Magnetoelectric Switching of Competing Magnetic Orders in Rhombohedral Graphene.

A finite Hall conductance in the absence of an external magnetic field indicates time-reversal symmetry (TRS) breaking arising from magnetic order. In rhombohedral (RH) stacked graphene, TRS can be broken through orbital angular momentum associated with the K and K' valleys of the Brillouin zone. This orbital mechanism gives rise to valley polarization- and occupation-dependent anomalous Hall resistance (AHR) due to the opposite Berry curvature chiralities of the two valleys. Here, we demonstrate magnetoelectric control of orbital magnetic order in crystalline rhombohedral hexalayer graphene (RHG), achieved without the introduction of a moiré superlattice. At moderate displacement fields and low carrier densities, we detect a non-volatile, hysteretic AHR that can be reversibly switched by tuning either the carrier density or the displacement field. When a small perpendicular magnetic field is applied, the AHR exhibits a characteristic double sign reversal, revealing competition between distinct magnetic ground states. This coupling between valley polarization and external electric and magnetic fields highlights the multiferroic nature of RHG. Our findings present crystalline RHG as a minimal, tunable platform for studying symmetry-breaking phases and magnetic order in flat-band systems, offering insight into the coupling between electronic structure and magnetoelectric response.