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 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 magnetically doped topological insulator 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.