The atomic thickness of two-dimensional materials provides a unique opportunity to control their electrical and optical properties as well as to drive the electronic phase transitions by electrostatic doping. The discovery of two-dimensional magnetic materials has opened up the prospect of the electrical control of magnetism and the realization of new functional devices. A recent experiment based on the linear magneto-electric effect has demonstrated control of the magnetic order in bilayer CrI by electric fields. However, this approach is limited to non-centrosymmetric materials magnetically biased near the antiferromagnet-ferromagnet transition. Here, we demonstrate control of the magnetic properties of both monolayer and bilayer CrI by electrostatic doping using CrI-graphene vertical heterostructures. In monolayer CrI, doping significantly modifies the saturation magnetization, coercive force and Curie temperature, showing strengthened/weakened magnetic order with hole/electron doping. Remarkably, in bilayer CrI, the electron doping above ~2.5 × 10 cm induces a transition from an antiferromagnetic to a ferromagnetic ground state in the absence of a magnetic field. The result reveals a strongly doping-dependent interlayer exchange coupling, which enables robust switching of magnetization in bilayer CrI by small gate voltages.

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Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moiré materials provide a highly tunable platform for studies of electron correlation 1-12 . Correlation-driven phenomena, including the Mott insulator 2-5 , generalized Wigner crystals 2, 6, 9 , stripe phases 10 and continuous Mott transition 11,12 , have been demonstrated. However, nontrivial band topology has remained elusive. Here we report the observation of a quantum anomalous Hall (QAH) effect in AB-stacked MoTe 2 /WSe 2 moiré heterobilayers. Unlike in the AAstacked structures 11 , an out-of-plane electric field controls not only the bandwidth but also the band topology by intertwining moiré bands centered at different highsymmetry stacking sites. At half band filling, corresponding to one particle per moiré unit cell, we observe quantized Hall resistance, 𝒉𝒉/𝒆𝒆 𝟐𝟐 (with h and e denoting the Planck's constant and electron charge, respectively), and vanishing longitudinal resistance at zero magnetic field. The electric-field-induced topological phase transition from a Mott insulator to a QAH insulator precedes an insulator-to-metal transition; contrary to most known topological phase transitions 13 , it is not accompanied by a bulk charge gap closure. Our study paves the path for discovery of a wealth of emergent phenomena arising from the combined influence of strong correlation and topology in semiconductor moiré materials.Two-dimensional moiré heterostructures of van der Waals materials present a new paradigm for engineering electron correlation, topology, and their interplay 8, 14-16 . In graphene systems, moiré patterns can produce topologically nontrivial bands with valleycontrasting Chern numbers to enforce time-reversal symmetry of the single-particle band structure 14 . With sufficiently flat bands, correlation-driven states with broken symmetry are favored. Orbital ferromagnetism and the QAH effect have been reported [17][18][19] following the initial discovery of superconductivity and correlated insulating states in graphene moiré systems 20 . Conversely, in semiconducting transition metal dichalcogenide (TMD) heterobilayers, the moiré bands are topologically trivial 1,7 . The

The interaction induced localization of electrons -the Mott transition -is expected to occur in the half-filled Hubbard model [1][2][3]24,25 . The ground state is a metal with a sharply defined electronic Fermi surface when the kinetic energy of the electrons -characterized by the bandwidth 𝑊far exceeds their interaction energy -characterized by the on-site Coulomb repulsion 𝑈 . Conversely, when 𝑈 ≫ 𝑊, the ground state is an electrical insulator with a charge-gap. The system undergoes a MIT when 𝑈 and 𝑊 become comparable. Although this picture is widely accepted from the seminal works of Mott and Hubbard, the nature of the transition remains poorly understood. In most materials, the transitions are driven first-order and often accompanied by simultaneous magnetic, structural or other forms of ordering 1,3 . Continuous MIT, which exhibits no symmetry

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