SUPPLEMENTARY INFORMATION

DOI: 10.1038/NPHYS576 Colossal Enhancement of Spin-Orbit Coupling in Weakly Hydrogenated Graphene Jayakumar Balakrishnan 1,, *, Gavin Kok Wai Koon 1,, 3, *, Manu Jaiswal 1,,, Antonio H. Castro Neto 1,, 4 1,, 3, 4, Barbaros Özyilmaz 1 Department of Physics, Science Drive 3, National University of Singapore, Singapore 11754 Graphene Research Centre, 6 Science Drive, National University of Singapore, Singapore 117546 3 Nanocore, 4 Engineering Drive 3, National University of Singapore, Singapore 117576 4 NUS Graduate School for Integrative Sciences and Engineering (NGS), Centre for Life Sciences (CeLS), 8 Medical Drive, Singapore 117456. *These authors contributed equally to this work Present address: Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India. On leave from Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 015, USA. e-mail: barbaros@nus.edu.sg This file includes: SOM Text Figures S1 to S1 References NATURE PHYSICS www.nature.com/naturephysics 1

DOI: 10.1038/NPHYS576 I. Device Fabrication and Characterization: 0.8 0.6 0.4 0. 0.0 Intensity (ab. units)1.0 0 1 3 5 8 1000 1500 000 500 3000 Raman Shift (cm -1 ) Figure S1. The Raman spectrum of graphene coated with HSQ after irradiation with e- beam (dose 0-8 mc/cm ). The progressive increase in the D-peak intensity results from the hydrogenation of the graphene. The graphene samples are prepared by the micromechanical cleavage of graphite onto a Si/SiO substrate. The single layer graphene samples are first identified from their optical contrast, which is then confirmed by Raman spectroscopy. The devices are then fabricated using standard e-beam lithography technique for electrodes. Following successful lift-off, a second e-beam step is performed to etch the graphene in to a Hall bar. For hydrogenation, we introduce small amounts of covalently bonded hydrogen atoms in graphene by coating a graphene Hall bar device with hydrogen silsesquioxane (HSQ) resist followed by an e-beam lithography (EBL) induced dissociation of HSQ resulting in the basal plane hydrogenation of graphene 1. This approach has a number of advantages over the hydrogenation of graphene using radio frequency (RF) hydrogen plasma,3. First, it provides hydrogenation without introducing vacancies. Second, the degree of hydrogenation can be precisely controlled and kept minimal. Last but not least, it enables EBL controlled local hydrogenation in the sub- NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION micron size range.the evolution of the D peak in the Raman spectrum (Fig S1) is a clear indication for the progressive hydrogenation of graphene with increasing e-beam dose. To study the influence of the hydrogenation percentage, the above device is exposed to varying doses of e-beam in the range 1-8 mc/cm. II. Additional Data on Hydrogenation: (a) (b) Figure S. (a) The evolution of the Si-H peak at 65 cm -1 as a function of e-beam dose. With increasing dose the peak intensity decreases drastically indicating the dissociation of the hydrogen from HSQ (b) The Raman spectrum for a single SHE device showing the reversibility of hydrogenation upon annealing in Ar environment at 50º C for hours. A constant Ar gas flow of 0.3l/min is maintained throughout the annealing process. The near vanishing of the D-peak after annealing confirms that HSQ e-beam irradiation induces minimum vacancies to the graphene system. That the e-beam irradiation of the HSQ results in hydrogenation of the underlying graphene can be concluded (a) from the decrease in the intensity of the Si-H peak due to the dissociation of hydrogen from HSQ with e-beam dose and (b) from the change in the I D /I G ratio of the Raman peaks with annealing in Ar environment 1. Figure S (a) shows the Si-H peak intensity for as coated HSQ samples and HSQ samples irradiated with e-beam doses 400 μc/cm and 1000 μc/cm. The gradual decrease in the Si-H peak intensity with e-beam dose is a clear indication for the dissociation of the hydrogen. This together with the increase in the D-peak intensity with e-beam dose points to the hydrogenation of the graphene lattice. NATURE PHYSICS www.nature.com/naturephysics 3

DOI: 10.1038/NPHYS576 Moreover, a decrease in the I D /I G ratio of the Raman peaks (more than 95% decrease) after annealing at 50º C in Ar environment for hours also confirm that the effect of e-beam irradiation of HSQ is mainly in the hydrogenation of graphene and the creation of vacancies is negligible (see fig Sb). III. Estimate of the concentration of impurities from Raman and transport data: Figure S3. (a) The evolution of the integrated I D /I G ratio of graphene coated with HSQ (G/HSQ) samples irradiated with increasing e-beam dose (b) the σ vs n plot for one of the G/HSQ samples irradiated with an e-beam dose of 1mC/cm. The red curve is the fit to the conductivity for resonant scatterers which gives an impurity density n imp = 1 10 1 /cm. A. From Raman Data: The concentration of impurities n imp can be estimated from the I D /I G ratio (see Fig S3 a) of the Raman peaks evaluated by irradiating the graphene/ HSQ sample with different e-beam dose. From the I D /I G ratio the spacing between the hydrogen atoms and hence, the impurity concentration can be determined using the relation 4. L D (nm ) = (1.8 ± 0.5) 10-9 λ L 4 (I G /I D ) (1) and n imp (cm - ) = 10 14 /(π L D ) () 4 NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION (where L D = separation between hydrogen atoms, λ L = wavelength of the Raman laser = 514 nm, I G = intensity of Raman G-peak and I D = intensity of Raman D-peak). The I D /I G ratio for 1 mc/cm and 3mC/cm HSQ dose, gives L D ~13 nm and 9 nm and n imp = 0.9 10 1 /cm and 1.6 10 1 /cm respectively. From the L D values, an estimate of the fraction of hydrogenation is obtained as 3 3 a 100 π LD The calculated value of hydrogenation for 1mC/cm and 3 mc/cm HSQ dose is thus 0.018% and 0.05% respectively. In order to confirm our inference, the n imp and hence the percentage of hydrogenation is also estimated from the conductivity vs. n data for these hydrogenated samples. B. Estimate from Transport Data: Figure S3 (b) show the conductivity vs. n data for the HSQ graphene sample e-beam irradiated with dose 1 mc/cm. The conductivity due to resonant scatterers in graphene is given by the relation σ = (4e /h) (k F /πn imp ) ln (k F R) (3) (where k F = (πn) 1/ is the Fermi wave vector, n imp is the concentration of impurity adatoms and R is the impurity radius) and a fit to the experimental data with this equation gives n imp ~ 1. 10 1 /cm and 10 1 /cm for 1 mc/cm and 3mC/cm HSQ irradiation respectively. The adatom concentration increases by a factor of two with 1 mc/cm and 3mC/cm HSQ irradiation. The percentage of hydrogenation is obtained as ~ (n imp /n c ) 100 is 0.05% and 0.051% for 1 mc/cm and 3mC/cm HSQ irradiation respectively, where n c is the density of carbon atoms in the hexagonal lattice. This estimate from the transport data is consistent with the above estimate from the Raman I D /I G ratio. NATURE PHYSICS www.nature.com/naturephysics 5

DOI: 10.1038/NPHYS576 IV. Additional resistivity data for weakly hydrogenated graphene: In addition to the data (sample S1) shown in fig of the main text, fig.s4 shows the ρ vs n curve for 0.01% hydrogenated graphene sample (Sample S discussed in main text). The mobility for this sample is calculated from the slope of the conductivity curve as, mobility 1 μ = σ ~ 14000 cm /Vs at RT and ~ 0,000 cm /Vs at LT, where σ is the conductivity, n is ne the carrier concentration and e is the electric charge. Figure S4. (a) Resistivity vs carrier density for the sample S (discussed in the main text) at RT and at T = 5 K. It should be noted that all junctions in a device are first characterized by charge transport measurements and only junctions where the channel resistance (R vs. V g ) across all the four electrodes of the Hall bar (see fig. 1b) show identical values are selected for further non-local spin Hall effect (SHE) measurements in the H-bar geometry 5,6. Here, a charge current (5 μa) is passed across transverse contacts, I S and I D, and the non-local voltage (V NL ) is measured across adjacent contacts (see fig. 1b). Note that, neither the spin injection nor the spin detection requires ferromagnetic leads, since the former is achieved by the SHE effect and the latter by the inverse SHE (ISHE). 6 NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION V. Carrier density dependence of the non-local signal: A comparison of the carrier density dependence of the non-local signal with that of the geometrical leakage contribution indicates a large enhancement of the non-local signal near the charge neutrality point (CNP). This is a consequence of the transport being bipolar at the CNP. The spin Hall resistivity ρ xy is inversely proportional to the charge carrier density n 7. At CNP due to disorder and two particle scattering, the smearing of the 1/n singularity of ρ xy occurs and resulting in a steep linear dependence of ρ xy in n 8. This implies that the near CNP the spin hall coefficient, given by ρ xy / n has a large value, giving rise to a giant SHE signal 8. VI. Nature of Transport in weakly Hydrogenated Graphene. Figure S5. Resistance as a function of temperature at CNP (Red solid circles) and at n =1 10 1 /cm (blue solid circles) (a) for pristine graphene and (b) for weakly hydrogenated graphene. Note that the data presented in (a) and (b) are for two distinct samples (c) low temperature R vs T for weakly hydrogenated graphene fitted for logarithmic corrections of the form ρ = ρ 0 + ρ 1 ln(t 0 /T); where ρ 0 = 1051 Ω, and ρ 1 = 166 Ω In Figure S5 (a&b) we compare the temperature dependence of the resistivity for a typical pristine graphene and for a typical weakly hydrogenated graphene sample (~0.0 %) at both the charge neutrality point (CNP) and at n = 1 10 1 /cm. At both doping levels the weakly hydrogenated graphene sample and pristine graphene sample shows qualitatively similar temperature dependence. A logarithmic increase in the resistivity at CNP with decreasing NATURE PHYSICS www.nature.com/naturephysics 7

DOI: 10.1038/NPHYS576 temperature of the form ρ = ρ 0 + ρ 1 ln (T 0 /T) (fig S5c) is observed in both samples. Thus in contrast to the strongly hydrogenated samples reported by Elias et al. our samples are not in the strong localization regime, but are instead in the metallic regime (disordered Fermi liquid) 3,9. The logorithmic correction to the resistivity is likely to originate from weak localization, disorder induced electron-electron interactions (Altshuler-Aronov effect) 9 or the Kondo effect 10. Further studies are needed to differentiate between these various contributions. Also to confirm that our spin transport measurements are in the diffusive regime and not in the ballistic regime, we have calculated the electron mean free path for our highest mobility sample at 4K and compared with our device dimension. For the device with the smallest width of 400 nm, and mobility 0,000 cm /Vs, the electron mean free path away from charge neutrality point 5 x 10 11 /cm is around 170 nm only (calculated using the equation ) and confirms our argument that the spin transport in our weakly hydrogenated samples are in the diffusive regime. 8 NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION VII. Analysis on the contribution of geometrical leakage to the measured non-local signal: Figure S6. R NL /R Ohmic as a function of L the length of the Hall bar junctions. The black circles are the experimental values and the blue curve is the simulated curve with w = 1µm, l s = 1 µm and γ = 0.56. As discussed in the main text, the measured non-local signal could either be due to the geometrical leakage or due to the spin Hall effect (SHE). In order to rule out the possible Ohmic contribution, we study the length dependence of the ratio of the measured non-local signal to the calculated Ohmic contribution. Theoretically R NL and R Ohmic are given by 11 R NL 1 = L w s γ ρ e λ λ s R Ohmic ρ cosh( πlw) + 1 = ln π cosh( πlw ) 1. Figure S6 shows the length dependence of the R NL / R Ohmic for the samples shown in Fig 3 of the main text. The measured R NL /R Ohmic for samples are in good agreement with the simulated curve (based on equation 1 and ) with w = 1µm, λ s = 1 µm and γ = 0.56 (obtained NATURE PHYSICS www.nature.com/naturephysics 9

DOI: 10.1038/NPHYS576 from fig 3 main text), thus confirming our inference of adatom induced SHE in weakly hydrogenated graphene samples. VIII. Additional data on the magnetic field dependence: A. Perpendicular magnetic field data: Figure S7. R NL vs. n for different perpendicular magnetic fields in the range 0-4 T for (a) sample S1 with L ( μm)/w (1 μm) = and (b) sample S with L ( μm)/w (0.4 μm) = 5 Figure S7 (a&b) shows the dependence of the non-local signal on the external magnetic field applied perpendicular to the plane of the sample. The measured R NL vs. n at RT for perpendicular magnetic fields in the range 0 4 T for the sample S1 (L = μm and W = 1 μm) and S (L = μm and W = 400 nm), show an increasing R NL with increasing B field. The large increase in the nonlocal signal near the charge neutrality point (CNP) can be understood as the combined effect of the bipolar transport at CNP and the Zeeman splitting in an applied external magnetic field. Both together lead to a steep increase in the Hall resistivity at the CNP and hence to an enhancement of non-local signals 8,11. B. Additional Parallel magnetic field data: 10 NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION The non-local signal R NL vs. n and precession data for an additional sample is shown in figure S8. The fitting of the precession data gives a spin relaxation length of λ s ~ 0.6 μm. Figure S8.(a) The non-local signal, R NL vs. n for sample S3. The black dashed lines show the calculated leakage current contribution and (b) the precession measurement for the same sample. The dashed red line is the fit to the precession curve using eq. () of the main text. It is important to note that, the oscillating non-local signal has an additional background signal. Such residual background signal can exist depending on the boundary conditions imposed on the spin current 1. As shown by Hankiewicz et al. 1, the presence of additional leads perpendicular to the H-bar electrodes, does not influence spin sgnal, but influences the residual background voltage. This appears to be the most plausible explanation for the offset in our data. The equation used for fitting the data strictly explains the precession part of the data and does not consider the offset involved. Moreover, to make sure that the observed non-local signal is not due to any thermoelectric effect like contribution from joule heating, we have studied the dependence of the non-local voltage as a function of the applied current. If the dominant contribution is from thermoelectric effect the voltage should show a non-linear dependence with current. NATURE PHYSICS www.nature.com/naturephysics 11

DOI: 10.1038/NPHYS576 However, our data clearly shows a linear dependence, thus excluding any possible contribution from thermoelectric effect. Moreover, it should be noted that the temperature gradient due to thermoelectric effect should be along the length of the sample, while the measured non-local voltage is across the width in the H-bar geometry, which also allows us to exclude any such contribution from thermoelectric effect on the measured non-local signal. Figure S9.The I-V characteristics of the non-local signal. The linear dependence of the I-V curve clearly excludes the possibility of any dominant thermoelectric contribution to the nonlocal signal. IX. A short explanation on the width dependence data: The width dependence of the non-local signal (fig. 4c of main text) in higher mobility samples shows a super-linear dependence. In such samples the finite width of the sample can no longer be neglected and the spin relaxation length as a function of the width W is given by λso λ s ( W ) =, where λ SO is the spin precession length defined as the length scale in which an W electron spin precesses a full cycle in a clean ballistic D electron system 13,14. This length scale λ SO remains unchanged as long as the width W of the wire is less than λ 13 SO. For such 1 NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION samples, the relation for the non-local signal can be written as R case W << λ SO, the expression can be Taylor expanded in W as NL LW W SO γ ρ e λ λ SO 1 =. For the 1 W LW = 1 +... RNL γ ρ λ so λ so i.e. for small W s ( λ SO >>W ) the non-local signal has a power law dependence in W and a log-log plot of R vs W should give a straight line. Figure S10 shows the ln R vs ln W plot for the same data shown in fig 4c of the main text. The figure clearly shows that the measured signal follows the expected linear dependency for non-local signal and the fitting gives a selfconsistent value for λ SO ~ 8 μm. It should also be noted that if the dominant signal came from Ohmic contribution, we should have seen a non-linear curve (grey dashed line in Fig S10). Figure S10. ln R vs ln W plot showing the power law dependence of the measured non-local signal with width W. The power law dependence confirms that the measured non-local signal is due to the SHE. The grey dashed line shows the expected curve if the dominant signal was from the Ohmic contribution. NATURE PHYSICS www.nature.com/naturephysics 13

DOI: 10.1038/NPHYS576 X. Short comment on possible magnetic moments formation due to weak hydrogenation: The recent experimental evidences in fluorinated and hydrogenated graphene clearly shows that only at low temperatures the functionalization induces non-interacting paramagnetic moments which interacts with the spins of the conduction electrons via exchange interaction 15,16. However, in these experiments on diluted functionalized graphene no signature of ferromagnetism is observed even at low temperatures. Figure S11. The absence of any anomalous Hall signal at zero applied magnetic field for the sample S3 at T = 3. 4K. In order to confirm that there are no ferromagnetic moments induced by hydrogenation in our experiments, we perform anomalous Hall effect (AHE) measurements. Figure S11 shows the AHE measurements for one of our samples at 3.4 K. The absence of the AHE signal is a clear indication that there is no ferromagnetic ordering in our weakly hydrogenated samples also. 14 NATURE PHYSICS www.nature.com/naturephysics

DOI: 10.1038/NPHYS576 SUPPLEMENTARY INFORMATION XI. Comparison of the SHE signal with the conventional spin-valve signals for hydrogenated graphene system: Figure S1: (a) The non-local spin-valve resistance as a function of the in-plane magnetic field. The horizontal arrows show the field sweep direction (Inset: optical picture of the four terminal spin-valve devices of hydrogenated graphene. The dotted lines show the outline of the graphene samples) and (b) the Hanle precession measurement for perpendicular magnetic field for the same junction. The fitting gives a spin relaxation time of 00 ps which is in good agreement with the values extracted from the spin Hall measurements. The spin relaxation time extracted from our spin Hall measurements are in the hundreds of picosecond range. Since this spin Hall measurements in the weakly hydrogenated graphene is demonstrated for the first time in this work, we have done a consistency check for the extracted spin relaxation by additional measurements based on the conventional spin-valve geometry in weakly hydrogenated samples (~0.01%). For this, conventional spin valve devices with MgO tunnel barrier and Co electrodes are made, followed by HSQ processing as explained in section I of this file. Figure S1 (a) shows the non-local bipolar spin-valve signal in an in-plane magnetic field swept in the range ± 150 mt. The clear bi-polar signal confirms the spin transport in weakly hydrogenated graphene. Moreover, from the Hanle spin precession measurements we estimate a spin relaxation time of the order of 00 ps, which is in excellent agreement with the data obtained independently from the spin Hall signal. NATURE PHYSICS www.nature.com/naturephysics 15

DOI: 10.1038/NPHYS576 Moreover, these results are also in good agreement with the recent results on hydrogenated spin-valves 16. REFERENCES 1. S. Ryu et al., Nano Lett. 8, 4597-460 (008).. D. C. Elias et al., Science 33, 610-613 (009). 3. M. Jaiswal et al., ACS Nano 5, 888-896 (011). 4. L. G. Cancado et al., Nano Lett. 11, 3190-3196 (011). 5. D. A. Abanin et al., Phys. Rev. B 79, 035304 (009). 6. G. Mihajlovic et al., Phys. Rev. Lett. 103, 166601 (009). 7. S. Maekawa, Ed., Concepts in Spin Electronics, Ch 8, p363-367 (Oxford University Press, 006). 8. D. A. Abanin et al.,. Phys. Rev. Lett.107, 096601(011). 9. S. Lara-Avila et al., Phys. Rev. Lett. 107, 16660(011). 10. J.-H. Chen et al., Nat. Phys. 7, 535-538 (011). 11. D. A. Abanin et al., Science 33, 38-330 (011). 1. Hankiewicz et al., Phys. Rev. B 70, 41301 (004). 13. S. Kettamann, Phys. Rev. Lett. 98, 176808 (007). 14. Paul Wenk and S. Kettamann, Handbook of Nanophysics:Nanotubes and Nanowires, Ch 8, p8-1 p8-18 (CRC Press, 010). 15. R. R. Nair et al., Nat. Phys. 8, 199-0 (01). 16. K. M. McCreary et al., Phys. Rev. Lett. 109,186604(01). 16 NATURE PHYSICS www.nature.com/naturephysics