Effective dynamics for ferromagnetic thin films: A rigorous justification

Robert V. Kohn; Valeriy V. Slastikov

doi:10.1098/rspa.2004.1342

Effective dynamics for ferromagnetic thin films: A rigorous justification

Robert V. Kohn, Valeriy V. Slastikov

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1098/rspa.2004.1342
State	Published - Jan 8 2005

Keywords

Effective dynamics
Micromagnetics: thin film

ASJC Scopus subject areas

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

Access to Document

10.1098/rspa.2004.1342

Fingerprint Dive into the research topics of 'Effective dynamics for ferromagnetic thin films: A rigorous justification'. Together they form a unique fingerprint.

Cite this

@article{44a0a320568845ecbb401be9d0c4e1e5,

title = "Effective dynamics for ferromagnetic thin films: A rigorous justification",

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 Garc{\'i}a-Cervera and E using asymptotic analysis: our contribution is a mathematically rigorous justification.",

keywords = "Effective dynamics, Micromagnetics: thin film",

author = "Kohn, {Robert V.} and Slastikov, {Valeriy V.}",

year = "2005",

month = jan,

day = "8",

doi = "10.1098/rspa.2004.1342",

language = "English (US)",

volume = "461",

pages = "143--154",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "0080-4630",

publisher = "Royal Society of London",

number = "2053",

}

TY - JOUR

T1 - Effective dynamics for ferromagnetic thin films

T2 - A rigorous justification

AU - Kohn, Robert V.

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

AN - SCOPUS:17144418191

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 -