The anomalous Hall effect in two-dimensional ferromagnets is discussed 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. This appears as the sharp peaks and the sign changes of the transverse conductance σxy as a function of the Fermi energy and/or the magnetization. The relevance to the experiments including the three dimensional systems is also discussed.
@article{arxiv.cond-mat/0110504,
title = {Topological Nature of Anomalous Hall Effect in Ferromagnet},
author = {Masaru Onoda and Naoto Nagaosa},
journal= {arXiv preprint arXiv:cond-mat/0110504},
year = {2009}
}