Spin inversion in graphene spin valves by gate-tunable magnetic proximity effect at one-dimensional contacts

Graphene has remarkable opportunities for spintronics due to its high mobility and long spin diffusion length, especially when encapsulated in hexagonal boron nitride (h-BN). Here, we demonstrate gate-tunable spin transport in such encapsulated graphene-based spin valves with one-dimensional (1D) ferromagnetic edge contacts. An electrostatic backgate tunes the Fermi level of graphene to probe different energy levels of the spin-polarized density of states (DOS) of the 1D ferromagnetic contact, which interact through a magnetic proximity effect (MPE) that induces ferromagnetism in graphene. In contrast to conventional spin valves, where switching between high- and low-resistance configuration requires magnetization reversal by an applied magnetic field or a high-density spin-polarized current, we provide an alternative path with the gate-controlled spin inversion in graphene.


Supplementary Note 3. Temperature dependence of ΔR NL for different backgate voltage
Compared to conventional graphene spin valves, there is stronger temperature dependence of ΔR NL for 1D contact devices. Supplementary Figure 4 shows the temperature dependence of ΔR NL for different backgate voltage. The negative ΔR NL is observable up to 75 K and vanishes at 100 K for V gate = 0 V, 20 V and 40 V, while positive ΔR NL persists to 200 K and disappears at room temperature for V gate = -20 V, -30 V and -50 V.
Supplementary Figure 4. Temperature dependence of ΔR NL for different gate (sample I).

Supplementary Note 4. Extracting the effective spin polarizations of contacts
For quantitative analysis we estimate the polarization of each contact using the model developed by Takahashi and Maekawa 1 .
where N = G , F = F F J represents the spin resistance of graphene and Co, and F are spin diffusion length of graphene and Co, and is the length and width of graphene (for sample II and III, we  7.5 μm , A * 2D = 2.5 μm , B * 2D = 5 μm , A * B = 2.5 μm and = 1 μm ), J is Co electrode cross section, C is contact resistance, σ F is Co spin polarization and Σ is contact spin polarization, which we consider to be gate-dependent. Because in our samples Σ is usually less than 0.1 and F is also much smaller than C , equation (1) can be simplified to where 12 ( C1 , C2 , N , , From equation (2) we can see that the spin signal is the product of spin polarization of spin injector and detector multiplied by a factor 12 ( C1 , C2 , N , , ) determined by C , N , and . Since the polarization of 2D contact does not change its polarity with gate voltage, to adopt a convention that its spin polarization is positive (i.e. we can only determine relative polarizations, so we must adopt a sign convention). Then we have Based on the three measured gate dependent non-local spin signal ∆ NL A * 2D , ∆ NL B * 2D and ∆ NL A * B , the contact resistance and graphene resistance at each gate voltage, we calculate the effective spin polarization of each contact using equation (4). The extracted effective spin polarization of each contact for sample II and III are shown in main text Figure 4 (c) and 4 (d). Supplementary

Supplementary Note 5. Backgate dependence of encapsulated spin valve devices with 2D tunneling contacts
Supplementary Figure 5 shows the backgate dependence of the non-local spin signal ΔR NL for an encapsulated spin valve device with 2D tunneling contacts (shown in Supplementary Figure 2 (c)). The device exhibits weak backgate dependence of ΔR NL from 20 K up to room temperature.

Supplementary Note 6. Gate tunable proximity effect with 1D tunneling contact
Our results also suggest that the tunable magnetic proximity effect can exist in the presence of 1D contacts with a tunnel barrier. We measured h-BN/graphene/h-BN 1D contact devices with 0.6 nm SrO tunneling barriers. Supplementary Figures 6 (a) and 6 (b) are the non-local magnetoresistance (MR) curves at V gate = -40 V and V gate = 40 V. It is clear that the polarity of ΔR NL still changes, even with 0.6 nm SrO tunneling barriers. This agrees with the theory prediction that the magnetic proximity effect can extend across a tunnel barrier 2 .
Supplementary Figure 6. Non-local MR curves for graphene spin valve device with 1D tunneling contact. (a) V gate = -40 V and (b) V gate = 40 V. The red (blue) curve is for increasing (decreasing) magnetic field (sample VIII).

Supplementary Note 7. Spin lifetime and diffusion length
To extract spin lifetime and diffusion length, we perform the analysis on the raw data as well as symmetrized data because the curves show significant asymmetry as a function of Bx. We speculate this asymmetry could be due to the non-collinearity between the spin orientation of the 1D interfaces at spin injector and detector. Supplementary Figures 7 (a) and 7 (b) show the raw and symmetrized data for V gate = -40 V, respectively. For raw data in Supplementary Figure 7 (a), we fitted with both standard model 3 (red curve) and modified model considering asymmetric component (blue curve). The origin of the asymmetry is not known but one possibility is the presence of a relative angle between the directions of the effective polarizations of the injector and detector. The extracted spin lifetime and diffusion length are 252 ± 62 ps (208 ± 12 ps for asymmetric fitting) and 8.6 ± 1.6 µm (7.7 ± 0.4 µm for asymmetric fitting). The extracted spin lifetime and diffusion length are 252 ± 12 ps and 8.6 ± 0.3 µm for symmetrized data in Supplementary Figure 7

Supplementary Note 8. Comparison of local Hall effect and our spin transport
One concern is the local Hall effect from the fringe fields of Co electrodes, which may cause some artifacts. Recently published work of B. Karpiak et al. 4 , suggests that in 1D edge ferromagnet/graphene contacts using a geometry and materials similar to ours, the observed results are dominated by such magnetic stray fields, not the magnetic proximity effects. To compare local Hall effect from fringe fields and our spin transport results, we fabricated a device (sample IX) with the geometry used in B.

Supplementary Note 9. Tunneling anisotropic magnetoresistance
Another concern is tunneling anisotropic magnetoresistance (TAMR) though one would not expect this effect to be substantial because it requires strong spin-orbit coupling. To rule out this possible artifact, we measured TAMR effect on the sample device presented in the main text. As shown in Supplementary   Figure 12, there is no observable TAMR signal, which rules out TAMR as the origin of the observed spin signal in the main text.
Supplementary Figure 12. TAMR effect measurement at T = 20 K and V gate = 20 V. (a) and (b) are two terminal measurement, (c) and (d) are three terminal measurement. In (a) and (c) the red (blue) curve is for increasing (decreasing) magnetic field. In (b) and (d) the wine (violet) curve is for Co magnetization along +y (-y) direction. The insets are the measurements set-up. There is no observable TAMR effect.

Supplementary Note 10. Additional data for samples I, II, III, and VIII
In the section, we show additional data for the samples presented in both the main text and section 6 of the supplementary information (tunneling contacts). Supplementary Figures 13-16 show additional data for sample I of the main text. Fig. 13 shows the non-local MR curves for different gate voltages, measured at 20 K. The black arrows represent the non-local MR values used for Figure 3 (a) of the main text. To ensure the signal comes from spin transport, in-plane Hanle curves for different gate voltages are measured in the parallel magnetization configuration (Fig. 14). This confirms the sign change in spin signal as a function of gate voltage. The data for gate voltage of -20 V are plotted separately in the inset because it possesses a large background drift unrelated to spin (the large drift is absent when antiparallel data are subtracted, as shown in Fig. 15). The Hanle curve for gate voltage of -10 V was not measured because it exhibited no spin signal in the non-local MR. For quantitative analysis, the Hanle curves for parallel and antiparallel magnetizations are subtracted and the symmetric and antisymmetric components are separated (Fig. 15). As mentioned in section 7 above, the origin of the antisymmetric component is unknown but might be related to the edge geometry. More generally, it is not uncommon to have some antisymmetric component in graphene spin valves, and if such components exist then the symmetric component can be used to extract spin lifetimes. The key point here, however, is to show again that the polarity of the spin signal reverses with gate voltage, as can be seen by the symmetric component of the Hanle curves (blue curves in Fig. 15). These Hanle curves are subsequently fit to extract a spin signal amplitude ( Fig. 16 (a)), spin lifetime ( Fig. 16 (b)), and spin diffusion length (Fig. 16 (c) Supplementary Figure 17. Non-local MR curves between electrode '2D' and 'A' of Sample II (first row in main text Figure 4 (a)) at different gate voltages, measured at 20 K. The red (blue) curve is for increasing (decreasing) magnetic field. For clarity, we only show the data once the magnetic field passes zero value.

Sample II electrode '2D' and 'A'
Supplementary Figure 20. Non-local MR curves between electrode '2D' and 'A' of Sample III (first row in main text Figure 4 (b)) at different gate voltages, measure at 20 K. The red (blue) curve is for increasing (decreasing) magnetic field. For clarity, we only show the data once the magnetic field passes zero value.

Sample III electrode '2D' and 'A'
Supplementary Figure 21. Non-local MR curves between electrode '2D' and 'B' of Sample III (second row in main text Figure 4 (b)) at different gate voltages, measured at 20 K. The red (blue) curve is for increasing (decreasing) magnetic field. For clarity, we only show the data once the magnetic field passes zero value for most gate voltage.
For V gate = -50 V and -40 V, we show data for the full sweep because of the observation of a 'hysteresis loop' like background, which could be due to some fringe field of the electrode.

Sample III electrode '2D' and 'B'
Supplementary Figure 22. Non-local MR curves between electrode 'A' and 'B' of Sample III (third row in main text Figure 4 (b)) at different gate voltages, measured at 20 K. The red (blue) curve is for increasing (decreasing) magnetic field. For clarity, we only show the data once the magnetic field passes zero value for most gate voltage.
For V gate = -20 V, 20 V, 30 V and 40 V, we show data for the full sweep because of the observation of a 'hysteresis loop' like background, which could be due to some fringe field of the electrode.