The layered antiferromagnetic MnBi2Te4 films have been proposed to be an intrinsic quantum anomalous Hall (QAH) insulator with a large gap. To realize this proposal, it is crucial to open a magnetic gap of surface states. However, recent experiments have observed gapless surface states, indicating the absence of out-of-plane surface magnetism, and thus the quantized Hall resistance can only be achieved at the magnetic field above 6 T. In this work, we propose to induce out-of-plane surface magnetism of MnBi2Te4 films via the magnetic proximity with magnetic insulator CrI3. Our calculations have revealed a strong exchange bias ~ 40 meV, originating from the long Cr-eg orbital tails that hybridize strongly with Te p-orbitals. By stabilizing surface magnetism, the QAH effect can be realized in the MnBi2Te4/CrI3 heterostructure. Our calculations also demonstrate the high Chern number QAH state can be achieved by controlling external electric gates. Thus, the MnBi2Te4/CrI3 heterostructure provides a promising platform to realize the electrically tunable zero-field QAH effect.
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