Domain branching in uniaxial ferromagnets: A scaling law for the minimum energy

Rustum Choksi, Robert Kohn, Felix Otto

Research output: Contribution to journalArticle

Abstract

We address the branching of magnetic domains in a uniaxial ferromagnet. Our thesis is that branching is required by energy minimization. To show this, we consider the nonlocal, nonconvex variational problem of micromagnetics. We identify the scaling law of the minimum energy by proving a rigorous lower bound which matches the already-known upper bound. We further show that any domain pattern achieving this scaling law must have average width of order L2/3, where L is the length of the magnet in the easy direction. Finally we argue that branching is required, by considering the constrained variational problem in which branching is prohibited and the domain structure is invariant in the easy direction. Its scaling law is different.

Original languageEnglish (US)
Pages (from-to)61-79
Number of pages19
JournalCommunications in Mathematical Physics
Volume201
Issue number1
StatePublished - 1999

Fingerprint

Ferromagnet
Scaling Laws
scaling laws
Branching
Energy
theses
Nonconvex Variational Problems
magnetic domains
Micromagnetics
energy
Energy Minimization
magnets
Variational Problem
optimization
Lower bound
Upper bound
Invariant

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Domain branching in uniaxial ferromagnets : A scaling law for the minimum energy. / Choksi, Rustum; Kohn, Robert; Otto, Felix.

In: Communications in Mathematical Physics, Vol. 201, No. 1, 1999, p. 61-79.

Research output: Contribution to journalArticle

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