Anomalous Hall effect due to spin chirality in the Kagome lattice

We consider a model for a two-dimensional electron gas moving on a Kagome lattice and locally coupled to a chiral magnetic texture. We show that the transverse conductivity sigma(xy) does not vanish even if spin-orbit coupling is not present and it may exhibit unusual behavior. The model parameters are the chirality, the number of conduction electrons, and the amplitude of the local coupling. Upon varying these parameters, a topological transition characterized by change of the band Chern numbers occurs. As a consequence, sigma(xy) can be quantized, proportional to the chirality, or have a nonmonotonic behavior upon varying these parameters.