Magnetic exchange field in magnetic multilayers can potentially reach tens or even hundreds of Tesla. 6 The single-atomic-layer (2D) materials, such as graphene, mono-layer WS 2 etc., is expected to experience the strongest MEF in heterostructures with magnetic insulators due to the short-range nature of magnetic exchange coupling. 4 2D material/magnetic insulator heterostructures enable local spin modulation by magnetic gates, 4,5,7 and the realization of efficient spin generation for spintronic applications. 8,9 As a proof of concept, here we demonstrate substantial MEF and spin polarization in CVD graphene/EuS heterostructures. We have chosen EuS as a model magnetic insulator because of its wide band-gap (1.65 eV), large exchange coupling J~10 meV, and large magnetic moment per Eu ion ௭~7 , 10 yielding large estimated exchange splitting ௭ in graphene. 4,5 EuS has also been shown to spin-polarize quasiparticles in materials including superconductors and topological insulators. 6,11 The strength of the MEF depends critically on the interface and EuS quality, 12,13 which we optimize with an in-situ cleaning and synthesis process (Methods and Fig. 1a). In contrast to other means, such as defect-or adatom-induced spin polarization, 14,15 depositing insulating EuS well preserves graphene's chemical bonding, confirmed by Raman spectroscopy (Fig. 1b) (Fig. S5-1), indicative of high graphene quality and well-preserved Dirac band structure.We utilize Zeeman spin-Hall effect (ZSHE) to probe the MEF in graphene which splits the Dirac cone via Zeeman effect and generates electron-and hole-like carriers with opposite 4 spins near the Dirac point ( Fig. 2a right panel). 8,9 Under a Lorentz force, these electrons and holes propagate in opposite directions, giving rise to a pure spin current and non-local voltage ( Fig. 2a left panel). We measure the non-local resistance of ZSHE using the device configuration in Fig. 2a where ௫ is the MEF. We further define the parameter :where ௭ denotes the Zeeman energy at the reference field . Given , deriving of graphene/AlO x is straightforward because ௭ is solely determined by . The inset of Fig. 3(b) shows the calculated using T, a proper reference field as we will explain below.To derive of graphene/EuS, we note that according to the theory of ZSHE, 9,17 depends on sample mobility, while other sample-dependents terms (including spin relaxation length, density of thermally activated carriers and Fermi velocity) cancel out (see S3 in SI). The mobility difference between our graphene/EuS and graphene/AlO x samples is~25% (see S1 in SI), which would only yield a~10% correction to  (see S3 in SI). Since~10% difference is 6 small, for an order-of-magnitude estimate of the MEF, we adopt the value of graphene/AlO x for graphene/EuS as an approximation. We then evaluate E Z in graphene/EuS usingTo obtain the lower bound of , we approximate , ignoring the ௫contribution. This constrains us to use a small such that ௫ is small. Meanwhile, should be high enough to ensure that , is much large...

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