  Recently, signatures of quantum anomalous Hall states with spontaneous
ferromagnetism were observed in twisted bilayer graphenes (TBGs) near 3/4
filling [1, 2]. Importantly, it was demon-strated that an extremely small
current can switch the direction of the magnetization. This offers the prospect
of realizing low energy dissipation magnetic memories. However, the mechanism
of the current-driven magnetization switching is poorly understood as the
charge currents in graphene layers are generally believed to be non-magnetic.
In this work, we demonstrate that, in TBGs, the twist-induced reduction of
lattice symmetry allows a charge current to generate net orbital magnetization
at a general filling factor through magnetoelectric effects. Substrate-induced
strain and sublattice symmetry breaking further reduce the symmetry such that
an out-of-plane orbital magnetization can be generated. Due to the large
non-trivial Berry phase of the flat bands, the orbital magnetization of a Bloch
state can be as large as tens of Bohr magnetons and therefore a small current
would be sufficient to generate a large orbital magnetization. We further
demonstrate how the charge current with orbital magnetization can switch the
magnetization of the quantum anomalous Hall state near 3/4 filling as observed
in the experiments [1, 2].
