Anomalous Hall effect in granular ferromagnetic metals and effects of weak localization

TL;DR

This paper provides a theoretical analysis of the anomalous Hall effect in granular ferromagnetic metals, highlighting differences from homogeneous metals and discussing experimental implications.

Contribution

It introduces a formalism for calculating anomalous Hall conductivity and resistivity in granular metals, including weak localization effects, revealing new scaling behavior.

Findings

Scaling relation between $ ho_{xy}$ and $ ho_{xx}$ does not hold in granular metals.

Weak localization corrections match those in homogeneous metals.

Results are relevant for interpreting experimental data on polycrystalline iron films.

Abstract

We theoretically investigate the anomalous Hall effect in a system of dense-packed ferromagnetic grains in the metallic regime. Using the formalism recently developed for the conventional Hall effect in granular metals, we calculate the residual anomalous Hall conductivity $\sigma_{xy}$ and resistivity $\rho_{xy}$ and weak localization corrections to them for both skew-scattering and side-jump mechanisms. We find that, unlike for homogeneously disordered metals, the scaling relation between $\rho_{xy}$ and the longitudinal resistivity $\rho_{xx}$ does not hold. The weak localization corrections, however, are found to be in agreement with those for homogeneous metals. We discuss recent experimental data on the anomalous Hall effect in polycrystalline iron films in view of the obtained results.