Magnetization Dynamics at Nanoscale

这项研究项目调查磁性材料领域的问题，重点是纳米级系统的建模、分析和数值探索。自从计算机时代到来以来，磁性材料一直是信息存储不可缺少的组成部分，目前对革命性的新计算机和信息技术的发展有着巨大的希望。纳米制造的最新进展使构建磁性多层结构具有前所未有的精度，使用厚度降至单原子层、横向宽度降至10纳米的超薄膜。在这些非常小的尺度上，新的物理效应变得突出，驱动了有趣的新现象，如自旋转移扭矩、手性磁场壁、磁天子、自旋、逆自旋和拓扑霍尔效应。这一新的物理学需要被纳入微磁建模框架中，该框架在以前对更大规模的磁系统的研究中被证明是非常成功的。这项研究项目探索了新模型的多尺度、非线性、非局部性和通常是随机的性质，这对理解和预测此类系统的行为是一个巨大的挑战。该项目的一个关键组成部分是新一代应用数学家参与这一高度交叉的研究领域。该项目旨在建立和分析存在反对称交换作用的超薄铁磁薄膜的模型，该相互作用与磁化的拓扑特征产生非平凡的相互作用。通过严格分析由全三维处理产生的适当的渐近薄膜极限，将特别注意将杂散场的非局部效应纳入到模型中。在所得到的简化薄膜模型中，将结合解析、形式渐近和数值工具来研究带电磁区壁、手性磁区壁和磁天区子场的性质。这些相干结构的存在和渐近性质的问题引发了能量驱动的图案形成和变分计算的挑战性问题。自旋电子学领域的迅速扩张有力地推动了这项研究。项目中将考虑的所有特殊磁化配置目前都是自旋电子器件中潜在应用的目标，特别是用于开发非易失性顺序和随机存取计算机存储器。

This research project investigates questions in the area of magnetic materials, emphasizing modeling, analysis, and numerical explorations of nanoscale systems. Magnetic materials have been an indispensable ingredient for information storage since the advent of the computer age and presently hold great promise for the development of revolutionary new computer and information technologies. Recent advances in nanofabrication allow an unprecedented precision in building magnetic multilayer structures, using ultrathin films with thickness down to a single atomic layer and a lateral extent down to ten nanometers. At these very small scales, new physical effects become prominent, driving interesting new phenomena such as spin transfer torque, chiral domain walls, magnetic skyrmions, spin, inverse spin, and topological Hall effects. This new physics needs to be incorporated into the micromagnetic modeling framework that proved very successful in the previous studies of magnetic systems at larger scales. This research project explores the multiscale, nonlinear, nonlocal, and often stochastic nature of the new models, which represents a significant challenge to understanding and predicting the behavior of such systems. A key component of the project is the involvement of a new generation of applied mathematicians in this highly interdisciplinary area of research.This project aims to formulate and analyze models of ultrathin ferromagnetic films in the presence of antisymmetric exchange interaction, which produces a non-trivial interplay with the topological characteristics of the magnetization. Particular care will be taken to incorporate into the models the non-local effects of the stray field via rigorous analysis of the appropriate asymptotic thin film limits arising from the full three-dimensional treatment. Within the obtained reduced thin film models, the properties of charged domain walls, chiral domain walls, and magnetic skyrmions will be investigated, using a combination of analytical, formal asymptotic, and numerical tools. The questions of existence and asymptotic properties of these coherent structures give rise to challenging problems of energy-driven pattern formation and calculus of variations. The research is strongly motivated by the rapidly expanding field of spintronics. All the special magnetization configurations that will be considered in the project are currently targets for potential applications in spintronics devices and, in particular, for the development of non-volatile sequential and random access computer memories.