Device and measurement

A schematic representation of a device along with the nonlocal (NL) technique for measurement of spin signal is shown in Fig. 1a. Spin polarization in CVD graphene is created by electrical spin injection (current I) from a ferromagnetic tunnel contact and the pure spin transport signal (voltage V) is detected by a similar contact placed nonlocally at a distance L. A modulation in the NL spin signal with magnetic field gives an estimate of induced spin polarization, and other spin parameters such as the spin lifetime τ s and diffusion length λ s in graphene. Essentially, two kinds of measurements are performed in all our CVD graphene devices having different channel lengths. First, the spin injection efficiency and spin transport distance are evaluated from spin valve measurement, where an in-plane magnetic field (B ‖ ) parallel to the ferromagnetic electrodes is swept to measure the change in pure spin signal between parallel and antiparallel configurations of magnetizations of the ferromagnetic electrodes. Next, the spin lifetime τ s , diffusion constant D s and diffusion length λ s are obtained by Hanle measurement, in which an out-of-plane magnetic field (B ⊥ ) perpendicular to the magnetization of ferromagnetic electrodes is swept to obtain continuous variation in spin signal due to spin precession. Devices having long CVD graphene channels with ferromagnetic tunnel contacts (TiO 2 /Co) were fabricated to achieve long-distance spin transport. We employed large-area CVD graphene grown on copper foil, which was transferred onto SiO 2 /Si substrate and patterned into long channels. The ferromagnetic tunnel contacts were prepared by electron beam lithography and liftoff techniques. The TiO 2 barrier in the tunnel contacts was prepared by an evaporation of 8 Å of Ti and oxidation in an oxygen atmosphere. Subsequently, 65 nm of Co and a capping layer of 4 nm of Al were deposited by electron beam evaporation. The details of the device fabrication process are described in the Methods section. An optical microscope image of a fabricated device with 16-μm-long graphene channel and multiple TiO 2 /Co contacts is presented in Fig. 1b. The spin transport measurements were performed using DC currents, in the temperature range of 4.2–300 K.

Figure 1: CVD graphene field effect device for pure spin transport. (a) Schematic representation of a graphene device with ferromagnetic tunnel contacts for spin injection and detection in NL geometry. The current (I) injection circuit creates spin polarization in graphene via electrical spin injection and the isolated voltage (V) measurement circuit probes the NL pure spin signal. The red colour represents the spin density, which diffuses away from the place of injection in the graphene channel. The highly doped Si with SiO 2 layer is used as the back gate to control the carrier density (n) in graphene. (b) Optical microscope image of a fabricated long channel CVD graphene device on SiO 2 /Si substrate with multiple ferromagnetic tunnel contacts of Co/TiO 2 patterned by electron-beam lithography. The NL measurement scheme is presented for 16-μm-long graphene channel with current (I) and voltage (V) circuits. Full size image

Structural and electrical characterization of CVD graphene

To understand the quality of graphene channel and the TiO 2 /Co tunnel contacts, we performed detailed structural and electrical characterization of the devices. Figure 2a displays an atomic force microscope image of the graphene channel in a device with relatively low density of ripples and resist residues on a region extending over 20 μm. Our optimized fabrication process ensured that the ripples introduced during the transfer process are sparse (height ∼1 nm shown in Fig. 2a). Figure 2b shows a representative Raman spectrum of CVD graphene, where a dominant 2D peak is observed compared to the G peak confirming its single-layer nature. In addition, the D peak was found to be of negligible intensity, indicating a low sp3-type or vacancy defect density46. Raman spectra taken at different places in all graphene channels yielded similar results, indicating uniformity in the CVD graphene.

Figure 2: Characterization of the CVD graphene and ferromagnetic tunnel contacts. (a) Atomic force microscope image of a graphene channel, with scale bar of 5 μm along with a magnified image of a ripple featuring region and its height profile scan. (b) Representative micro Raman spectrum of CVD graphene channel. (c) Graphene channel resistance (R ch ) for different channel lengths as a function of gate voltage (V g )–Dirac point (V D ) (Dirac curves) at room temperature. (d) The linear enhancement of the resistance with graphene channel length at V g −V D =0. (e) Three-terminal I–V characteristics of a Co/TiO 2 /graphene contact at different temperatures. (f) Differential conductance g(dI/dV) plot of the contact as a function of bias voltage at different temperatures. Full size image

Next, the quality of the graphene was electrically assessed by the Dirac curves obtained from four probe channel resistance measured as a function of the gate voltage (V g ). As shown in Fig. 2c, the resistance scales linearly with channel lengths, indicating a global uniformity of the CVD graphene. The carrier mobility evaluated from the Dirac curves was found to be ∼2,000 cm2 V−1 s−1 with sheet resistance ∼5 kΩ/□ for different channels at room temperature. The similar sheet resistance of channels indicates a similar diffusion constant (D c ) over a large area (see Supplementary Note 1 and Supplementary Table 1). The Dirac points (V D ) were seen to lie in the range of −3 to −10 V, indicating a low doping of graphene. The typical temperature dependence of the Dirac curves of a graphene channel are shown in Supplementary Fig. 1. It reveals a weak temperature dependence of graphene resistivity, indicating a dominating role of static scatterers. We obtain momentum scattering time τ p ∼20–50 fs and electron mean free path l mfp ∼20–50 nm (depending on the gate voltage) for all graphene channels. The low mean free path compared with the device dimension (several μm) along with a similar charge diffusion constant (D c ) confirms the diffusive regime of electrical transport in CVD graphene (see Supplementary Note 1 and Supplementary Table 1). Grain boundaries in CVD graphene can contribute substantially to the residual resistance R ch (4.2 K)37, and the nature of impurities at the grain boundaries can further affect spin transport in CVD graphene. The grain size in the CVD graphene employed here was found to lie between 1 and 10 μm with median grain size ∼2 μm over a large scale. We also note that the grain concentration varied from device to device (as the device dimensions are comparable to the grain size, especially for shorter channels). In spite of this, we obtained a fairly linear dependence of resistance with length of the channel (shown in Fig. 2d), indicating a low contribution of grain boundary scattering to the resistance. In addition, the low mean free path further indicates the dominance of intra-grain scattering to the momentum relaxation and thus the spin relaxation. Such intra-grain scattering can be attributed to substrate-induced disorder effects and defects induced during transfer process39,45. The interface resistance (R i ) of the ferromagnetic tunnel contacts obtained from three-terminal measurements was found to be 4–5 kΩ at room temperature. Figure 2e shows typical nonlinear tunnelling current–voltage (I–V) characteristics of a TiO 2 /Co contact with weak temperature dependence. The corresponding differential conductance in Fig. 2f also shows a minimum at zero voltage at all the temperatures. These characteristics indicate the dominating tunnelling transport in Co/TiO 2 /graphene contacts47. The contact resistances R i are found to be of the order of the square resistance of graphene channel R Sq (see Supplementary Fig. 2) and can circumvent the conductivity mismatch problem48,49 for spin injection.

Long-distance spin transport and precession in CVD graphene

To demonstrate the long-distance spin transport in CVD graphene, systematic measurements were performed on various channel lengths extending up to 16 μm. The spin valve and Hanle precession measurements were carried out in four-terminal NL configurations (as depicted in Fig. 3). Spin-polarized electrons are electrically injected from the ferromagnetic tunnel contact in the current circuit, which diffuse in the graphene channel and are detected by the NL voltage circuit. The isolated current and voltage circuits in the NL configuration ensure measurement of pure spin signals without spurious charge-related magneto-resistive contributions from ferromagnetic contacts or graphene channel. For an NL spin signal V=V NL measured at the detector (Det) with respect to reference electrode, an NL resistance is defined as R NL =V NL /I, with I being the current through the injector (Inj). A change in the magnetization configuration of the injector (Inj) and detector (Det) ferromagnets from parallel (↑↑ or ↓↓) to antiparallel (↑↓ or ↓↑) alignment leads to a spin valve signal change ΔV NL , characterized by an NL resistance change ΔR NL =ΔV NL /I. It is a measure of the spin splitting (Δμ=μ ↑ −μ ↓ , with μ ↑ and μ ↓ being the chemical potentials of up (↑) and down (↓) spins, respectively) present in the graphene channel under the detector contact. The different shape anisotropies of the ferromagnets (Inj and Det) ensure different switching fields for the observation of spin valve signal by sweeping an in-plane magnetic field B ‖ . In Fig. 3a, we show the spin valve signal obtained on a graphene channel with L =16 μm at room temperature and a gate voltage V g =0 V. Spin valve signals with clear switching in such long channels have not been observed before in any form of pristine graphene on conventional Si/SiO 2 substrates at room temperature. The spin signals for channel lengths beyond 16 μm were dominated by noise in our measurements.

Figure 3: Long-distance spin transport in CVD graphene device at room temperature. (a) NL spin valve signal with channel length L=16 μm with in-plane magnetic field (B ‖ ) sweep as depicted in the figure. The high and low values of NL resistance R NL correspond to the parallel (↑↑ or ↓↓) and antiparallel (↑↓ or ↓↑) configurations of the ferromagnetic injector (Inj) and detector (Det) electrodes, respectively. The blue and red colours indicate the direction of magnetic field sweep as represented by the arrows with respective colours. (b) NL Hanle spin precession signal obtained by a perpendicular magnetic field (B ⊥ ) sweep in parallel configuration (↑↑) of ferromagnetic electrodes for L=16 μm graphene channel. The raw data points are fitted with the Hanle equation, to extract spin lifetime τ s and spin diffusion constant D s . Full size image

We further establish the spin transport in such long channels and evaluate the spin parameters through NL Hanle spin precession measurements (Fig. 3b). In the Hanle geometry, although the ferromagnetic electrodes are kept parallel, the injected spins undergo Larmor precession (frequency ; Landé g-factor g=2) about the perpendicular magnetic field (B ⊥ ) resulting in a modulation of the detected spin signal. To evaluate the spin parameters (signal amplitude ΔR NL , lifetime τ s , diffusion length λ s , diffusion constant D s ), we fit the data with the empirical formula Eq. (1) encompassing the spin diffusion, precession and dephasing contributions9,11,13.

where L is the effective channel length between the injector and the detector in our devices. The width W of the graphene channel is 5 μm and the measured graphene square conductivity σ s ∼200 μS. At 300 K, for V g =0 and L=16 μm, we obtain a spin lifetime of τ s =1.23±0.101 ns with spin diffusion constant D s =0.0264±0.002 m2 s−1, yielding a spin diffusion length λ s ∼6 μm. These values are the highest spin parameters achieved so far in CVD graphene and also in any form of pristine graphene on SiO 2 /Si substrate at room temperature. The parameters are also higher than the reports of high-quality exfoliated graphene on h-BN substrate2 or suspended devices15,26 and comparable to the most recent h-BN encapsulated high-quality exfoliated graphene devices27,28.

Channel length dependence of the spin signal

Systematic NL measurements were performed on various channel lengths L=2–16 μm at room temperature. Figure 4a shows representative spin valve and Hanle measurements for channel lengths of 4, 6 and 12 μm. The NL spin valve resistance ΔR NL is found to decrease for increasing channel lengths, from 4 Ω in L=2 μm to 20 mΩ in L=16 μm at room temperature. Figure 4b presents the corresponding Hanle data measured for different channels along with fits to equation (1). The extracted spin parameters from Hanle fits are found to be in the range of τ s =0.4–1.2 ns, D s =0.018–0.026 m2 s−1 and λ s ∼3–6 μm for various channel lengths with V g =40 V at room temperature (see Supplementary Table 1). Note that for each channel the charge diffusion constants (D c ) evaluated from the Dirac curves matched reasonably well with the spin diffusion constants (D s ), which supports our current analysis. Although at a constant carrier density, small disparity and variations between the D c and D s are observed, including device to device variation, but the differences are very close and well within affordable limits (D c =0.022±0.005) as widely reported2,10,20. We observe higher values of extracted τ s and λ s for longer graphene channels as presented in Fig. 4c. Notably, the longer channels increase the diffusion time, ensuring a higher accuracy in probing the graphene channel properties and hence the spin parameters. Such devices with longer channels also reduce the effect of contacts and dimensionality problems that can lead to possible underestimation of spin parameters50,51.

Figure 4: Channel length-dependent spin transport in CVD graphene. (a) Spin valve measurements in device with different graphene channel lengths at room temperature and V g =0 V. (b) Hanle spin precession measurements at room temperature in device with different graphene channel lengths along with fitting with equation (1) and extracted spin parameters τ s and D s at V g =40 V. (c) Spin lifetime τ s and spin diffusion length λ s with graphene channel L=2–16 μm at V g =0 (blue circles) and 40 V (red circles) at room temperature as extracted from the Hanle fitting. (d) Length dependence of the spin signal and scaling fit () to spin signal for graphene channel L=2–6 μm on a device using one injection contact at 100 and 300 K for V g =0 V. Full size image

To avoid any ambiguity, we also evaluated the spin parameters in an alternative way from the length dependence of the spin signal . Figure 4d shows the length dependence of the ΔR NL for L=2–6 μm graphene channels at 300 and 100 K for V g =0 V. It has to be noted that the measurements with L=2–6 μm belong to a single device with the same contact being used for spin injection. With a fairly good uniformity in the electronic quality of our CVD graphene over a large area, we obtained spin diffusion lengths λ s =8.5 and 6.3 μm at 100 and 300 K, respectively. We did not consider devices having different injector contacts or devices from different batches of fabrication, as they might lead to uncertainty arising out of varied contact properties. The spin diffusion length obtained here complements the results of the Hanle measurements (λ s ∼6 μm) for the longest channel fairly well.

Temperature and carrier density dependence of spin parameters

We now present the detailed temperature and gate-dependent measurements showing the evolution of the spin transport in CVD graphene. The temperature dependence of spin parameters in devices with different channel lengths (shown in Fig. 5a,b) indicates an increase in ΔR NL and τ s at lower temperatures. Such increase has also been observed in previous studies on exfoliated graphene crystals11. Similarly, enhancement of ΔR NL and τ s are also observed with increase in applied gate voltage V g (increased carrier concentration n in graphene) as displayed in Fig. 5c,d. Increased carrier concentrations can effectively reduce the spin–orbit coupling in graphene on SiO 2 substrate, as theoretically proposed recently52. This can significantly reduce the spin flip scattering and enhance the spin lifetime as observed in our devices. Such enhancement of ΔR NL and τ s can also be attributed to the competition between the resistances of graphene channel R ch and the tunnel contacts R i , as R ch is observed to decrease with gate voltage. A high R i is expected to prevent back diffusion of spins into the ferromagnet and faster spin relaxation48. The observed enhancement in ΔR NL and τ s in our case is in agreement with behaviour expected for relatively low resistive tunnel barriers (R i ∼R ch )10,53. In addition, recent theoretical results based on spin–pseudo spin interaction in graphene also show reduction of spin parameter at low energy (closer to Dirac point)54. In convergence with theoretical predictions, the increasing trends of ΔR NL and τ s were reproducibly observed in all CVD graphene channels in our study. These observations also clearly indicate that the spin parameters at room temperature can be further enhanced with higher carrier density in graphene, which can be achieved by using ultra-thin gate dielectrics on graphene channels. The data presented here were measured using an injection current of 30 μA. No significant variation of either the ΔR NL or τ s was detected for bias currents in the range 5–50 μA.