### 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 L^{2/3}, 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 language | English (US) |
---|---|

Pages (from-to) | 61-79 |

Number of pages | 19 |

Journal | Communications in Mathematical Physics |

Volume | 201 |

Issue number | 1 |

State | Published - 1999 |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*201*(1), 61-79.

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 201, no. 1, pp. 61-79.

}

TY - JOUR

T1 - Domain branching in uniaxial ferromagnets

T2 - A scaling law for the minimum energy

AU - Choksi, Rustum

AU - Kohn, Robert

AU - Otto, Felix

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033450334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033450334&partnerID=8YFLogxK

M3 - Article

VL - 201

SP - 61

EP - 79

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -