### Abstract

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 language | English (US) |
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Pages (from-to) | 143-154 |

Number of pages | 12 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 461 |

Issue number | 2053 |

DOIs | |

State | Published - Jan 8 2005 |

### Keywords

- Effective dynamics
- Micromagnetics: thin film

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

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## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*461*(2053), 143-154. https://doi.org/10.1098/rspa.2004.1342