  We present a theoretical study of an interaction-driven quantum phase diagram
of twisted bilayer MoTe$_2$ at hole filling factor $\nu_h=1$ as a function of
twist angle $\theta$ 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 $\theta$
regime and topologically trivial multiferroic states with coexisting
ferroelectricity and magnetism in both small and large $\theta$ 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$^\circ$ 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$^\circ$ 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.
