Magnetoelectric Switching of Magnetic Order in Rhombohedral Graphene

A finite Hall conductance under zero magnetic field implies time reversal symmetry (TRS) breaking due to magnetic order. In rhombohedral stacked multilayer graphene, the angular momentum that breaks TRS can result from the orbital degree of freedom at the $K$ and $K'$ valleys. This leads to valley polarization and occupation-dependent anomalous Hall resistance (AHR) due to the chirality in Berry curvature at the valleys. We report magnetoelectric control of orbital magnetic order in crystalline rhombohedral hexalayer graphene (R6G), achieved without the introduction of a moiré superlattice. At moderate displacement fields and low carrier densities, we observe a non-volatile and hysteretic AHR that can be electrically toggled by sweeping either the carrier density or the displacement field. Upon the application of small perpendicular magnetic fields, the system reveals a characteristic double sign reversal of the AHR, indicating a competition between distinct magnetic ground states. This interplay between valley polarization and electric and magnetic field tuning demonstrates the rich multiferroic behavior of R6G. Our findings present crystalline R6G as a minimal, tunable platform for studying symmetry-breaking phases and magnetic order in flat-band systems, offering insights into the coupling between electronic structure and magnetoelectric response.