A consistent theory of Gilbert damping in pure metallic ferromagnets at T=0
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Accepted version
Author(s)
Edwards, DM
Type
Journal Article
Abstract
Damping of magnetization dynamics in a ferromagnetic metal, arising from spin-orbit coupling,
is usually characterised by the Gilbert parameter α. Recent calculations of this quantity, using
a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband
scattering term which is of third order in the spin-orbit parameter ξ. This surprising result conflicts
with recent work by Costa and Muniz who study damping numerically by direct calculation of
the dynamical transverse susceptibility in the presence of spin-orbit coupling. We resolve this
inconsistency by following the approach of Costa and Muniz for a slightly simplified model where
it is possible to calculate α analytically. We show that to second order in ξ one retrieves the
Kambersky result for α, but to higher order one does not obtain any divergent intraband terms.
The present work goes beyond that of Costa and Muniz by pointing out the necessity of including
the effect of long-range Coulomb interaction in calculating damping for large ξ. A direct derivation
of the Kambersky formula is given which shows clearly the restriction of its validity to second order
in ξ so that no intraband scattering terms appear. This restriction has an important effect on the
damping over a substantial range of impurity content and temperature. The experimental situation
is discussed.
is usually characterised by the Gilbert parameter α. Recent calculations of this quantity, using
a formula due to Kambersky, find that it is infinite for a perfect crystal owing to an intraband
scattering term which is of third order in the spin-orbit parameter ξ. This surprising result conflicts
with recent work by Costa and Muniz who study damping numerically by direct calculation of
the dynamical transverse susceptibility in the presence of spin-orbit coupling. We resolve this
inconsistency by following the approach of Costa and Muniz for a slightly simplified model where
it is possible to calculate α analytically. We show that to second order in ξ one retrieves the
Kambersky result for α, but to higher order one does not obtain any divergent intraband terms.
The present work goes beyond that of Costa and Muniz by pointing out the necessity of including
the effect of long-range Coulomb interaction in calculating damping for large ξ. A direct derivation
of the Kambersky formula is given which shows clearly the restriction of its validity to second order
in ξ so that no intraband scattering terms appear. This restriction has an important effect on the
damping over a substantial range of impurity content and temperature. The experimental situation
is discussed.
Date Acceptance
2015-11-10
Citation
Journal of Physics: Condensed Matter
ISSN
0953-8984
Publisher
IOP Publishing
Journal / Book Title
Journal of Physics: Condensed Matter
Publication Status
Accepted