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Supporting Online Material

Colossal Enhancement of Spin-Orbit Coupling in Weakly

Hydrogenated Graphene

Jayakumar Balakrishnan1, 2, *, Gavin Kok Wai Koon1, 2, 3, *, Manu Jaiswal1, 2, †, Antonio H. Castro Neto1, 2, 4 §, Barbaros Özyilmaz1, 2, 3, 4 ‡

1 Department of Physics, 2 Science Drive 3, National University of Singapore, Singapore

117542

2 Graphene Research Centre, 6 Science Drive 2, National University of Singapore, Singapore

117546

3Nanocore, 4 Engineering Drive 3, National University of Singapore, Singapore 117576

4NUS Graduate School for Integrative Sciences and Engineering (NGS), Centre for Life

Sciences (CeLS), 28 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 02215, USA.

‡e-mail: [email protected]

This file includes: SOM Text Figures S1 to S12 References

SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS2576

NATURE PHYSICS | www.nature.com/naturephysics 1

http://www.nature.comdoifinder/10.1038/nphys2576

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I. Device Fabrication and Characterization:

Figure S1. The Raman spectrum of graphene coated with HSQ after irradiation with e-beam (dose 0-8 mC/cm2). 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/SiO2 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

graphene1. This approach has a number of advantages over the hydrogenation of graphene

using radio frequency (RF) hydrogen plasma2,3. 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-

1000 1500 2000 2500 3000

0.0

0.2

0.4

0.6

0.8

1.0

Inte

nsity

(ab.

uni

ts)

Raman Shift (cm-1)

01

3

58

2 NATURE PHYSICS | www.nature.com/naturephysics

SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS2576


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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/cm2.

II. Additional Data on Hydrogenation:

Figure S2. (a) The evolution of the Si-H peak at 2265 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 250º C for 2 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 ID/IG

ratio of the Raman peaks with annealing in Ar environment1. Figure S2 (a) shows the Si-H

peak intensity for as coated HSQ samples and HSQ samples irradiated with e-beam doses 400

μC/cm2 and 1000 μC/cm2. 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.

(a) (b)




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Moreover, a decrease in the ID/IG ratio of the Raman peaks (more than 95% decrease) after

annealing at 250º C in Ar environment for 2 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 S2b).

III. Estimate of the concentration of impurities from Raman and transport data:

Figure S3. (a) The evolution of the integrated ID/IG 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/cm2. The red curve is the fit to the conductivity for resonant scatterers which gives an impurity density nimp = 1 × 1012/cm2.

A. From Raman Data:

The concentration of impurities nimp can be estimated from the ID/IG ratio (see Fig S3 a) of

the Raman peaks evaluated by irradiating the graphene/ HSQ sample with different e-beam

dose. From the ID/IG ratio the spacing between the hydrogen atoms and hence, the impurity

concentration can be determined using the relation4

. LD2 (nm2) = (1.8 ± 0.5) × 10-9 λL

4(IG/ID) (1)

and nimp (cm-2) = 1014/(π LD2) (2)




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(where LD = separation between hydrogen atoms, λL = wavelength of the Raman laser =

514 nm, IG = intensity of Raman G-peak and ID = intensity of Raman D-peak). The ID/IG ratio

for 1 mC/cm2 and 3mC/cm2 HSQ dose, gives LD ~13 nm and 9 nm and nimp = 0.9 × 1012/cm2

and 1.6 × 1012/cm2 respectively. From the LD values, an estimate of the fraction of

hydrogenation is obtained as 2

3 3 100D

aLπ

×

The calculated value of hydrogenation for 1mC/cm2 and 3 mC/cm2 HSQ dose is thus

0.018% and 0.05% respectively. In order to confirm our inference, the nimp 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/cm2. The conductivity due to resonant scatterers in graphene is

given by the relation

σ = (4e2/h) (kF2/2πnimp) ln2 (kFR) (3)

(where kF = (πn) 1/2 is the Fermi wave vector, nimp is the concentration of impurity adatoms

and R is the impurity radius) and a fit to the experimental data with this equation gives nimp ~

1.2 × 1012/cm2 and 2 × 1012/cm2 for 1 mC/cm2 and 3mC/cm2 HSQ irradiation respectively.

The adatom concentration increases by a factor of two with 1 mC/cm2 and 3mC/cm2 HSQ

irradiation. The percentage of hydrogenation is obtained as ~ (nimp/nc) 100 is 0.025% and

0.051% for 1 mC/cm2 and 3mC/cm2 HSQ irradiation respectively, where nc 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 ID/IG ratio.




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IV. Additional resistivity data for weakly hydrogenated graphene:

In addition to the data (sample S1) shown in fig 2 of the main text, fig.S4 shows the ρ vs

n curve for 0.01% hydrogenated graphene sample (Sample S2 discussed in main text). The

mobility for this sample is calculated from the slope of the conductivity curve as, mobility

1n eσμ ∂=

∂~ 14000 cm2/Vs at RT and ~ 20,000 cm2/Vs at LT, where σ is the conductivity, n is

the carrier concentration and e is the electric charge.

Figure S4. (a) Resistivity vs carrier density for the sample S2 (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. Vg) 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 geometry5,6. Here, a charge current (5 μA)

is passed across transverse contacts, IS and ID, and the non-local voltage (VNL) 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).




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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 ρxy is inversely proportional to the charge carrier density n7.

At CNP due to disorder and two particle scattering, the smearing of the 1/n singularity of ρxy

occurs and resulting in a steep linear dependence of ρxy in n8 . This implies that the near CNP

the spin hall coefficient, given by ∂ρxy/∂n has a large value, giving rise to a giant SHE signal8.

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 × 1012/cm 2(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 = ρ0 + ρ1ln(T0/T); where ρ0 = 10251 Ω, and ρ1 = 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 (~0.02 %) at both

the charge neutrality point (CNP) and at n = 1× 1012/cm2. 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




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temperature of the form ρ = ρ0 + ρ1ln (T0/T) (fig S5c) is observed in both samples. Thus in

contrast to the strongly hydrogenated samples reported by Elias et al.2 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 effect10. 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 20,000 cm2/Vs, the electron mean free path away

from charge neutrality point 5 x 1011/cm2 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.




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VII. Analysis on the contribution of geometrical leakage to the measured non-local signal:

Figure S6. RNL/ROhmic 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, ls = 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 RNL and ROhmic are given by11

21

2s

L

NLs

wR e λγ ρλ

−=

cosh( ) 1lncosh( ) 1Ohmic

L wRL w

ρ ππ π

+= − .

Figure S6 shows the length dependence of the RNL / ROhmic for the samples shown in Fig 3 of

the main text. The measured RNL/ROhmic for samples are in good agreement with the

simulated curve (based on equation 1 and 2) with w = 1µm, λs = 1 µm and γ = 0.56 (obtained




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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. RNL vs. n for different perpendicular magnetic fields in the range 0- 4 T for (a) sample S1 with L (2 μm)/W (1 μm) = 2 and (b) sample S2 with L (2 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 RNL vs. n at RT for

perpendicular magnetic fields in the range 0 – 4 T for the sample S1 (L = 2 μm and W = 1

μm) and S2 (L = 2 μm and W = 400 nm), show an increasing RNL 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 signals8,11.

B. Additional Parallel magnetic field data:




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The non-local signal RNL 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 λs ~ 0.6 μm.

Figure S8.(a) The non-local signal, RNL 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. (2) 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 current12. As shown by Hankiewicz et al.12, 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.




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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 non-local 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

( )2SO

s WWλλ = , where SOλ is the spin precession length defined as the length scale in which an

electron spin precesses a full cycle in a clean ballistic 2D electron system13,14. This length

scale SOλ remains unchanged as long as the width W of the wire is less than SOλ 13. For such




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samples, the relation for the non-local signal can be written as 2

22

2

12

SO

LW

NLSO

WR e λγ ρλ

−

= . For the

case W << SOλ , the expression can be Taylor expanded in W as

22

2 2

1 1 .......2NL

so so

W LWR γ ρλ λ

= − +

i.e. for small W’s ( SOλ >>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 self-

consistent value for SOλ ~ 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.




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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 interaction15,16. 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.




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XI. Comparison of the SHE signal with the conventional spin-valve signals for hydrogenated graphene system:

Figure S12: (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 200 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 S12 (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 200 ps, which is

in excellent agreement with the data obtained independently from the spin Hall signal.




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Moreover, these results are also in good agreement with the recent results on hydrogenated

spin-valves16.

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2006). 8. D. A. Abanin et al.,. Phys. Rev. Lett.107, 096601(2011). 9. S. Lara-Avila et al., Phys. Rev. Lett. 107, 166602(2011). 10. J.-H. Chen et al., Nat. Phys. 7, 535-538 (2011). 11. D. A. Abanin et al., Science 332, 328-330 (2011). 12. Hankiewicz et al., Phys. Rev. B 70, 241301 (2004). 13. S. Kettamann, Phys. Rev. Lett. 98, 176808 (2007). 14. Paul Wenk and S. Kettamann , Handbook of Nanophysics:Nanotubes and Nanowires, Ch 28,

p28-1 – p28-18 (CRC Press, 2010). 15. R. R. Nair et al., Nat. Phys. 8, 199-202 (2012). 16. K. M. McCreary et al., Phys. Rev. Lett. 109,186604(2012).




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