Topological Nature of Anomalous Hall Effect in Ferromagnets

Abstract

The anomalous Hall effect in two-dimensional (2D) ferromagnets is considered to be the physical realization of the parity anomaly in (2+1)D, and the band crossing points behave as the topological singularity in the Brillouin zone. These band crossing points appear as sharp peaks and sign changes of the transverse conductance σ_xy as a function of the Fermi energy and/or the magnetization. The relevance to the experiments including three-dimensional (3D) systems is also discussed.