TY - JOUR
T1 - Fermi-surface calculation of the anomalous Hall conductivity
AU - Wang, Xinjie
AU - Vanderbilt, David
AU - Yates, Jonathan R.
AU - Souza, Ivo
N1 - Copyright:
Copyright 2007 Elsevier B.V., All rights reserved.
PY - 2007/11/9
Y1 - 2007/11/9
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=36049030269&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36049030269&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.76.195109
DO - 10.1103/PhysRevB.76.195109
M3 - Article
AN - SCOPUS:36049030269
VL - 76
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
SN - 1098-0121
IS - 19
M1 - 195109
ER -