  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.
