论文标题
在薄铁磁性膜中，具有非局部相互作用的域壁及其重新规定的能量的分离
Separation of domain walls with nonlocal interaction and their renormalised energy by $Γ$-convergence in thin ferromagnetic films
论文作者
论文摘要
我们根据小参数$ε> 0 $分析了来自具有非本地能量功能的微磁性的非convex变量模型的两个变体。该模型产生了过渡层，称为Néel墙，我们在限制$ε\至0 $中研究了它们的行为。该分析与金茨堡 - 兰道涡流的理论有一定的相似之处。特别是，它产生了重新归一化的能量，该能量决定了Néel壁之间的相互作用（吸引或排斥）到领先顺序。但是，尽管金茨堡 - 兰道涡流显示出相同符号和排斥程度的吸引力，但对于相反的符号程度，该模式在此模型中却相反。 在上一篇论文中，我们确定了这里研究的一种模型的重新归一化能量，假设Néel壁保持彼此分离。在本文中，我们提出了更深入的分析，特别是消除了这一假设。该理论引起了墙壁位置的有效变分问题，该墙壁封装在$γ$ - 范围的结果中。在本文的第二部分中，我们将注意力转向了另一个更多的物理模型，包括各向异性术语。我们表明，它允许一种类似的理论，但是各向异性以意外的方式改变了重量化的能量，并且需要不同的方法才能找到它。
We analyse two variants of a nonconvex variational model from micromagnetics with a nonlocal energy functional, depending on a small parameter $ε> 0$. The model gives rise to transition layers, called Néel walls, and we study their behaviour in the limit $ε\to 0$. The analysis has some similarity to the theory of Ginzburg-Landau vortices. In particular, it gives rise to a renormalised energy that determines the interaction (attraction or repulsion) between Néel walls to leading order. But while Ginzburg-Landau vortices show attraction for degrees of the same sign and repulsion for degrees of opposite signs, the pattern is reversed in this model. In a previous paper, we determined the renormalised energy for one of the models studied here under the assumption that the Néel walls stay separated from each other. In this paper, we present a deeper analysis that in particular removes this assumption. The theory gives rise to an effective variational problem for the positions of the walls, encapsulated in a $Γ$-convergence result. In the second part of the paper, we turn our attention to another, more physical model, including an anisotropy term. We show that it permits a similar theory, but the anisotropy changes the renormalised energy in unexpected ways and requires different methods to find it.
