Effective dynamics for ferromagnetic thin films: a rigorous justification

RV Kohn*, VV Slastikov

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

36 Citations (Scopus)


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 alpha, then the damping coefficient of the two-dimensional effective equation is alpha + 1/alpha; thus reducing the damping in three dimensions can actually increase the damping of the effective equation. This result was previously shown by Garcia-Cervera and E using asymptotic analysis; our contribution is a mathematically rigorous justification.

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


  • micromagnetics
  • thin film
  • effective dynamics

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