Oscillatory Buckling Mode in Thin-Film Nucleation
Oscillatory Buckling Mode in Thin-Film Nucleation
复制标题
薄膜成核中的振荡屈曲模式
DOI：
10.1007/s00332-004-0684-z
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发表时间：
2006
影响因子：
3
通讯作者：
F. Otto
中科院分区：
文献类型：
--
作者：
R. Cantero-Álvarez;F. Otto
我们感兴趣的是开关的细长薄膜元件所描述的微磁模型。当饱和分支在临界场处变得不稳定时，就会发生成核。它的特点是由微磁能的海森简并。退化子空间描述了不稳定模式。 在先前的工作中， [Cantero-Alvarez和Otto，《非线性科学杂志》] ，我们表明，有四个制度的成核。我们证明了这一点，通过确定的无量纲参数的临界场的标度。这与Aharoni关于最多有三个政权的说法相矛盾。 这些制度中的两个是屈曲制度，其中磁化被钉扎在样品的横向小平面和平面内。如我们先前的工作所示，这些制度在临界场的尺度上有所不同。在这里，我们表明，不稳定的模式也有质的不同：只有在一个制度，他们在长方向振荡。通过应用于Hessian的Rayleigh商的Γ-收敛性来渐近地识别不稳定模式。
We are interested in switching of elongated thin-film elements as described by the micromagnetic model. Nucleation occurs when the saturation branch becomes unstable at a critical field. It is characterized by a degeneracy of the Hessian of the micromagnetic energy. The degenerate subspace describes the unstable mode. In a prior work [Cantero-Alvarez and Otto, Journal of Nonlinear Science] , we showed that there are four regimes for nucleation. We proved this by identifying the scaling of the critical field in the non-dimensional parameters. This contradicts a claim by Aharoni that there are at most three regimes. Two of these regimes are buckling regimes, where the magnetization is pinned at the lateral facets of the sample and buckles in-plane. As shown in our prior work, these regimes differ in the scaling of the critical field. Here we show that the unstable modes are also qualitatively different: Only in one of the regimes do they oscillate in the long direction. The unstable modes are asymptotically identified by Γ-convergence, which is applied to the Rayleigh quotient of the Hessian.