Topological Hall effect studied in simple models

Recently, a chirality-driven contribution to the anomalous Hall effect has been found that is induced by the Berry phase and does not directly involve spin-orbit coupling. In this paper, we will investigate this effect numerically in a two-dimensional electron gas with a simple magnetic texture model. Both the adiabatic and nonadiabatic regimes are studied, including the effect of disorder. By studying the transition between both regimes the discussion about the correct adiabaticity criterion in the diffusive limit is clarified.