First-principles calculation of anomalous Hall and Nernst conductivity by local Berry phase

TL;DR

This paper introduces a finite-difference algorithm for calculating anomalous Hall and Nernst conductivities using Berry curvature, extending previous methods to metallic systems and enabling efficient thermoelectric material screening.

Contribution

The study develops a finite-difference approach for Berry curvature calculation applicable to metals, improving numerical stability over existing methods and facilitating high-throughput thermoelectric material discovery.

Findings

Calculated conductivities for FeCl₂, bcc-Fe, hcp-Co, and fcc-Ni.

Results agree with previous Kubo and Wannier-based calculations.

Method reduces numerical instability in Nernst coefficient evaluation.

Abstract

In this study, we implemented a finite-difference algorithm for computing anomalous Hall and Nernst conductivity. Based on the expression to evaluate the Berry curvature in an insulating system [J. Phys. Soc. Jpn. 74 1674(2005)], we extended the methods to a metallic system. We calculated anomalous Hall conductivity and Nernst conductivity in a two-dimensional ferromagnetic material FeCl$_2$ and three-dimensional ferromagnetic transition metals bcc-Fe, hcp-Co, and fcc-Ni. Our results are comparable to previously reported results computed by Kubo-formula or Wannier representation. To evaluate anomalous Nernst coefficients, the detailed Fermi-energy dependence of the anomalous Hall conductivity is required. Nonetheless, previous methods based on Wannier representation or Kubo-formula have numerical instability due to the ${\boldsymbol k}$-space Dirac monopole. The present method will open an efficient thermoelectric material design based on the high-throughput first-principles screening.