Competing magnetic states on the surface of multilayer ABC-stacked graphene

We study interaction-mediated magnetism on the surface of ABC-multilayer graphene driven by its zero-energy topological flat bands. Using the random-phase approximation we treat onsite Hubbard repulsion and find multiple competing magnetic states, due to both intra- and inter-valley scattering, with the latter causing an enlarged magnetic unit cell. At half-filling and when the Hubbard repulsion is weak, we observe two different ferromagnetic orders. Once the Hubbard repulsion becomes more realistic, new ferrimagnetic orders arise with distinct incommensurate intra- or inter-valley scattering vectors depending on interaction strength and doping, leading to a multitude of competing magnetic states.