Effective dynamics for ferromagnetic thin films: A rigorous justification

Robert V. Kohn, Valeriy V. Slastikov

Research output: Contribution to journalArticlepeer-review


In a thin-film ferromagnet, the leading-order behaviour of the magnetostatic energy is a strong shape anisotropy, penalizing the out-of-plane component of the magnetization distribution. We study the thin-film limit of Landau-Lifshitz Gilbert dynamics, when the magnetostatic term is replaced by this local approximation. The limiting two-dimensional effective equation is overdamped, i.e. it has no precession term. Moreover, if the damping coefficient of three-dimensional micromagnetics is α, then the damping coefficient of the two-dimensional effective equation is α + 1/α; thus reducing the damping in three dimensions can actually increase the damping of the effective equation. This result was previously shown by García-Cervera and E using asymptotic analysis: our contribution is a mathematically rigorous justification.

Original languageEnglish (US)
Pages (from-to)143-154
Number of pages12
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2053
StatePublished - Jan 8 2005


  • Effective dynamics
  • Micromagnetics: thin film

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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