Anomalous Hall effect in magnetized graphene: intrinsic and extrinsic transport mechanisms approaching the quantized regime
We present a unified theory of the anomalous Hall effect (AHE) in magnetized graphene sheets in the presence of dilute disorder. The analytical study of Berry curvature and transport coefficients in a 4-band Dirac model [2 (spin) $\times$ 2 (pseudo-spin)] unveils a delicate balance between intrinsic and extrinsic contributions owing to the skyrmionic spin texture of magnetic Dirac bands. We show that the anomalous Hall conductivity changes sign when the Fermi energy approaches the topological gap as result of competing spin Lorentz forces. The predicted effect foreruns the quantum anomalous Hall regime and allows estimation of proximity spin-orbit strength directly from a Hall measurement. Our findings are relevant to outline a systematic route towards the demonstration of novel topological insulating phases in magnetized Dirac fermion systems.