Current Driven Magnetization Reversal in Orbital Chern Insulators

Graphene multilayers with flat moir\'e minibands can exhibit the quantized anomalous Hall effect due to the combined influence of spontaneous valley polarization and topologically non-trival valley-projected bands. The sign of the Hall effect in these Chern insulators can be reversed either by applying an external magnetic field, or by driving a transport current through the system. We propose a current-driven mechanism whereby reversal occurs along lines in the (current $I$, magnetic-field $B$) control parameter space with slope $dI/dB = (e/h)\, M A_{M} \, (1-\gamma^2)/\gamma$, where $M$ is the magnetization, $A_M$ is the moir\'e unit cell area, and $\gamma <1$ is the ratio of the chemical potential difference between valleys along a domain wall to the electrical bias $eV$.