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 $1/c^4$ gives the intrinsic inertia of a pure system through the 2${}^{\mathrm{nd}}$ order time-derivative of magnetization in the dynamical equation of motion. Thus, the inertial damping $\mathcal{I}$ is a higher order spin-orbit coupling effect, $\sim 1/c^4$, as compared to the Gilbert damping $\Gamma$ that is of order $1/c^2$. Inertia is therefore expected to play a role only on ultrashort timescales (sub-picoseconds). 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.

8 pages, 1 figure

References in corpus (11)

• Identification of the dominant precession damping mechanism in Fe, Co, and Ni by first-principles calculations
• Intrinsic and non-local Gilbert damping in polycrystalline nickel studied by Ti:Sapphire laser fs spectroscopy
• Functional Keldysh Theory of Spin Torques
• Transverse spin diffusion in ferromagnets
• Connecting the timescales in picosecond remagnetization experiments
• Relativistic theory of spin relaxation mechanisms in the Landau-Lifshitz-Gilbert equation of spin dynamics
• General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
• The magnetic monopole and the separation between fast and slow magnetic degrees of freedom
• Signatures of relativistic spin-light coupling in ultrafast magneto-optical pump-probe experiments
• Magnetic moment of inertia within the breathing model
• Origin of intrinsic Gilbert damping

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