Orbital longitudinal magnetoelectric coupling in rhombohedral multilayer graphene
2026-01-29
Magnetoelectric coupling enables the manipulation of magnetization by electric fields and polarization by magnetic fields. While typically found in heavy element materials with large spin–orbit coupling, recent experiments on rhombohedral-stacked pentalayer graphene have demonstrated a longitudinal magnetoelectric coupling (LMC) without spin–orbit coupling. Here, we develop a microscopic theory of LMC in layered quantum materials and identify how it is controlled by a “layer-space” quantum geometry. Focusing on rhombohedral multilayer graphene systems, we find that the interplay between LMC and valley-polarized order produces a butterfly shaped magnetic hysteresis controlled by out-of-plane electric field: a signature of LMC and a multiferroic valley order. Furthermore, we identify a nonlinear LMC in rhombohedral multilayer graphene under time-reversal symmetry, while the absence of centrosymmetry enables the generation of a second-order nonlinear electric dipole moment in response to an out-of-plane magnetic field. Our theoretical framework provides a quantitative understanding of LMC, as well as the emergent magnetoelectric properties of rhombohedral multilayer graphene.