Non-Trivial Band Topology Criteria for Magneto-Spin–Orbit Graphene

Band structure and topology of magneto-spin–orbit graphene is investigated using the proposed tight-binding model that incorporates both Rashba and sublattice-resolved collinear exchange couplings in a generic ferrimagnetic (FIM) setting for in-plane and out-of-plane magnetization directions. The resulting band structures were analyzed for possibilities to extract the strengths of exchange and Rashba couplings from experimental spin-resolved ARPES measurements of the valley gaps and π-state spin-splittings. It was shown that the topologically trivial in-plane FIM situation admits simple expressions for these quantities, whereas the out-of-plane FIM, which admits a nontrivial band topology, is harder to analyze. The obtained topological phase diagrams for the out-of-plane FIM case show that the anomalous Hall conductance is quite stable with respect to the antiferromagnetic (AFM) interaction, which tends to interfere with the QAHE phase; moreover, the topological phase transition has a rather smooth character with respect to the AFM coupling strength.