### 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) |
---|---|

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 |

### Fingerprint

### Keywords

- Effective dynamics
- Micromagnetics: thin film

### ASJC Scopus subject areas

- General

### 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

**Effective dynamics for ferromagnetic thin films : A rigorous justification.** / Kohn, Robert; Slastikov, Valeriy V.

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 461, no. 2053, pp. 143-154. https://doi.org/10.1098/rspa.2004.1342

}

TY - JOUR

T1 - Effective dynamics for ferromagnetic thin films

T2 - A rigorous justification

AU - Kohn, Robert

AU - Slastikov, Valeriy V.

PY - 2005/1/8

Y1 - 2005/1/8

N2 - 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.

AB - 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.

KW - Effective dynamics

KW - Micromagnetics: thin film

UR - http://www.scopus.com/inward/record.url?scp=17144418191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17144418191&partnerID=8YFLogxK

U2 - 10.1098/rspa.2004.1342

DO - 10.1098/rspa.2004.1342

M3 - Article

VL - 461

SP - 143

EP - 154

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

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

SN - 0080-4630

IS - 2053

ER -