Spin and valley quantum Hall ferromagnetism in graphene

Electronic systems with multiple degenerate degrees of freedom can support a rich variety of broken symmetry states. In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin–valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can break this symmetry, manifesting as further Hall plateaus outside the normal integer sequence. Here we report the observation of a number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using tilted field magnetotransport. The large activation gaps confirm the Coulomb origin of all the broken symmetry states, but the order depends strongly on LL index. In the high-energy LLs the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets hosting skyrmionic excitations at half filling, whereas in the ‘relativistic’ zero LL lattice scale interactions drive the system to a spin unpolarized state.