Fermi-surface calculation of the anomalous Hall conductivity

Xinjie Wang, David Vanderbilt, Jonathan R. Yates, and Ivo Souza
Phys. Rev. B 76, 195109 – Published 9 November 2007

Abstract

While the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its “nonquantized part”) may alternatively be expressed as a Fermi-surface property. Here we present an ab initio approach for computing the anomalous Hall conductivity that takes advantage of this observation by converting the integral over the Fermi sea into a more efficient integral on the Fermi surface only. First, a conventional electronic-structure calculation is performed with spin-orbit interaction included. Maximally localized Wannier functions are then constructed by a postprocessing step in order to convert the ab initio electronic structure around the Fermi level into a tight-binding-like form. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi-surface sheets with the slice by standard contour methods, organize these into a set of closed loops, and compute the Berry phases of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices. Illustrative calculations are performed for Fe, Co, and Ni.

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  • Received 6 August 2007

DOI:https://doi.org/10.1103/PhysRevB.76.195109

©2007 American Physical Society

Authors & Affiliations

Xinjie Wang1, David Vanderbilt1, Jonathan R. Yates2,3, and Ivo Souza2,3

  • 1Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854-8019, USA
  • 2Department of Physics, University of California, Berkeley, California 94720, USA
  • 3Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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Issue

Vol. 76, Iss. 19 — 15 November 2007

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