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

Abstract

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 ${\mathrm{FeCl}}_{2}$ and three-dimensional ferromagnetic transition-metals bcc-Fe, hcp-Co, and fcc-Ni. Our results are comparable to previously reported results computed by the Kubo formula or Wannier representation. To evaluate anomalous Nernst coefficients, the detailed Fermi-energy dependence of the anomalous Hall conductivity is required. The present method will open an efficient thermoelectric material design based on the high-throughput first-principles screening.