  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.
