Large spin-relaxation anisotropy in bilayer-graphene/${\mathrm{WS}}_2$ heterostructures

We study spin transport in bilayer graphene (BLG), spin-orbit coupled to a tungsten di sulfide (${\mathrm{WS}}_{\text{2}}$) substrate, and measure a record spin lifetime anisotropy $\sim 40–70$, i.e., the ratio between the out-of-plane ${\tau }_{\perp }$ and in-plane spin relaxation time ${\tau }_{\left|\right|}$. We control the injection and detection of in-plane and out-of-plane spins via the shape anisotropy of the ferromagnetic electrodes. We estimate ${\tau }_{\perp }\sim 1–2\mathrm{ns}$ via Hanle measurements at high perpendicular magnetic fields and via a new tool we develop: oblique spin valve measurements. Using Hanle spin-precession experiments we find a low ${\tau }_{\left|\right|}\sim 30\mathrm{ps}$ in the electron-doped regime which only weakly depends on the carrier density in the BLG and conductivity of the underlying ${\mathrm{WS}}_{\text{2}}$, indicating proximity-induced spin-orbit coupling (SOC) in the BLG. Such high ${\tau }_{\perp }$ and spin lifetime anisotropy are clear signatures of strong spin-valley coupling for out-of-plane spins in $\mathrm{BLG}/{\mathrm{WS}}_{\text{2}}$ systems in the presence of SOC and unlock the potential of BLG/transition metal dichalcogenide heterostructures for developing future spintronic applications.

Figure 1

(a) Nonlocal spin-transport measurement scheme. The ferromagnetic electrodes C2-C3 are premagnetized along the $y$ axis by applying an in-plane magnetic field. The outer electrodes C1 and C4 act as reference electrodes. (b) An optical image of a part of ${\mathrm{WS}}_{\text{2}}/\mathrm{BLG}$ sample (stack A) where the measurements are performed. The BLG is outlined with a black dashed line which extends further to the right.

Figure 2

(a) Parallel (P) and antiparallel (AP) Hanle curves for $L=1\mu \mathrm{m}$ ($V_{\text{bg}}=0V$) show a strong increase in the nonlocal resistance with the applied out-of-plane magnetic field $B_{\perp }$, which indicates a large spin-relaxation anisotropy and the high spin-relaxation time for the out-of-plane spins. Signs of P and AP configurations are reversed because one electrode has a negative contact polarization for in-plane spins. (b) The Hanle spin signal $R_{\text{nl}}^{\left|\right|}$ and the fit result in low ${\tau }_{\left|\right|}\sim 30$ ps (stack A).

Figure 3

(a) In-plane SV signals at the injector-detector separation $L=1.3\mu \mathrm{m}$ (black) and $2.3\mu \mathrm{m}$ (red) with their values on the left and right axis, respectively. A background signal of $0.5\mathrm{\Omega }$ ($7\mathrm{m}\mathrm{\Omega }$) which corresponds to Hanle signal at $B_{\perp }=0\mathrm{T}$ in Fig. 3 has been subtracted from the measured spin signal at $L=1.3\left(2.3\right)\mu \mathrm{m}$ for a clear representation. (b) Measured and symmetrized Hanle curves for the same $L$ values for the parallel configuration of FM electrodes.

Figure 4

(a)–(c) Steps for oblique spin-valve (OSV) measurements. The magnetization vector for the injector and detector (in black) makes an angle $\theta$ with the easy axis and the applied magnetic field $B$ (red vector) for the magnetization reversal remains fixed at an angle ${\theta }_{\text{B}}$ throughout the measurement. The magnetization reversal for the detector and the injector are shown in (b) and (c), respectively. (d) OSV measurements at different ${\theta }_{\text{B}}$ values for the injector-detector separation $L=1\mu \mathrm{m}$. Due to the negative spin polarization of one electrode, $R_{\text{AP}}$ is higher in magnitude than $R_{\text{P}}$. The OSV spin signal $\mathrm{\Delta }{R}_{\text{nl}}$ is defined as half of the magnitude of the switch, labeled with the black arrow. The increase in the spin-valve signal magnitude at higher ${\theta }_{\text{B}}$ confirms the presence of a large spin-relaxation anisotropy. A background signal ($\sim 0.5–1\mathrm{\Omega }$) has been removed from the measured signal for a clear representation (see the Supplemental Material [40] for the original measurement).

Figure 5

(a) $\eta -V_{\text{bg}}$ plot (in red) on the left $y$ axis and respective ${\tau }_{\left|\right|}$ and ${\tau }_{\perp }$ as a function $V_{\text{bg}}$ on the right $y$ axis. (b) OSV measurements at $L=4.3\mu \mathrm{m}$ at ${\theta }_{\text{B}}=0^{\circ }$ (black curve), ${\theta }_{\text{B}}={82}^{\circ }$ (config.-I) and for the swapped injector detector (config.-II) at ${\theta }_{\text{B}}={82}^{\circ }$. Arrows in the figure indicate the switching of electrode $C2$ in Fig. 4.