Effective dynamics for ferromagnetic thin films: a rigorous justification
Effective dynamics for ferromagnetic thin films: a rigorous justification
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铁磁薄膜的有效动力学：严格的论证
DOI：
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发表时间：
2005
期刊：
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通讯作者：
V. Slastikov
中科院分区：
文献类型：
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作者：
R. Kohn;V. Slastikov
在薄膜铁磁体中，静磁能量的前序行为是一个很强的形状各向异性，使磁化强度分布的平面外分量变差。我们研究了用这种局域近似代替静磁项时Landau-Lifshitz-Gilbert动力学的薄膜极限。极限二维有效方程是过阻的，即它没有进动项。此外，如果三维微磁学的阻尼系数为a，则二维有效方程的阻尼系数为a+1/a；因此，在三维空间中降低阻尼实际上可以增加有效方程的阻尼。这一结果以前由García-Cervera和E使用渐近分析证明；我们的贡献是严格的数学证明。
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 a, then the damping coefficient of the two–dimensional effective equation is a + 1/a; 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.