction strength of ∼ 2.5 meV for samples with 0.05% hydrogenation. These findings are crucial for the development of graphene-based spintronics applications, as the need for magnetic elements is eliminated from the device architecture. Last but not least, the demonstration of the non-local SHE due to impurity adatoms in graphene is a major step in the realization of a robust 2D topological states6 and a SHE-based spin transistor at room temperature.