Spontaneous Anomalous Hall effects in magnetic and non-magnetic systems

Abstract

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