  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.
