Intrinsic vs. extrinsic anomalous Hall effect in ferromagnets

TL;DR

This paper presents a unified theory of the anomalous Hall effect in ferromagnets, highlighting the crossover from extrinsic to intrinsic mechanisms depending on impurity scattering and band structure features.

Contribution

It introduces a comprehensive framework that combines intrinsic and extrinsic AHE mechanisms, emphasizing the resonance enhancement near band anti-crossings.

Findings

Intrinsic AHE is resonantly enhanced near band anti-crossings.

Extrinsic skew-scattering dominates in the clean limit.

Crossover occurs when relaxation rate matches spin-orbit energy.

Abstract

A unified theory of the anomalous Hall effect (AHE) is presented for multi-band ferromagnetic metallic systems with dilute impurities. In the clean limit, the AHE is mostly due to the extrinsic skew-scattering. When the Fermi level is located around anti-crossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its non-perturbative nature, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit interaction energy.