III. Spin Hall effect
3.4 Spin hall effect in graphene
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Also, Weeks and coworker91 proposed that the strength of the intrinsic spin-orbit coupling can be largely enhanced in single-layer graphene by heavy adatom such as indium (In) and thallium (Tl). The enhancement is due to second-neighbor hopping that is mediated by the p orbitals of the adatoms, which strongly hybridize with the unoccupied level of graphene. The enhancement of the intrinsic spin-orbit coupling can lead to a band gap of the ~20 meV, and they demonstrated that dilute heavy adatoms can stabilize a robust quantum spin Hall state in graphene, theoretically91.
In 2013, the spin Hall effect in hydrogenated graphene92, which has been used as a model system to enhance spin orbit coupling in graphene, was observed with non-local measurement. Here, the non- local measurement is method to find spin Hall effect with inverse spin hall effect in an H-bar device proposed by Hankiewicz et al. similarly to the Mott double-scattering experiment. As shown in figure 25 (a), the charge current generates a transverse spin current due to spin Hall effect, and the spin current injected into channel generates an electrical voltage across the second leg from inverse spin Hall effect.
Balakrishnan and co-worker introduced small amounts of covalently bonded hydrogen atoms to the graphene lattice by the dissociation of hydrogen silsesquioxane resist, and the extent of hydrogenation was ~0.05%. With increasing hydrogenation, non-local resistance (RNL) at charge neutral point (carrier density(n) = 0) showed increase as shown figure 25 (c). Whether the non-local resistance is spin signal or not was confirmed by the non-monotonic oscillatory behavior of the non-local signal in an applied in-plane magnetic field. Figure 25 (d) shows the in-plane field dependence of non-local resistance for the device with 0.01% hydrogenation at T=4K, and a fitting oscillating non-local signal using93
𝑅𝑁𝐿=1
2𝛾2𝜌𝑊𝑅𝑒 [(√1 + 𝑖𝜔𝐵𝜏𝑠/𝜆𝑠)𝑒−(√1+𝑖𝜔𝐵𝜏𝑠/𝜆𝑠)|𝐿|] (58)
where is the spin Hall angle, L is length of spin channel, W is width of channel and 𝜔𝐵 is Larmor frequency. The spin Hall angle of the graphene device with 0.01% hydrogenation was 0.18. this oscillatory behavior of non-local resistance can be a direct signature of spin Hall effect arising from the enhancement of spin orbit coupling due to hydrogenation.
Besides, in same group94, they showed that the CVD (chemical vapour deposition) graphene from Cu foil can have a spin orbit coupling larger than that of pristine graphene because of the presence of residual Cu adatoms introduced during the growth and transfer process as shown figure 26. From a non- monotonic oscillatory dependence of the non-local signal with equation 58, the spin Hall angle of the CVD graphene was ~ 0.2 at room temperature. Also, they reported that Au and Ag can be used to induce the strong spin orbit coupling in pristine graphene.
However, these experiments for spin hall effect in graphene with H type device cause controversy whether non-local resistance is signal from spin hall effect or any other mechanism.
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Figure 25. The spin Hall effect in hydrogenated graphene. (a) Measurement schematics for the non- local spin Hall resistance. Insert is schematics showing the deformation of the graphene hexagonal lattice due to hydrogenation. (b). Nonlocal resistance versus carrier density for pristine graphene and hydrogenated graphene. Ohmic contribution is considered in both samples. (c) Dependence of the nonlocal resistance on the percentage on hydrogenation. The dark grey dashed lines are the Ohmic contribution for this sample. The inset is SEM image of hydrogenated graphene Hall bar device. Scale bar is 5 m. (d) Magnetic field dependence of nonlocal resistance for the device with 0.01%
hydrogenation at 4K92.
Figure 26. The spin Hall effect in CVD graphene. (a) AFM three-dimensional surface topography of a spin Hall device with details of actual measurement configurations. (b) Nonlocal resistance versus carrier density for pristine graphene and CVD graphene. Ohmic contribution is considered in both samples. (c) the in-plane magnetic field dependence of the non-local signal for CVD graphene. The inset is magnetic field dependence of pristine exfoliated graphene94.
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In 2015, Kaverzin and van Wees95 modified Hall bar-shaped graphene samples by covering them with a hydrogen silsesquioxane film to hydrogenate into graphene and measured non-local resistance as shown figure 27 (a-c). They also observed reproducibly and consistently a presence of non-local resistance at charge neutral point in a number of different devises. However, the spin hall angle of ~ 1.5 was obtained from channel length dependence. This high value is unrealistic because the 100%
conversion between the charge and spin currents means ~ 1. Moreover, spin precession was not observed with the applied in-plane magnetic field up to 7T. Therefore, they argued that the non-local resistance at charge neutral point in hydrogenated graphene is an effect of unknown origin and an alternative interpretation is required.
Wang and coworker96 reported that the non-local resistance in the Au or Ir-decorated graphene was observed reproducibly but the evidence of spin signal induced spin hall effect cannot be found in the in-plane magnetic field up to 6T as shown figure 27 (f). They suggested the possibility of neutral Hall effect from disorder induced valley Hall effect in that system, not spin Hall effect.
Figure 27. No spin Hall effect in hydrogenated (a-c)95 and adatom-decorated graphene(d-f) 96. (a) SEM image of hydrogenated graphene. The inset is schematic of the measuring circuit and the measured region of the sample. (b) The nonlocal resistance as a function of gate voltage for different exposures.
(c) The nonlocal resistance at charge neutral point along with the corresponding values of Ohmic contribution. (d) AFM image of adatom-decorated graphene. (e) Nonlocal resistance versus gate voltage curves for pristine graphene and Au-decorated graphene. (f) Nonlocal resistance as a function of parallel magnetic field. The red lines are calculated Hanle precession.
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