#
2008 APS March Meeting

## Volume 53, Number 2

##
Monday–Friday, March 10–14, 2008;
New Orleans, Louisiana

### Session S5: Theory of Orbital Magnetization and Related Properties

2:30 PM–5:30 PM,
Wednesday, March 12, 2008

Morial Convention Center
Room: RO1

Sponsoring
Unit:
DCMP

Chair: Raffaele Resta, University of Trieste

Abstract ID: BAPS.2008.MAR.S5.2

### Abstract: S5.00002 : Optical sum rules for the orbital magnetization and anomalous Hall conductivity

3:06 PM–3:42 PM

Preview Abstract
Abstract

####
Author:

Ivo Souza

(Dept. of Physics, University of California Berkeley)

Magnetic circular dichroism (MCD), the differential absorption of
left- and
right-circularly-polarized light by ferromagnets, results from
the interplay between spin polarization and spin-orbit interaction.
The same two ingredients are responsible for their spontaneous
(``anomalous'')
Hall conductivity (AHC) and orbital magnetization.
I will discuss how the three phenomena are related by two sum rules
for the interband MCD
spectrum.\footnote{I. Souza and D. Vanderbilt, {\tt
arXiv:0709.2389} (2007).}
The sum rules are of the form
$\int_0^\infty \omega^{-p}\sigma''_{{\rm
A},\alpha\beta}(\omega)d\omega$,
where $\sigma''_{\rm A}$ is the absorptive part of the
antisymmetric optical conductivity.
The sum rule with $p=0$ is the dichroic counterpart of the
familiar $f$-sum
rule for
linearly-polarized light. I will show that it yields a
contribution to the
ground-state orbital magnetization which in insulators
is associated with the circulation of the Wannier orbitals
around their centers (more precisely, to the gauge-invariant part
thereof).
This differs from the net circulation, or total
orbital magnetization,\footnote{ D. Xiao, J. Shi, and Q. Niu,
Phys. Rev. Lett. {\bf 95}, 137204 (2005).}$^{,}$\footnote{T.
Thonhauser, D. Ceresoli,
D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205
(2005).}
which has two additional contributions: (i) the
remaining Wannier self-rotation, and
(ii) the ``itinerant'' circulation arising from the
center-of-mass motion of the Wannier orbitals.
Contributions (i) and (ii) are not
separately meaningful, since their individual values depend on the
particular choice of Wannier functions. Their sum is however
gauge-invariant, and can be inferred from a
combination of gyromagnetic and magneto-optical experiments.
The $p=1$ sum rule is the dc limit of the dichroic Kramers-Kronig
relation which
yields $\sigma'_{\rm A}(0)$, the Karplus-Luttinger AHC.
{\it Ab-initio} studies have shown that it is necessary to sample
over millions of
$k$-points to converge the calculation of this quantity. I will
describe an
efficient real-space method for
computating the AHC\footnote{ X. Wang, J.~R. Yates, I. Souza, and
D. Vanderbilt,
Phys. Rev. B {\bf 74}, 195118 (2006).}
and MCD\footnote{J.~R. Yates, X. Wang, D. Vanderbilt, and I. Souza,
Phys. Rev. B {\bf 75}, 195121 (2007).}
using Wannier functions, and present some illustrative calculations
for ferromagnets as well as field-polarized solid and liquid heavy
metals.\footnote{G. Busch and H.--J. G\"untherodt, Solid State
Phys. {\bf 29}, 235 (1974).}
The possible role of
configurational disorder in enhancing the field-induced AHC of
liquid metals
by introducing low-frequency Drude-related
features in the MCD spectrum will be explored.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2008.MAR.S5.2