Generalization of the Landau-Lifshitz-Gilbert equation for conducting ferromagnets

Shufeng Zhang, Steven S.L. Zhang

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


We propose an extension of the Landau-Lifshitz-Gilbert (LLG) equation by explicitly including the role of conduction electrons in magnetization dynamics of conducting ferromagnets. The temporal and spatial dependent magnetization order parameter m(r,t) generates both electrical and spin currents that provide dissipation of the energy and angular momentum of the processing magnet. The resulting LLG equation contains highly spatial dependence of damping term and thus micromagnetic simulations based on the standard LLG equation should be reexamined for magnetization dynamics involving narrow domain walls and spin waves with short wavelengths.

Original languageEnglish (US)
Article number086601
JournalPhysical review letters
Issue number8
StatePublished - Feb 23 2009

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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