论文标题
在Dzyaloshinskii-Moriya相互作用的存在下薄膜的微磁学
Micromagnetics of thin films in the presence of Dzyaloshinskii-Moriya interaction
论文作者
论文摘要
在本文中，我们研究了在散装Dzyaloshinskii-Moriya相互作用（DMI）的情况下，微磁能的薄膜极限（DMI）。我们的分析包括微磁能的固定$γ$ convergence结果，以及鉴定相关的Landau-Lifshitz-Gilbert方程的渐近行为。特别是，我们证明，在极限模型中，DMI项的一部分的行为就像将磁矩投射到膜上的正态分子上，从而使这种方式促进了磁体静态自我能量产生的形状各向异性。最后，我们讨论了一种有限的有限元方法，以实现时间依赖性情况的近似，并将其使用数值将原始三维模型与二维薄膜限制进行比较。
In this paper, we study the thin-film limit of the micromagnetic energy functional in the presence of bulk Dzyaloshinskii-Moriya interaction (DMI). Our analysis includes both a stationary $Γ$-convergence result for the micromagnetic energy, as well as the identification of the asymptotic behavior of the associated Landau-Lifshitz-Gilbert equation. In particular, we prove that, in the limiting model, part of the DMI term behaves like the projection of the magnetic moment onto the normal to the film, contributing this way to an increase in the shape anisotropy arising from the magnetostatic self-energy. Finally, we discuss a convergent finite element approach for the approximation of the time-dependent case and use it to numerically compare the original three-dimensional model with the two-dimensional thin-film limit.
