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 FeCl2 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 k-space Dirac monopole. The present method will open an efficient thermoelectric material design based on the high-throughput first-principles screening.
@article{arxiv.2204.05949,
title = {First-principles calculation of anomalous Hall and Nernst conductivity by local Berry phase},
author = {Hikaru Sawahata and Naoya Yamaguchi and Susumu Minami and Fumiyuki Ishii},
journal= {arXiv preprint arXiv:2204.05949},
year = {2023}
}