Anomalous Hall Effect in Ferromagnetic Metals: Role of Phonons at Finite Temperature

TL;DR

This study numerically investigates the anomalous Hall effect in ferromagnetic metals, revealing a new scaling law that holds across various parameters and showing how the intrinsic mechanism varies with temperature under certain conditions.

Contribution

It introduces a comprehensive numerical analysis of the anomalous Hall effect considering both elastic and inelastic scattering, and confirms a new scaling law consistent with experimental findings.

Findings

The new scaling law accurately describes the Hall conductivity over a wide parameter range.

The intrinsic mechanism's temperature dependence is significant under resonance conditions.

The study aligns numerical results with recent experimental observations.

Abstract

The anomalous Hall effect in a multiband tight-binding model is numerically studied taking into account both elastic scattering by disorder and inelastic scattering by the electron-phonon interaction. The Hall conductivity is obtained as a function of temperature $T$, inelastic scattering rate $\gamma$, chemical potential $\mu$, and impurity concentration $x_{\rm imp}$. We find that the new scaling law holds over a wide range of these parameters; $-\sigma_{xy}= (\alpha \sigma_{xx0}^{-1} + \beta \sigma_{xx0}^{-2}) \sigma_{xx}^2 + b$, with $\sigma_{\mu \nu}$ ($\sigma_{\mu \nu 0}$) being the conductivity tensor (with only elastic scattering), which corresponds to the recent experimental observation [Phys. Rev. Lett. {\bf 103} (2009) 087206]. The condition of this scaling is examined. Also, it is found that the intrinsic mechanism depends on temperature under a resonance condition.