Study of the topological Hall effect on 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 non-adiabatic regimes are studied, including the effect of disorder. By studying the transition between both regimes the discussion about the correct adiabaticity criterium in the diffusive limit is clarified.