Observation of Spin-Valley-Coupling-Induced Large Spin-Lifetime Anisotropy in Bilayer Graphene

We report the first observation of a large spin-lifetime anisotropy in bilayer graphene (BLG) fully encapsulated between hexagonal boron nitride. We characterize the out-of-plane (${\tau }_{\perp }$) and in-plane (${\tau }_{\parallel }$) spin lifetimes by oblique Hanle spin precession. At 75 K and the charge neutrality point (CNP), we observe a strong anisotropy of ${\tau }_{\perp }/{\tau }_{\parallel }=8\pm 2$. This value is comparable to graphene–transition-metal-dichalcogenide heterostructures, whereas our high-quality BLG provides with ${\tau }_{\perp }$ up to 9 ns, a spin lifetime more than 2 orders of magnitude larger. The anisotropy decreases to $3.5\pm 1$ at a carrier density of $n=6\times {10}^{11}{\mathrm{cm}}^{-2}$. Temperature-dependent measurements show above 75 K a decrease of ${\tau }_{\perp }/{\tau }_{\parallel }$ with increasing temperature, reaching the isotropic case close to room temperature. We explain our findings with electric-field-induced spin-valley coupling arising from the small intrinsic spin-orbit fields in BLG of $12\mu \mathrm{eV}$ at the CNP.

Figure 1

(a) Schematic and (b) optical image of the device geometry. BLG is encapsulated by a 1 nm thick $h$-BN tunnel barrier ($t\text{−}h$-BN) and a 5 nm bottom $h$-BN flake ($b\text{−}h$-BN). A low-frequency ac current ($I_{\mathrm{ac}}$) injects a spin accumulation into the BLG. The nonlocal signal ($V_{\mathrm{nl}}$) is measured using standard lock-in technique. The precession of injected in-plane spins around the magnetic field ($B_{\beta }$) is illustrated in the encapsulated BLG channel. Note that the outer reference contacts ($R$) are not covered by the $h$-BN tunnel barrier. The injector ($I$) and detector contact ($D$) used for the measurements discussed in the main text are labeled and have a spacing of $L=7\mu \mathrm{m}$. (c) Gate voltage and carrier concentration dependence of the BLG square resistance.

Figure 2

Oblique Hanle spin precession data for (a) $n=6\times {10}^{11}{\mathrm{cm}}^{-2}$, (b) $n=4\times {10}^{11}{\mathrm{cm}}^{-2}$, and (c) the charge neutrality point (CNP). $R_{\mathrm{nl}0}$ denotes the nonlocal resistance at zero field and $R_{\mathrm{nl}\beta }$ the nonlocal resistance where the perpendicular spin component has fully dephased. $R_{\mathrm{nl}\beta }$ is obtained by averaging $R_{\mathrm{nl}}$ over the shaded area (50–100 mT). The bottom panels (d)–(f) show the comparison between the ratios $R_{\mathrm{nl}\beta }/R_{\mathrm{nl}0}$ and our model for different anisotropy values. The shaded area corresponds to the estimated error margin with the denoted anisotropy values. Note that panels (a)–(c) have a small background in $R_{\mathrm{nl}}$ of 9.3, 18, and $17.8\mathrm{\Omega }$ subtracted.

Figure 3

High-field Hanle spin precession curves measured at $\beta =90°$ and $T=75\mathrm{K}$ for (a) $n=6\times {10}^{11}{\mathrm{cm}}^{-2}$, (b) $n=4\times {10}^{11}{\mathrm{cm}}^{-2}$, (c) CNP. We simulate the spin precession using the parameters from Fig. 2. The gray line corresponds to the isotropic case. The perpendicular saturation field of the cobalt contacts is 1.5 T. Note that the same background as in Fig. 2 has been subtracted.

Figure 4

(a) Temperature dependence of the ratio $R_{\mathrm{nl}\beta }/R_{\mathrm{nl}0}$ measured at $\beta =45°$. The trend towards $R_{\mathrm{nl}\beta }/R_{\mathrm{nl}0}=0.5$ with increasing temperature implies that the anisotropy decreases. (b) Extraction of the ${\tau }_{\perp }/{\tau }_{\parallel }$ for $T=300\mathrm{K}$ analogous to Fig. 2. We conclude that ${\tau }_{\perp }\sim {\tau }_{\parallel }$ at room temperature.