Competition between canted antiferromagnetic and spin-polarized quantum Hall states at $\nu$ = 0 in graphene on a ferrimagnetic insulator.

The $\nu$ = 0 quantum Hall state in graphene has attracted experimental and theoretical interest. Graphene supports four zero-energy Landau levels which are described by spin and valley degeneracies. These lead to a number of approximately degenerate symmetry-broken states. Electron-electron and electron-phonon interactions break valley-symmetry and determine the ground state of the $\nu$ = 0 state. The consensus emerging from theory and experiment is that these interactions favour an antiferromagnetic insulating state which supports long-range spin-polarized edge transport. Here we report a competition between canted antiferromagnetic and ferromagnetic quantum Hall states in graphene placed on a ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$ (YIG), which induces a uniform magnetic exchange field in graphene of the order 60 T. The magnetic order and energy gap of the edge modes in graphene are tunable with an 8 T out-of-plane magnetic field at 2.7 K.