Voltage-Controlled Magnetic Reversal in Orbital Chern Insulators

Chern insulator ferromagnets are characterized by a quantized anomalous Hall effect, and have so far been identified experimentally in magnetically-doped topological insulator (MTI) thin films and in bilayer graphene moir{\'e} superlattices. We classify Chern insulator ferromagnets as either spin or orbital, depending on whether the orbital magnetization results from spontaneous spin-polarization combined with spin-orbit interactions, as in the MTI case, or directly from spontaneous orbital currents, as in the moir{\'e} superlattice case. We argue that in a given magnetic state, characterized for example by the sign of the anomalous Hall effect, the magnetization of an orbital Chern insulator will often have opposite signs for weak $n$ and weak $p$ electrostatic or chemical doping. This property enables pure electrical switching of a magnetic state in the presence of a fixed magnetic field.