Order from Disorder in Graphene Quantum Hall Ferromagnet

Valley-polarized quantum Hall states in graphene are described by a Heisenberg O(3) ferromagnet model, with the ordering type controlled by the strength and sign of valley anisotropy. A mechanism resulting from electron coupling to strain-induced gauge field, giving leading contribution to the anisotropy, is described in terms of an effective random magnetic field aligned with the ferromagnet z axis. We argue that such random field stabilizes the XY ferromagnet state, which is a coherent equal-weight mixture of the $K$ and $K^{\mathrm{\prime }}$ valley states. Other implications such as the Berezinskii-Kosterlitz-Thouless ordering transition and topological defects with half-integer charge are discussed.