Domain Branching in Uniaxial Ferromagnets: A Scaling Law for the Minimum Energy

被引：0
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作者：
Rustum Choksi
Robert V. Kohn
Felix Otto
机构：
[1] Department of Mathematics and Statistics,
[2] Simon Fraser University,undefined
[3] Burnaby,undefined
[4] BC,undefined
[5] Canada V5A 1S6.¶E-mail: choksi@math.sfu.ca,undefined
[6] Courant Institute,undefined
[7] New York University,undefined
[8] New York,undefined
[9] NY 10012,undefined
[10] USA. E-mail: kohn@cims.nyu.edu,undefined
[11] Department of Mathematics,undefined
[12] University of California,undefined
[13] Santa Barbara,undefined
[14] CA 93106,undefined
[15] USA.¶E-mail: otto@math.ucsb.edu,undefined
来源：
Communications in Mathematical Physics | 1999年 / 201卷
关键词：
Energy Minimization; Domain Structure; Variational Problem; Magnetic Domain; Average Width;
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学科分类号：
摘要：
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.
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页码：61 / 79
页数：18
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