Domain Branching in Uniaxial Ferromagnets: A Scaling Law for the Minimum Energy
Domain Branching in Uniaxial Ferromagnets: A Scaling Law for the Minimum Energy
复制标题
单轴铁磁体中的磁畴分支：最小能量的缩放定律
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
F. Otto
中科院分区：
文献类型：
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作者：
Rustum Choksi;R. Kohn;F. Otto
摘要：我们解决了单轴铁磁体中磁畴的分支问题。我们的论点是，能量最小化需要分支。为了证明这一点，我们考虑微磁学的非局部、非凸变分问题。我们通过证明与已知上限相匹配的严格下限来确定最小能量的标度定律。我们进一步表明，实现此缩放定律的任何磁畴图案必须具有 L2/3 量级的平均宽度，其中 L 是磁体在易方向上的长度。最后，通过考虑禁止分支且域结构在简单方向上不变的约束变分问题，我们认为分支是必要的。其标度规律不同。
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.