Spin transport in high-mobility graphene on ${\mathrm{WS}}_2$ substrate with electric-field tunable proximity spin-orbit interaction

Graphene supported on a transition metal dichalcogenide substrate offers a novel platform to study the spin transport in graphene in the presence of a substrate-induced spin-orbit coupling while preserving its intrinsic charge transport properties. We report the first nonlocal spin transport measurements in graphene completely supported on a 3.5-nm-thick tungsten disulfide (${\mathrm{WS}}_{\text{2}}$) substrate, and encapsulated from the top with an 8-nm-thick hexagonal boron nitride layer. For graphene, having mobility up to 16 000 ${\mathrm{cm}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$, we measure almost constant spin signals both in electron and hole-doped regimes, independent of the conducting state of the underlying ${\mathrm{WS}}_2$ substrate, which rules out the role of spin-absorption by ${\mathrm{WS}}_2$. The spin-relaxation time ${\tau }_{\text{s}}$ for the electrons in graphene-on-${\mathrm{WS}}_2$ is drastically reduced down to $\sim 10$ ps from ${\tau }_{\text{s}}\sim 800$ ps in graphene-on-${\mathrm{SiO}}_2$ on the same chip. The strong suppression of ${\tau }_{\text{s}}$ along with a detectable weak antilocalization signature in the quantum magnetoresistance measurements is a clear effect of the ${\mathrm{WS}}_2$-induced spin-orbit coupling (SOC) in graphene. Via the top-gate voltage application in the encapsulated region, we modulate the electric field by 1 V/nm, changing ${\tau }_{\text{s}}$ almost by a factor of four, which suggests electric-field control of the in-plane Rashba SOC. Further, via the carrier-density dependence of ${\tau }_{\text{s}}$, we also identify the fingerprints of the D'yakonov-Perel' type mechanism in the hole-doped regime at the graphene-${\mathrm{WS}}_2$ interface.

Figure 1

(a) Stack A: a $\mathrm{hBN}/\mathrm{Gr}/{\mathrm{WS}}_2$ stack with $\mathrm{Co}/{\mathrm{AlO}}_{\text{x}}$ ferromagnetic (FM) tunnel contacts and a top gate. (b) Top-view of stack A. White region marked by C' represents the top-gate electrode contacting the ${\mathrm{WS}}_2$ substrate. The connection scheme for measuring the $I-V$ behavior of ${\mathrm{WS}}_2$ is also shown. (c) Stack B: graphene supported on a bottom ${\mathrm{WS}}_2$ substrate. (d) Optical image of stack A before the contact deposition. The graphene flake is outlined by a white dotted line, and the orange dotted line denotes the ${\mathrm{WS}}_2$ flake region to be contacted by the top-gate electrode after the contact deposition. On the top left corner outlined with a black square, a graphene flake (ref A) with the developed contacts can be seen on the same ${\mathrm{SiO}}_2$/Si substrate. (e) Optical image of stack B, i.e., a graphene (white dashed lines)$/{\mathrm{WS}}_2$ heterostructure after the contact deposition. It also has a reference Gr flake “ref B” on the same ${\mathrm{SiO}}_2$ substrate (not shown in the image).

Figure 2

(a) For region I of stack A, the $R_{\text{sq}}-V_{\text{bg}}$ dependence at RT and 4 K is shown on the left axis. The $I_{\text{DS}}-V_{\text{bg}}(V_{\text{DS}}=0.2\mathrm{V})$ behavior of ${\mathrm{WS}}_2$ at 4 K is shown on the right-$y$ axis (open circle). For region II (b) the $R_{\text{sq}}-V_{\text{bg}}$ and (c) the $R_{\text{sq}}-V_{\text{tg}}$ behavior of Gr encapsulated between ${\mathrm{WS}}_2$ and hBN flakes. The corresponding $\sigma -V_{\text{bg(tg)}}$ behaviors are plotted in (d)–(f).

Figure 3

(a) Spin-valve measurements for Gr-on-${\mathrm{WS}}_2$ (region I of stack A) at different $V_{\text{bg}}$ for the injector-detector separation $L=0.8\mu \mathrm{m}$, and the corresponding (b) $\mathrm{\Delta }{R}_{\text{NL}}$ as a function of carrier density in graphene at RT and 4 K. (c) Normalized Hanle signal $\mathrm{\Delta }{R}_{\text{NL}}$, i.e., $\mathrm{\Delta }{R}_{\text{NL}}\left(B_{\perp }\right)/\mathrm{\Delta }{R}_{\text{NL}}(B_{\perp }=0)$ for graphene-on-${\mathrm{SiO}}_2$ (green) and on-${\mathrm{WS}}_2$ (red) at 4 K. (d) Parallel (P) and antiparallel (AP) Hanle signals $R_{\text{NL}}$ for graphene-on-${\mathrm{SiO}}_2$ and (e) for graphene-on-${\mathrm{WS}}_2$ (region I of stack A). A large linear background can also be seen in both P and AP configurations and in electron and hole-doped regimes. (f) Normalized $\mathrm{\Delta }{R}_{\text{NL}}$ in region I of stack A at different $V_{\text{bg}}$ at 4 K.

Figure 4

(a) Spin-valve measurements across the encapsulated region (region II) of stack A at different top-gate voltages, changing the carrier density of the encapsulated region from hole- to electron-doped regime. (b) A contour plot of $R_{\text{sq}}$ for the encapsulated region as a function of $V_{\text{bg}}$ and $V_{\text{tg}}$. The gray circles on the horizontal dotted line at $V_{\text{bg}}=-40$ V denote the $V_{\text{tg}}$ values at which spin valve and Hanle measurements are taken. Hanle measurements for the encapsulated region for the hole doped regime at the CNP and electron-doped regime are shown in (c)–(e), respectively. The corresponding Hanle signals are shown in (f)–(h).

Figure 5

Exponentially decaying spin signal $\mathrm{\Delta }{R}_{\text{NL}}$ in stack A (region I) for an increasing injector-detector separation $L$. Black square and circle data points are taken for two different injector electrodes. Here, we assume equal spin polarization for all the contacts. The data are fitted using Eq. (3).

Figure 6

(a) ${\tau }_{\text{s}}$ vs ${\tau }_{\text{p}}$ for the reference graphene on ${\mathrm{SiO}}_2$ substrate in the electron-doped regime shows an enhanced ${\tau }_{\text{s}}$ with the increase in ${\tau }_{\text{p}}$, suggesting the EY-type spin-relaxation. (b) ${\tau }_{\text{s}}$ vs ${\tau }_{\text{p}}$ (red squares) for graphene-on-${\mathrm{WS}}_2$ substrate (region I of stack A) shows an enhanced ${\tau }_{\text{s}}$ for a reduced ${\tau }_{\text{p}}$, suggesting the DP-type spin relaxation in presence of a substrate-induced SOC. Black line represents a linear fit of $1/{\tau }_{\text{s}}-{\tau }_{\text{p}}$ data (black spheres). (c) ${\tau }_{\text{s}}$ as a function of carrier density $n$ and (d) electric field $E$ at different values of $V_{\text{bg}}$ for the electron and hole transport regime in region II of stack A. $E$ and $n$ in the encapsulated region due to a combined effect of the top and bottom gates are calculated by following the procedure in Ref. [20].

Figure 7

(a) A WL signal for ref B flake on a ${\mathrm{SiO}}_2$ substrate (red) and no WL/WAL signature was detected for graphene-on-${\mathrm{WS}}_2$ (region I of stack A). (b) A narrow WAL signature in the encapsulated region was detected due to more spatial averaging in a longer region (region II of stack A). All the data shown here are taken at 4 K.