$24-\mu \mathrm{m}$ spin relaxation length in boron nitride encapsulated bilayer graphene

We have performed spin and charge transport measurements in dual gated high mobility bilayer graphene encapsulated in hexagonal boron nitride. Our results show spin relaxation lengths ${\lambda }_s$ up to $13\mu \mathrm{m}$ at room temperature with relaxation times ${\tau }_s$ of 2.5 ns. At 4 K, the diffusion coefficient rises up to $0.52{\mathrm{m}}^2/\mathrm{s}$, a value five times higher than the best achieved for graphene spin valves up to date. As a consequence, ${\lambda }_s$ rises up to $24\mu \mathrm{m}$ with ${\tau }_s$ as high as 2.9 ns. We characterized three different samples and observed that the spin relaxation times increase with the device length. We explain our results using a model that accounts for the spin relaxation induced by the nonencapsulated outer regions.

Figure 1

(a) Square resistance obtained between contacts 2 and 3 (in color scale) with respect to $V_{\text{tg}}$ ($y$ axis) and $V_{\text{bg}}$ ($x$ axis) (b) Square resistance of the nonencapsulated region measured between contacts 3 and 4. Inset: Schematics of the device.

Figure 2

Hanle precession curves obtained at 4 K for $V_{\text{bg}}=-50$ V, $V_{\text{tg}}=-5$ V (top panel) and $V_{\text{bg}}=50$ V, $V_{\text{tg}}=4.35$ V (bottom panel) with the corresponding fitting curves and extracted spin parameters.

Figure 3

Spin transport parameters obtained by fitting the Hanle curves at 4 K as a function of $V_{\text{tg}}$ for $V_{\text{bg}}=-50, -10$, and 50 V. (a) Spin diffusion coefficient (dots) compared with the charge diffusion coefficient (solid lines), (b) spin relaxation time, and (c) the relaxation length. The lines connecting the spin parameters are a guide to the eye.

Figure 4

Effective spin relaxation time in the system as a function of ${\tau }_{\text{enc}}$ for three different values of ${\tau }_{\text{non}}$ at $V_{\text{bg}}=-50$ V and $V_{\text{tg}}=-5$ V (a) and $V_{\text{bg}}=50$ V and $V_{\text{tg}}=4.35$ V (b), the dashed line is the experimental value of ${\tau }_{\text{eff}}$, taken from Fig. 2 (top panel). The inset shows a cartoon device of the simulated system.