Electrically tuned topology and magnetism in twisted bilayer MoTe_2 at ν_h=1

We present a theoretical study of an interaction-driven quantum phase diagram of twisted bilayer MoTe_2 at hole filling factor ν_h=1 as a function of twist angle θ and layer potential difference V_z, where V_z is generated by an applied out-of-plane electric field. At V_z=0, the phase diagram includes quantum anomalous Hall insulators in the intermediate θ regime and topologically trivial multiferroic states with coexisting ferroelectricity and magnetism in both small and large θ regimes. There can be two transitions from the quantum anomalous Hall insulator phase to topologically trivial out-of-plane ferromagnetic phase, and finally to in-plane 120^∘ antiferromagnetic phase as |V_z| increases, or a single transition without the intervening ferromagnetic phase. We show explicitly that the spin vector chirality of various 120^∘ antiferromagnetic states can be electrically switched. We discuss the connection between the experimentally measured Curie-Weiss temperature and the low-temperature magnetic order based on an effective Heisenberg model with magnetic anisotropy.