Supplementary information for ’ Proximity induced room-temperature ferromagnetism in graphene probed with spin currents ’

I. Characterisation of the YIG/GGG films 2 II. Charge and spin transport properties of the graphene flake 2 III. Characterisation of the graphene flake and cobalt electrodes 4 IV. Discussion of the full data sets. Effect of the cobalt stray field on the YIG magnetisation direction 4 V. Potential stray fields arising from the YIG film and their absence in our measurements 6 VI. Absence of a parallel magnon transport channel 7 VII. Comparison to a reference sample 8 VIII. Full set of spin transport modulation data 8 IX. Comparison with spin transport modulation in metal/YIG systems 9 X. Modelling 10 References 12

The introduction and control of ferromagnetism in graphene opens up a range of new directions for fundamental and applied studies [1,2]. Several approaches have been pursued so far, such as introduction of defects, functionalisation with adatoms, and shaping of graphene into nanoribbons with welldefined zigzag edges [3][4][5][6][7][8]. A more robust and less invasive method utilises the introduction of an exchange interaction by a ferromagnetic insulator (FMI) in proximity with graphene [9][10][11][12][13][14][15][16]. The magnetic proximity effect describes the introduction of ferromagnetic order into an intrinsically nonmagnetic material by an adjacent ferromagnet due to the exchange interaction between the spins in the magnetic and non-magnetic material. Being atomically thin, graphene presents an ideal platform for studying such interaction, in particular when combined with a FMI. Theory predicts that for the idealised case of (super) lattice matching an exchange splitting of tens of meV can be obtained [16]. Up to date it has been studied experimentally in a number of FMI/graphene systems using materials with low Curie temperature such as EuO = ( ) T 69 K c and EuS = ( ) T 16.5 K c [13,14]. In comparison, yttrium-iron-garnet (YIG) provides the advantage of a Curie temperature of 550 K, along with chemical stability in atmospheric conditions, the preservation of the charge transport properties in the graphene and the possibility to directly exfoliate or transfer graphene onto the surface for fabricating graphene-based spintronic devices.
As indication of a ferromagnetic exchange interaction in graphene/YIG heterostructures the observation of an anomalous Hall effect was reported [9]. More recently, the presence of an exchange interaction in YIG/CVD graphene devices was invoked to explain magnetoresistance measurements and ferromagnetic resonance spin pumping [15]. So far, in all the reports the authors employ charge transport, where in addition to exchange interaction also spin-orbit interaction is needed for the understanding, both a priori unknown parameters.
In this work, we probe the induced exchange interaction in graphene in the most direct way using only the spin degree of freedom. The magnetic interaction between the YIG magnetisation and the graphene spins is expected to produce an exchange term in the Hamiltonian and to spin split the graphene energy bands ( figure 1(a)). It can be described as an additional effective exchange field that is determined by the direction and magnitude of the YIG magnetisation. By studying its effect on spin transport and precession, and fitting the results with the modified Bloch spin diffusion equation we are able to describe our results qualitatively and quantitatively. We further Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
demonstrate that the precession induced by the exchange field can be used for an efficient modulation of spin currents.
The device is shown in figures 1(b) and (c). A single layer graphene flake of approximately 12 μm by 1.2 μm is first exfoliated on SiO 2 and transferred to YIG. Ferromagnetic contacts are defined via e-beam lithography followed by Ti deposition, in situ oxidation to form TiO 2 , Co deposition and liftoff. A nonlocal spin valve characterisation [17] is shown in figure 2. A charge current is sent from the injector to the reference electrode. As a result a pure spin current diffuses through the channel and is detected as a voltage difference between the detecting and another reference electrode. The spin-transport measurements are obtained using contacts 1 and 2 as injector and detector with contact spacing m = d 1.2 m. The magnetisation direction of the injector (detector) can be controlled by sweeping the applied magnetic field along the easy axis of the electrodes. Figure 2(b) shows the change of the non-local resistance (R NL ) when the electrode configuration is switched between parallel and antiparallel alignment. The change in R NL is a pure spin signal that increases from 90 mΩ at room temperature to 650 mΩ at 75 K. To determine the spin relaxation length λ, we fit the dependence of the spin signal on d and extract λ=(490±40) nm (see footnote 2). These values are comparable to our other graphene devices on YIG or SiO 2 [18], which confirms that the basic spin transport properties of graphene are conserved after transfer to YIG.
To investigate the presence of the exchange field, we study the Hanle spin precession (figure 3(a)). A perpendicular magnetic field causes injected spins to precess while diffusing along the channel, changing the average polarisation and direction of the spins at tot app exch B app is swept perpendicular to the sample plane and causes the Zeeman splitting of the graphene spins, Zeeman B app The exchange field is determined by the YIG magnetisation direction M and the interface properties and is defined as Here g is the gyromagnetic factor (∼2 for graphene) and m B the Bohr magnetron 2 .
Typical Hanle curves for graphene devices on SiO 2 [19] or hBN [20] substrates are smooth in the full measured range, whereas we clearly observe a sharp transition atB 180 mT app in our sample. The kink is seen for both parallel and antiparallel injector/detector magnetisations at all measured temperatures although it becomes more pronounced at 75 K. The appearance of such transition requires an additional spin precession caused by the exchange field B exch that is constant in magnitude and collinear with M. When no external field is applied, M together with B exch lies within the sample plane and is gradually pulled out of the plane with increasing B .
app The transition point coincides with the saturation field of the YIG  To further confirm the presence and magnitude of the exchange field, we utilise the low in-plane coercivity of YIG. By applying and rotating a small magnetic field of 20 mT in the sample plane we can control the magnetisation direction of the YIG without applying a significant spin precession with the applied field. Furthermore, we maintain the parallel/antiparallel alignment of the injector/detector electrodes (figure 4(a)), leaving the injected/detected spins unaffected. When B exch is collinear with the injected spin polarisation b =   ( ) 90 it has no influence on the spin transport, whereas at b =  0 the diffusing spins experience the maximum precession and dephasing. In figure 4(b) the dependence of the spin signal on β is shown for both parallel and antiparallel magnetisation alignment. For m = d 0.9 m (contacts 2 and 3, figure 1(c)) the observed modulation is around 50%, which is substantial and cannot be explained by the effect of extrapolating the data to = d 0, we find ∼35% modulation which can be described with our model: which resembles the l extracted from distance dependent spin signal, again suggesting an inhomogeneous exchange field.
In summary, we have demonstrated the detection of ferromagnetic exchange field in graphene by spin transport at room temperature, 75 and 4.7 K. The exchange field strength is quantified in two different experimental configurations to be approximately 0.2 T. Given the theoretical results on idealised systems, substantial enhancement should be possible by appropriate interface optimisation [16]. We proposed spin-transport measurements as the most direct way to study the exchange field in graphene. Furthermore, we showed that a spin current can be efficiently modulated by controlling the exchange field, which opens up new directions to control spins in graphene based spintronic devices.

Methods
Our graphene flakes are exfoliated from HOPG graphite crystals (HQ Graphene) on silicon oxide substrates. Single layer graphene flakes are selected by optical contrast and transferred to target substrates with a custom-built transfer stage using a polycarbonate based pickup technique. The commercially available (111) single crystal YIG films (Matesy GmbH) are grown by liquid phase epitaxy with 210 nm YIG thickness on GGG substrates. The films are cleaned with acetone, isopropanol and 180 s in 200 W oxygen plasma to remove organic residues. To minimise water contamination at the interface between graphene and YIG, the substrates are kept for 15 min in a furnace at 500°C, until the graphene is transferred at 140°C.
After transfer, the polycarbonate is dissolved in chloroform and the graphene is cleaned for one hour in a furnace at 350°C in an Ar/H 2 atmosphere. The flake is connected with electrodes made of titanium oxide tunnel barriers (0.8 nm), ferromagnetic cobalt electrodes (45 nm) and an aluminium capping layer (5 nm) using e-beam lithography. The samples are characterised in a cryostat with standard AC-lock-in measurement techniques at room as well as low temperatures. We apply typical AC currents between 1 and 20 μA with frequencies between 1 and 13 Hz. At 75 K the electrodes show a contact resistance of the order of 1-3 kΩ and a spin signal between 7 Ω at 500 nm contact spacing and 10 mΩ at 3.9 μm spacing. Measurements of Shubnikov-de Haas oscillations at T=2 K, reveal a carrier density of the order of´-3 10 cm 12 2 and a mobility of 720 cm 2 V −1 s −1 . In different graphene/YIG samples we observe holes as charge carriers resulting from doping during the transfer process. Further details are discussed in the supplementary information.

Acknowledgments
We acknowledge A Aqeel, P Zomer, M de Roosz and J G Holstein for technical assistance, J Ingla-Aynes and A M Kamerbeek for fruitful discussions. This research has received funding from the European Union's 7th Framework Programme within the Marie Curie initial training network 'Spinograph' (grant 607904), the 'Graphene Flagship' (grant 604391) and the Dutch 'Foundation for Fundamental Research on Matter' (FOM).
Author contributions BJvW, JCL, AAK and MW conceived the experiments. JCL and AAK designed and carried out the experiments. JCL, AAK and BJvW analysed and discussed the data and wrote the manuscript.
Competing financial interests The authors declare no competing financial interests.