Linear scaling between momentum and spin scattering in graphene

Spin transport in graphene carries the potential of a long spin-diffusion length at room temperature. However, extrinsic relaxation processes limit the current experimental values to $1–2\mu \text{m}$. We present Hanle spin precession measurements in gated lateral spin valve devices in the low to high (up to ${10}^{13}{\text{cm}}^{-2}$) carrier density range of graphene. A linear scaling between the spin-diffusion length and the diffusion coefficient is observed. We measure nearly identical spin- and charge diffusion coefficients indicating that electron-electron interactions are relatively weak and transport is limited by impurity potential scattering. When extrapolated to the maximum carrier mobilities of $2\times {10}^5{\text{cm}}^2/\text{Vs}$, our results predict that a considerable increase in the spin-diffusion length should be possible.

Figure 1

(Color online) (a) SEM image of a spin valve device. A $0.3\times 13\mu \text{m}$ strip with a cross shape in the middle (brown/light gray) was etched with oxygen plasma out of the original graphene flake (dark gray). The Co electrodes 1–10 of widths 90–800 nm and spacings 1 to $3.1\mu \text{m}$ are also visible. (b) Hanle precession measurements (dots) and fits (solid lines) at the Dirac neutrality point and in the metallic regime, with the injector/detector magnetization aligned parallel $\left(p\right)$ and antiparallel.

Figure 2

(Color online) Charge- and spin transport parameters plotted against charge-carrier density and gate voltage. (a) Square resistance; (b) nonlocal spin valve signal determined from spin valve and from Hanle precession measurements; (c) charge- and spin-diffusion coefficients; (d) spin relaxation time; and (e) spin-relaxation length.

Figure 3

(Color online) Spin vs charge diffusion coefficient with the unbroadened DOS from Eq. (1) and the broadened version from Eq. (5) using a Gaussian broadening of $\text{FWHM}\simeq 176\text{meV}$.

Figure 4

(Color online) Linear relationship between the spin-relaxation length and the spin-diffusion coefficient, extracted from Fig. 2 panels (c) and (e).