Controlling Spin Relaxation in Hexagonal BN-Encapsulated Graphene with a Transverse Electric Field

We experimentally study the electronic spin transport in hexagonal BN encapsulated single layer graphene nonlocal spin valves. The use of top and bottom gates allows us to control the carrier density and the electric field independently. The spin relaxation times in our devices range up to 2 ns with spin relaxation lengths exceeding $12\mu \mathrm{m}$ even at room temperature. We obtain that the ratio of the spin relaxation time for spins pointing out-of-plane to spins in-plane is ${\tau }_{\perp }/{\tau }_{||}\approx 0.75$ for zero applied perpendicular electric field. By tuning the electric field, this anisotropy changes to $\approx 0.65$ at $0.7\mathrm{V}/\mathrm{nm}$, in agreement with an electric field tunable in-plane Rashba spin-orbit coupling.

Figure 1

(a) Side-view schematics and (b) top-view optical microscope image of a h-BN encapsulated graphene spin valve. The numbers show the contact electrodes, and the top (bottom) gate electrodes are indicated as tg (bg). The graphene is outlined by the dashed line. (c) Square resistance ($R_{\text{sq}}$) as a function of $V_{\text{tg}}$ and $V_{\text{bg}}$.

Figure 2

(Spin) diffusion coefficient ($D_s$), spin relaxation time ${\tau }_s$, and spin relaxation length ${\lambda }_s$ as a function of $V_{\text{tg}}$ for three different values of $V_{\text{bg}}$. The error bars are smaller than the dot size. The dashed red (blue) lines show the charge diffusion coefficient $D_c$ for $V_{\text{bg}}=+52.5\mathrm{V}(-52.5\mathrm{V})$.

Figure 3

Effective spin relaxation times extracted for different values for ${\tau }_o$ and ${\tau }_i$ (lines) compared to our experimental data for $V_{\text{bg}}=-52.5\mathrm{V}$ (dots). The inset shows a schematic of the simulated system.

Figure 4

(a) $R_{nl}$ as a function of $B$ showing Hanle precession at low fields and a saturation of the signal at high fields when the magnetization of the electrodes point out of plane. Inset: A cartoon showing the magnetization of the contacts: in plane at low fields and out of plane at high fields. (b) The ratio ${\tau }_{\perp }/{\tau }_{||}$ as a function of electric field $\overline{E}$ for different values of carrier density $n$. Inset: The same data points for ${\tau }_{\perp }/{\tau }_{||}$ used in the main graph, but plotted as a function of $n$ where different colors and symbols represent the different values of $\overline{E}$.