# Relativistic theory of magnetic inertia in ultrafast spin dynamics

Relativistic theory of magnetic inertia in ultrafast spin dynamics The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of 1/c4 gives the intrinsic inertia of a pure system through the second order time derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping I is a higher order spin-orbit coupling effect, ∼1/c4, as compared to the Gilbert damping Γ that is of order 1/c2. Inertia is therefore expected to play a role only on ultrashort timescales (subpicoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor, respectively. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

# Relativistic theory of magnetic inertia in ultrafast spin dynamics

, Volume 96 (2) – Jul 18, 2017

## Relativistic theory of magnetic inertia in ultrafast spin dynamics

Abstract

The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of 1/c4 gives the intrinsic inertia of a pure system through the second order time derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping I is a higher order spin-orbit coupling effect, ∼1/c4, as compared to the Gilbert damping Γ that is of order 1/c2. Inertia is therefore expected to play a role only on ultrashort timescales (subpicoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor, respectively.

/lp/aps_physical/relativistic-theory-of-magnetic-inertia-in-ultrafast-spin-dynamics-xSysgs2mJf
Publisher
American Physical Society (APS)
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.024425
Publisher site
See Article on Publisher Site

### Abstract

The influence of possible magnetic inertia effects has recently drawn attention in ultrafast magnetization dynamics and switching. Here we derive rigorously a description of inertia in the Landau-Lifshitz-Gilbert equation on the basis of the Dirac-Kohn-Sham framework. Using the Foldy-Wouthuysen transformation up to the order of 1/c4 gives the intrinsic inertia of a pure system through the second order time derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping I is a higher order spin-orbit coupling effect, ∼1/c4, as compared to the Gilbert damping Γ that is of order 1/c2. Inertia is therefore expected to play a role only on ultrashort timescales (subpicoseconds). We also show that the Gilbert damping and inertial damping are related to one another through the imaginary and real parts of the magnetic susceptibility tensor, respectively.

### Journal

Physical Review BAmerican Physical Society (APS)

Published: Jul 18, 2017

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