Introduction

Graphene has emerged as an ideal spin transport platform due to its extremely small spin-orbital coupling, negligible hyperfine interaction as well as ultra-high charge mobility1,2,3. Electrical spin injection by direct deposition of ferromagnetic (FM) metal on graphene mostly forms a transparent contact with small contact resistance, which results in extremely low spin injection efficiency4,5. To maximize the potential of graphene for spintronic applications, various dielectric materials, such as metal oxides and van der Waals (vdW) hexagonal boron nitride (hBN)6,7,8,9,10,11, have been exploited and inserted between the FM electrode and graphene to form a tunnel contact in order to improve the injection efficiency12,13,14. In fact, the growth of a uniform oxide barrier is non-trivial and ubiquitous pinholes form due to high surface diffusivity on the dangling-bond-free graphene surface. By using TiO2 as a seed layer, an atomically smooth MgO barrier has been grown on graphene, so far with the widely accepted highest spin injection efficiency of 26–30%15. However, reaching such high efficiency relies on complex and delicate growth control based on ultra-high vacuum molecular beam epitaxy (MBE) technique, which hinders its widespread applications. Two-dimensional (2D) vdW hBN has been predicted as an ideal pinhole-free tunnel barrier16. Nevertheless, the precise control of its layer thickness and avoidance of transfer-process-induced contamination and bubbles/wrinkles are challenging, making the reported efficiency vary widely from device to device17,18,19,20,21.

A promising way to achieve reliable spin injection with simple processing is based on dielectric-barrier-free vdW contact between FM electrode and graphene, where naturally formed vdW gap serves as the tunnel barrier22,23. Recent studies using transfer techniques to stack 2D ferromagnet on graphene to form vdW contacts have claimed successful spin injection, but most without the explicit proof of Hanle precession signal24,25,26,27. Moreover, the efficiency remains low and scalability has yet to be addressed, as large-scale growth and transfer of 2D ferromagnets are immature. To advance toward scalable applications, making vdW contact based on three-dimensional (3D) FM metal instead of 2D ferromagnet is more promising28,29. Yet, directly evaporating 3D FM metal on 2D materials hardly forms vdW contact. Theoretical calculations have shown that FM metal, such as cobalt (Co), generates a strongly hybridized chemisorption interface when adsorbed on graphene, being the reason for forming a transparent contact with a negligible barrier and extremely small contact resistance30,31. A viable solution is to insert a buffer metal layer, which forms a physisorption interface with graphene, before depositing the FM metal layer so as to mitigate their direct hybridization. Inspiring results have been shown32,33, whereas, unambiguous demonstration of room-temperature spin injection via combinational observation of nonlocal spin valve signal and Hanle spin precession as well as achieving high spin injection efficiency, has yet to be realized.

In this work, by growing an indium (In) buffer layer between ferromagnetic Co electrode and graphene, we show that vdW contact with a gap of ~2.83 Å and an effective tunnel barrier height of ~62.8 meV has been successfully established. Analysis based on a one-dimensional drift-diffusion model of spin transport further corroborates the vdW-gap-mediated efficient spin tunnelling and transport in our Co/In-contacted devices. Both the nonlocal spin valve signal and Hanle spin precession have been explicitly observed at room temperature, which unambiguously proves successful spin injection via the vdW tunnel contact. Upon optimizing the In buffer layer thickness and gate control, a spin injection efficiency of ~25% at room temperature and ~ 35% at low temperature has been achieved, comparable to the best values reported in oxide-tunnel-barrier-based graphene lateral spin vales (LSV). By making a multi-channel LSV device on an ultra-long graphene sample, both high device yield and performance uniformity were demonstrated, further supporting the scalability of our approach. Finally, we show that our strategy is readily applicable to other 2D materials such as semiconducting MoS2, where an averaged spin injection efficiency as high as ~19.7% was obtained explicitly for the first time.

Results and discussion

Spin signals in Co/In-contacted graphene lateral spin valves

In order to make a direct comparison, LSV devices with both Co/In contacts and Co contacts were fabricated on a single graphene sample side by side as shown in Fig. 1a and Supplementary Fig. 1a. Experimental details can be found in Methods. First, two-terminal current-voltage (I-V) curves at different temperatures for the Co/In-contacted channel and the Co-contacted channel were measured and shown in Fig. 1b. It can be seen that with an In buffer layer, the Co/In-contacted I-V shows nonlinear behaviour with weak temperature dependence, which is characteristic of tunnel contact. The bias-dependent differential resistance of the contact (i.e., dV/dI) is calculated and shown in Supplementary Fig. 1b. The range of our two-terminal resistance (100 ~ 300 kΩ) is comparable to that reported in the MBE-grown pinhole-free Co/MgO/graphene tunnel contacts (100 ~ 200 kΩ)15, indicating the potential for efficient spin injection. In contrast, the Co-contacted I-V shows linear behaviour with much smaller resistance, indicating a transparent contact was formed between Co and graphene5.

Fig. 1: Comparison of spin signals in Co/In- and Co-contacted graphene lateral spin valves.
Fig. 1: Comparison of spin signals in Co/In- and Co-contacted graphene lateral spin valves.The alternative text for this image may have been generated using AI.
Full size image

a Schematic of device structure and measurement configuration. b Two-probe current-voltage curves of Co/In-contacted channel (upper panel) and Co-contacted channel (lower panel) measured between the injection and detection electrodes under different temperatures. Indium thickness in this device is 4 nm. c Nonlocal spin valve signal of Co/In-contacted channel measured at room temperature. d Hanle spin precession data for Co/In-contacted channel measured at parallel and anti-parallel states. The red solid lines are fitted curves.

Next, the spin valve signal was measured in the standard nonlocal four-terminal geometry with AC lock-in technique (see Methods for details). By sweeping the magnetic field along the easy axis of magnetic electrodes (By), the nonlocal voltage VNL was recorded with a fixed current I injecting in the local circuit loop. Figure 1c shows the standard spin valve signal measured for the Co/In-contacted device, where RNL is defined as the nonlocal VNL divided by the local I. When By is swept back and forth, RNL jumps from parallel state to anti-parallel state and then back to parallel state, due to the difference of coercive fields between the injector and detector electrodes as determined by their respective widths34. The difference of RNL between the parallel and antiparallel states, marked as ΔRNL, is indicative of the strength of spin-polarized current injected and transported in the graphene channel. As can be seen, for Co/In-contacted device, ΔRNL is as large as ~30 Ω, while for the Co-contacted device, it is negligibly small (~60 mΩ, refer to Supplementary Fig. 1c) as previously reported4. The large spin signal observed in Co/In-contacted device allows us to measure its Hanle spin precession under perpendicular magnetic field Bz, as shown in Fig. 1d. The standard Hanle curves showing maximized/minimized signal at zero field and diminishing signal at increased field for both parallel and anti-parallel states are characteristic of spin dephasing due to Larmor precession, which further confirms that spin polarized current has been injected into graphene through the Co/In tunnel contacts. Spin parameters can be obtained by fitting the data to the solution of one-dimensional Bloch equations5:

$${R}_{{{{\rm{NL}}}}}\propto \pm {\int }_{0}^{\infty }\frac{1}{\sqrt{4\pi {Dt}}}\exp \left(\frac{-{L}^{2}}{4{Dt}}\right)\exp \left(\frac{-t}{{\tau }_{{{{\rm{s}}}}}}\right)\cos \left({\omega }_{{{{\rm{L}}}}}t\right){{{\rm{d}}}}t$$
(1)

where ± is for the parallel (antiparallel) magnetization state, L is the channel length between injector electrode and detector electrode, D is the spin diffusion constant (approximately equal to charge diffusion constant), τs is the spin lifetime, and \({\omega }_{{{{\rm{L}}}}}=g{\mu }_{{{{\rm{B}}}}}{B}_{{{{\rm{z}}}}}/\hslash\) is Larmor frequency with g-factor of ~ 2.0 for graphene6. D can be calculated independently by using the Einstein relation with parameters extracted from the transfer curve shown in Supplementary Fig. 1d, so τs is the only fitting parameter and a value of ~ 80 ps was obtained, yielding a spin diffusion length \({\lambda }_{{{{\rm{s}}}}}\) of ~ 1.55 μm (\({\lambda }_{{{{\rm{s}}}}}\equiv \sqrt{D{\tau }_{{{{\rm{s}}}}}}\)). We did not observe any Hanle spin precession signal for the Co-contacted device, probably due to the extremely small spin signal and low signal-to-noise ratio. We can further calculate the spin polarization P, i.e. the averaged spin injection/detection efficiency, by the following equation5

$$\Delta {R}_{{{{\rm{NL}}}}}=\frac{{P}^{2}{\lambda }_{{{{\rm{s}}}}}}{W\sigma }\exp \left(\frac{-L}{{\lambda }_{{{{\rm{s}}}}}}\right)$$
(2)

where W and \(\sigma\) are the width and conductivity of the graphene channel respectively. By substituting the ΔRNL and \({\lambda }_{{{{\rm{s}}}}}\) obtained above into the equation, we get a large spin polarization of ~ 25% at room temperature. This value is comparable to the best one reported in oxide tunnel barrier-based graphene LSVs and surpasses most hBN tunnel barrier-based graphene LSVs (refer to Supplementary Table 1).

Atomic STEM characterizations of interfacial structure

To understand the large spin signal observed in our Co/In-contacted graphene LSV device, Co (35 nm)/In electrodes with different In thicknesses were deposited on multilayer graphene (MLG), followed by a high-resolution scanning transmission electron microscopy (STEM) study. For comparison, a control sample with direct deposition of Co electrodes was also fabricated. Bright-field (BF) images of the interfaces between metal and MLG without and with the insertion of In buffer layer are shown in Fig. 2a–c, respectively. Apparently, without In buffer layer, the layered structure of MLG is disrupted, as evidenced by the formation of a disordered transition slab with depth of ~4 nm (brighter region between the yellow dashed lines in Fig. 2a, detailed analysis in Supplementary Fig. 2). Both energy-dispersive X-ray spectroscopy (EDS) mappings and electron energy loss spectroscopy (EELS) profile show that Co diffuses into the disordered graphene region, further confirming the chemisorption nature of the interface between Co and graphene as predicted by theoretical calculations30,31. In stark contrast, with an In buffer layer, the surface of the MLG is protected from any damage as manifested by its perfect layered patterns, forming an intact interface between Co/In and graphene (yellow dashed lines in Fig. 2b and 2c). Specifically, for the 4 nm-In sample (Fig. 2b), EDS mappings show that In and Co inter-diffuses into each other, forming a uniform Co/In mixture with very sparse In embedded in Co. Such Co/In inter-diffusion presumably prevents further diffusion of Co into MLG and a physisorption interface is thus established. Zoomed-in annular-bright-field (ABF) and BF images shown in Supplementary Fig. 3 clearly resolve a well-defined vdW gap of ~2.83 Å between Co/In lattice and MLG. For the thicker In sample (6 nm, Fig. 2c), similar results were observed except that the Co/In mixture started to be delaminated with more In aggregating near the interface. Therefore, 4 nm In sets a critical thickness for preventing Co from destroying the interface and diffusing into graphene. Raman spectroscopy shown in Supplementary Fig. 4 further confirms that 4 nm-In buffered graphene is intact without any emergence of defect peak, while direct Co-contacted graphene becomes highly defective. The formation of a vdW interface in the Co/In-contacted graphene samples underscores the efficacy of the In buffer layer in mitigating physical damage and chemical hybridization at the FM metal/graphene interface.

Fig. 2: Atomic STEM characterizations of the Co/MLG and Co/In/MLG interfacial structure.
Fig. 2: Atomic STEM characterizations of the Co/MLG and Co/In/MLG interfacial structure.The alternative text for this image may have been generated using AI.
Full size image

a BF image (top) and EDS element mappings (middle) of the cross-sectional interface of Co/MLG. Yellow dashed lines highlight the disordered layer region. EDS spectrum (bottom) of the whole region show no other elemental signal except Co and C. The Cu peak comes from the TEM grid. b, c BF images (top) and EDS elemental mappings (middle) of the cross-sectional interface of Co/In (4 nm)/MLG (b) and Co/In (6 nm)/MLG (c). A sharp and clean interface between Co and MLG is observed in (b), while excessive In aggregates near the interface in (c). EDS spectra (bottom) unambiguously indicate the presence of In inside the Co electrode. Scale bars: 5 nm (top), 20 nm (middle).

Understanding the vdW-gap-mediated tunnelling and spin transport

It has been shown that a finite vdW gap in the top-contact interface can act as a tunnel barrier for carriers22,23, which is also the case in our devices. The effective barrier height of the vdW tunnel contact can be estimated using the Brinkman, Dynes and Rowell (BDR) model35, which describes the tunnel conductance of asymmetric barriers as

$$\frac{G}{{G}_{0}}=1-\left(\frac{{A}_{0}\Delta \varphi }{16{\varphi }^{\frac{3}{2}}}\right){eV}+\left(\frac{9}{128}\frac{{A}_{0}^{2}}{\varphi }\right){\left({eV}\right)}^{2}$$
(3)

where G/G0 is the normalized channel conductance with G0 being the zero-bias conductance, \(\varphi\) is the effective barrier height as schematically depicted in Supplementary Fig. 5a, \(\Delta \varphi\) is barrier height difference between the two sides of the trapezoidal tunnel barrier, \({A}_{0}=4{\left(2m\right)}^{\frac{1}{2}}d/3\hslash\), m is the electron mass and \(d\) is the barrier thickness (assumed to be equal to the vdW gap of ~ 2.83 Å). By fitting the experimental data in Supplementary Fig. 5b to the above equation, we obtained \(\varphi=62.8{meV}\) with \(\Delta \varphi=18.9{meV}\).

The role of the vdW tunnel barrier can be further explained based on the one-dimensional drift-diffusion model of spin transport proposed by Takahashi and Maekawa36. The non-local spin valve signal \(\Delta {R}_{{NL}}\) is given by

$$\Delta {R}_{{NL}}=4{R}_{G}{e}^{-\frac{L}{{\lambda }_{G}}}{\left(\frac{P\times \frac{{R}_{C}}{{R}_{G}}}{1-{P}^{2}}+\frac{{P}_{F}\times \frac{{R}_{F}}{{R}_{G}}}{1-{P}_{F}^{2}}\right)}^{2}\times \,{\left[{\left(1+\frac{\frac{2{R}_{C}}{{R}_{G}}}{1-{P}^{2}}+\frac{\frac{2{R}_{F}}{{R}_{G}}}{1-{P}_{F}^{2}}\right)}^{2}-{e}^{-\frac{2L}{{\lambda }_{G}}}\right]}^{-1}$$
(4)

where P is the spin polarization of the injected current, PF is the spin polarization of the FM electrode, RC is the contact resistance between the graphene and FM electrode, L is the spacing between the injector and detector electrodes, \({R}_{G}=\frac{{\lambda }_{G}}{{\sigma }_{G}{W}}\) and \({R}_{F}=\frac{{{\rho }_{F}\,\lambda }_{F}}{A}\) are the spin resistances of the graphene and FM electrode, respectively, W is the width of the graphene channel, A is the contact area between graphene and FM electrode, \({\lambda }_{G}\) (\({\lambda }_{F}\)) is the spin diffusion length in the graphene (FM electrode), \({\sigma }_{G}\) is the conductivity of graphene, \({\rho }_{F}\) is the resistivity of the FM electrode. We take the typical parameters from the device shown in Fig. 1 and from literatures as follows: \(W=1{um}\), \(L=2.6{um}\), \({\lambda }_{G}=1.55{um}\), \({\sigma }_{G}=0.6{mS}\), \({P}_{F}=0.4\)37, \({\rho }_{F}=6\times {10}^{-8}\varOmega m\)38 and \({\,\lambda }_{F}=0.06\,{um}\)39. The nonlocal spin valve signal (ΔRNL) as a function of the RC is calculated for three different \(P\) and shown in Supplementary Fig. 6. For the experimentally determined spin polarization of P = 25%, the calculated ΔRNL saturates at ~ 31 Ω when the contact resistance RC becomes large enough, agreeing almost exactly with the measured value as shown in Fig. 1c. This perfect agreement further corroborates the vdW-gap-mediated efficient spin tunnelling and transport in our Co/In-contacted devices.

In-thickness-dependent and gate-tunable spin signal

We now turn our attention to optimizing the thickness of the In buffer layer for efficient spin injection. A series of Co/In-contacted graphene LSV devices with varied In thickness (up to 15 nm) and fixed Co thickness (35 nm) were measured, and selected results are shown in Fig. 3a, where all devices show a standard spin valve signal, but with different ΔRNL. The corresponding Hanle spin precession curves can be found in Supplementary Fig. 7. Two-terminal I-V curves of these devices were measured and plotted in Fig. 3b, showing nonlinear characteristics with distinct differential resistances. Figure 3c shows the calculated zero-bias differential resistance-area product (\({R}_{{{{\rm{ZB}}}}}A\)), which increases with the thickness of the In buffer layer and saturates at > 6 nm. We plot the measured ΔRNL and the calculated spin polarization as a function of the In thickness in Fig. 3d and 3e, respectively. It can be clearly seen that there is an optimal window around 4 ~ 5 nm for generating maximal P, coinciding with the critical thickness of the In buffer layer for effective interface protection as evidenced by the STEM analyses. For either thinner or thicker In buffer layer, the spin polarization diminishes rapidly. This is understandable because if In is too thin, it is non-continuous (refer to Supplementary Fig. 8), thus weakening the buffering effect and a partially chemisorbed interface can still be formed; if In is too thick, it starts to aggregate at the interface (refer to Fig. 2c) so that spin dephasing becomes non-negligible due to the presence of the In layer. Therefore, in the following experiments, 4 nm-thick In buffer layer is always deposited if otherwise noted.

Fig. 3: In-thickness dependent spin signal.
Fig. 3: In-thickness dependent spin signal.The alternative text for this image may have been generated using AI.
Full size image

a Nonlocal spin valve signals measured for a series of Co/In-contacted devices with different In buffer layer thickness. Device with direct Co contact (In thickness: 0 nm) is also shown for comparison. All curves are vertically offset for clarity purpose. b Two-terminal I-V curves of the devices for selected In buffer layer thicknesses. c, d In-thickness-dependent zero-bias resistance-area product (c), ΔRNL (d) and spin polarization (e) calculated for all devices measured. All error bars represent standard deviations.

Next, we show that the spin signal is highly gate-tuneable in our Co/In-contacted graphene LSV device. The spin valve signals measured at different gate voltages for a typical device at low temperature are shown in Fig. 4a, with the magnitude being tuned by nearly tenfold in our measured range. This can be seen more clearly in Fig. 4b, where ΔRNL taken from Fig. 4a as a function of Vg are plotted together with the transfer curve of the device. Overall, ΔRNL changes proportionally (inversely) with the trans-resistance (trans-conductance) of the graphene channel and exhibits a peak around the Dirac point (VDP = 1.7 V), which agrees well with the behaviour of LSV with tunnel contacts as predicted by the drift-diffusion theory of spin transport15,40,41. This again proves that the spin signal is governed by the vdW-gap-mediated spin tunnelling and transport in our Co/In-contacted device. By fitting Hanle curves (refer to Supplementary Fig. 9) to Eq. (1), both spin lifetimes and spin diffusion lengths can be obtained, based on which the spin polarizations are calculated according to Eq. (2) and shown in Fig. 4c, where a peak value as high as ~ 35% was achieved by tuning gate voltages.

Fig. 4: Gate-tunable spin signal.
Fig. 4: Gate-tunable spin signal.The alternative text for this image may have been generated using AI.
Full size image

a Nonlocal spin valve signals measured at different gate voltages. All curves are vertically offset for clarity purpose. b Gate-dependence of ΔRNL taken from (a). Transfer curve is also shown. c Variation of spin polarization as a function of gate voltage. Measurements were carried out at 3 K. All error bars represent standard deviations.

Scalability and versatility of Co/In vdW tunnel contact

Finally, we demonstrate two advantages of our approach – scalability and general applicability to other material systems. To show the first merit, we fabricated two LSV devices based on chemical vapour deposited (CVD) graphene (refer to Supplementary Fig. 10). The details of the proton-assisted CVD growth of ultra-flat graphene can be found in our previous work42. The first LSV device has a total of seven identical channels as shown in Fig. 5a. Inspiringly, we obtained spin valve signals and corresponding Hanle spin precession signals in all these channels at room temperature (refer to Supplementary Fig. 11 and Supplementary Table 2). The calculated spin polarization (Fig. 5c) lies in a narrow range of 14% ~ 18.5% with an average value of ~16.5%, which shows good uniformity. It should be noted that the potential spin sink effect due to nonideal contact in LSV with multiple electrodes could limit the observation of the entire spin signal; therefore, the spin injection efficiency we extracted actually sets the lower bound of the real value. The second device has an ultra-long channel of 15 μm as shown in Fig. 5d. Room-temperature spin valve signals and corresponding Hanle spin precession were measured and shown in Fig. 5e and 5f, respectively. By fitting the Hanle curves to Eq. (1), we obtained a spin lifetime of ~ 0.9 ns and a spin diffusion length of ~ 5.9 μm, which are comparable to a previous report on long-channel graphene LSV with oxide tunnel barriers43. We want to point out that the ΔRNL of ~ 3 Ω obtained in our device is one to two orders of magnitude larger than that observed in LSV devices with similar channel length10,44,45. The spin polarization P in our device was further calculated to be ~13%. A higher spin polarization of ~ 20% was achieved at a lower temperature (refer to Supplementary Fig. 12). All these results are significant considering that the etching procedure in the fabrication process may induce defects and extra contaminants in our CVD-grown graphene samples. With fast development of graphene growth and transfer techniques, wafer-scale device applications are anticipatable. To show the second merit, we made two MoS2 LSV devices based on the Co/In vdW tunnel contact as shown in Fig. 5g and Supplementary Figs. 13−15, where multilayer samples were used for our in-plane spin injection experiment in order to avoid the D’yakonov-Perel type spin relaxation induced by the Rashba-like spin-orbit coupling46. The measured spin valve signals for different channels of the first device are shown in Fig. 5h. The channel-length-dependent ΔRNL is further plotted in Fig. 5i and fitted based on Eq. (2), yielding a spin diffusion length of ~ 364 nm, which is longer than that reported previously47. The average spin polarization was calculated to be as high as ~ 19.7% (refer to Supplementary Note 1). Strikingly, we were able to measure both spin valve signal and Hanle spin precession in the second device (refer to Supplementary Fig. 14) which is, to our best knowledge, the first unambiguous observation of such signals in MoS2.

Fig. 5: Spin injection and transport in CVD graphene and multilayer MoS2.
Fig. 5: Spin injection and transport in CVD graphene and multilayer MoS2.The alternative text for this image may have been generated using AI.
Full size image

a Optical image of LSV device made on CVD graphene with multiple identical channels as marked from 1 to 7. Scale bar: 10 μm. b ΔRNL measured on respective channels in (a) at room temperature. c Calculated spin polarizations of respective channels in (a) at room temperature. Dashed line marks the average P value. d Optical image of LSV device made on CVD graphene with ultra-long channel. Scale bar: 15 μm. e, f Nonlocal spin valve signal (e) and Hanle spin precession (f) measured for device in (d) at room temperature. g Optical image of LSV device made on multilayer MoS2. Scale bar: 5 μm. h Nonlocal spin valve signals measured from different channels in (g) at 3 K. Gate voltage was set to be +10 V. i Channel-length-dependent ΔRNL taken from (h). The black dashed line is a fitted curve. All error bars represent standard deviations.

In summary, we have developed a simple method for efficient spin injection via forming a vdW tunnel contact between three-dimensional FM metal and 2D channel materials by inserting an In buffer layer. The inert nature of In, as compared to the reactive nature of Co, on 2D materials surface makes the formation of the physisorption-type interface possible. Based on the vdW-gap-mediated tunnelling, efficient spin injection into graphene with large spin polarization comparable to the best values reported so far without bias tuning has been achieved. By making a multi-channel LSV device on an ultra-long graphene sample, both high device yield and performance uniformity have been demonstrated. Through demonstrating efficient spin injection and transport in long-channel CVD graphene and exfoliated multilayer MoS2, we show that our strategy is readily applicable to different material systems. Our approach establishes an effective tunnel contact for efficient spin injection with only two consecutive metal depositions in industry-compatible e-beam or thermal evaporator, without the need of ultra-high vacuum metal deposition technique or intricate 2D material transfer process, which is cost-efficient and favourable for future large-scale and efficient spintronic applications.

Methods

Device fabrication

Monolayer Graphene was prepared by mechanically peeling high-quality graphite (natural graphite from HQ Graphene) onto SiO2(285 nm)/Si substrate and identified by optical contrast as well as Raman spectra. Strip-shaped graphene was specially chosen for spin valve device fabrication. Spin injection and detection electrodes with different widths were obtained by standard e-beam lithography, followed by e-beam evaporation and a lift-off process. In a vacuum chamber with a base pressure of <10⁻⁷ torr, an In layer with a different thickness was first deposited at a rate of 0.2 Å/s, followed by depositing a 35-nm-thick Co layer at a rate of 0.4 Å/s. Subsequently, a 5-nm-thick Au layer was deposited on top to protect Co from oxidation. The sample then underwent a standard lift-off process in acetone, followed by rinsing with isopropanol and blowing dry with nitrogen. For the ultralong spin valve device, proton-assisted, CVD-grown ultra-flat graphene was used. The graphene film was first transferred onto SiO2(285 nm)/Si substrate and then patterned into a long strip by e-beam lithography, followed by oxygen plasma etching. The same device fabrication procedure applies.

Electrical and spin transport measurements

The electrical transport measurements were carried out in a Cryofree superconducting magnet system (CFMS-12T-30VTI, Cryogenic Co.) using two source metres (Model 2400 and Model 2450, Keithley Inc.). To apply back gate voltage, the source terminal was connected to the back gate, and the leakage current through the SiO2 dielectric layer was monitored. For the spin transport measurements, an alternating current with a frequency of 13.171 Hz was applied by a Keithley 6221 current source, and the nonlocal voltage was measured by an SR830 lock-in amplifier equipped with a high impedance pre-amplifier SR551. The spin valve signal was collected by scanning the in-plane magnetic field along the easy axis of the ferromagnetic electrodes. Hanle measurements were conducted by first aligning the injector electrode and detector electrode in a parallel state or anti-parallel through applying an in-plane magnetic field, followed by rotating the sample 90 degrees and scanning the magnetic field perpendicularly to the sample surface.

STEM characterization

The cross-sectional STEM specimens were prepared using a Cryo-focused Ion Beam (FIB) in high vacuum (<10−6 mbar) in a liquid-nitrogen temperature environment. STEM imaging, EDS, and EELS analysis of vertical heterojunctions of Co/In/MLG were performed on a FEI Titan Themis with an X-FEG electron gun and a DCOR aberration corrector operating at 300 kV. The inner and outer collection angles for the ABF-STEM images (β1 and β2) were 9 and 36 mrad, respectively, and the β2 for BF-STEM images was 4 mrad, with a convergence semi-angle of 25 mrad. The beam current was about 100 pA for imaging and spectrum collection. All STEM experiments were performed at room temperature.