Spontaneous anomalous Hall effect in magnetic and non-magnetic systems

We consider two cases of spontaneous anomalous Hall current. In a non-magnetic system with spin-orbit coupling (SOC), the applied bias results in the appearance of non-equilibrium magnetization and an anomalous Hall current. The latter demonstrates non-linear dependence on the applied bias. In a magnetic system with SOC, an anomalous current appears without applied bias. We perform the calculations in the framework of the free-electron model, whereas the common approach to this type of phenomenon is based on Berry connection. We demonstrate that anomalous currents acquire a measurable magnitude for reasonable model parameters.