Spin transport in graphene nanostructures

Graphene is an interesting material for spintronics, showing long spin relaxation lengths even at room temperature. For future spintronic devices it is important to understand the behavior of the spins and the limitations for spin transport in structures where the dimensions are smaller than the spin relaxation length. However, the study of spin injection and transport in graphene nanostructures is highly unexplored. Here we study the spin injection and relaxation in nanostructured graphene with dimensions smaller than the spin relaxation length. For graphene nanoislands, where the edge length to area ratio is much higher than for standard devices, we show that enhanced spin-flip processes at the edges do not seem to play a major role in the spin relaxation. On the other hand, contact induced spin relaxation has a much more dramatic effect for these low dimensional structures. By studying the nonlocal spin transport through a graphene quantum dot we observe that the obtained values for spin relaxation are dominated by the connecting graphene islands and not by the quantum dot itself. Using a simple model we argue that future nonlocal Hanle precession measurements can obtain a more significant value for the spin relaxation time for the quantum dot by using high spin polarization contacts in combination with low tunneling rates.

Figure 1

(a) Phase contrast atomic force micrograph of a typical graphene nanoisland device. The graphene is outlined by the dashed line and the contacts are represented by the lighter semitransparent blocks. The measurement scheme for nonlocal spin transport is shown below. (b) Nonlocal spin signal as a function of a perpendicular magnetic field. The line in red is a fit using Eq. (2) to extract the values for $D_s$ and ${\tau }_s$. Left inset: Nonlocal spin signal as a function of a parallel magnetic field. The arrows indicate the direction of the magnetic field sweep. Right inset: Hanle precession for $R_{A\left(B\right)}$ in black (gray).

Figure 2

Nonlocal resistance normalized by the maximum value obtained in an infinite (unbound) system as a function of the ratio $R/{\lambda }_s$ for systems of length (a) $L={\lambda }_s/10$ and (b) $L={\lambda }_s/2$. The values considering one spin injector and one spin detector aligned in parallel are shown by the solid black lines. The case of two spin injectors and two spin detectors in parallel and antiparallel alignment are represented by the dashed blue and solid red lines, respectively. For comparison, the case of an unbound system with one spin injector and one detector is represented by the dashed black line. The schematics of the system showing the dimensions and the four contacts is shown in the inset of (b).

Figure 3

The ratio ${\tau }_{\text{fit}}/{\tau }_s$ as a function of $R/{\lambda }_s$ for finite systems (bound systems) of length (a) $L={\lambda }_s/10$ and (b) $L={\lambda }_s/2$. The results obtained by fitting the simulated Hanle precession curves using Eq. (2) are represented by the black circles and the results obtained by fitting using Eq. (3) are shown by the gray circles. The solid black line shows the results for the infinite (unbound) system using Eq. (2).

Figure 4

(a) Phase contrast atomic force micrograph of a graphene quantum dot device. The graphene is outlined by the solid line and the contacts are represented by the lighter semitransparent blocks. The electrodes are numbered 1–6. (b) Four-terminal resistance as a function of $V_{\text{bg}}$ with $V_{\text{pg}}=V_{\text{sg}}=0$ V for 293 K (red) and 4.2 K (blue). For this measurement a current was driven between electrodes 1 and 5, and the voltage detected between electrodes 3 and 4.

Figure 5

(a) Nonlocal spin valve measurement in a graphene quantum dot with $V_{\mathrm{bg}}=-20$ V and $V_{\text{pg}}=V_{\text{sg}}=0$ V at 4.2 K. (b) Nonlocal Hanle precession with the same gate voltages as in (a). The fit using Eq. (2) is shown by the red line. Inset: Data for the nonlocal resistance as a function of a perpendicular magnetic field for the two levels A and B shown in (a).

Figure 6

(a) ${\tau }_{\text{fit}}$ versus ${\tau }_s^{\text{QD}}$ for different values of ${\tau }_d$. The dotted line shows ${\tau }_{\text{fit}}={\tau }_s^{\text{QD}}$. Inset: Schematics of the system used for the simulations. Two semi-infinite regions with spin relaxation time ${\tau }_s^o$ are connected by a central region representing the QD with spin relaxation time ${\tau }_s^{\text{QD}}$. The diffusion time between spin injection and detection ${\tau }_d$ is represented by the dotted line. (b) ${\tau }_{\text{fit}}$ versus ${\tau }_d$ for different values of ${\tau }_s^{\text{QD}}$. The corresponding tunneling rate $\Gamma =2/{\tau }_d$ is shown in the upper axis. The horizontal lines show the values used for ${\tau }_s^{\text{QD}}$.