Two-Electron Model of the Anomalous Hall Effect

First discovered in 1879, the anomalous Hall effect (AHE) is ubiquitous in ferromagnetic materials. As the AHE depends directly on the magnetization of the material, it is a useful method to measure magnetization responses to external fields. As such, the AHE in materials like the iron-nickel alloy permalloy (Py) has been studied extensively. There is a well-reported sign change in the anomalous Hall conductivity which is attributed to competing mechanisms. The proposed microscopic model for AHE includes two mechanisms; intrinsic, which arises from the Barry curvature, and extrinsic, originating from defect and interface scattering. However, this microscopic model does not explicitly give consideration to separate conductivities for the two spin species.

We propose a two-electron model where spin-dependent anomalous Hall conductivity and mean free path are considered in the microscopic model of the AHE. We demonstrate evidence for this by showing that modifying spin up/down conductivities in permalloy samples by adding a Cu capping layer of varying thickness can cause a sign change and significant enhancement in the anomalous Hall conductivity. We observe that the magnitude change in anomalous Hall conductivity saturates at a Cu thickness comparable to the mean-free path of Cu. This supports the validity of our hypothesis and emphasizes the significance of analyzing the individual conductivities of spin up and spin down electrons in the AHE mechanisms.