Winding domain walls in thin ferromagnetic films

薄膜铁磁材料是现代数字技术中大量数据存储应用的核心。这些材料的广泛使用是由于它们能够以不同磁化状态的形式保留信息，而不需要供电，并且能够以快速可靠的方式读写信息。在铁磁薄膜中，磁畴壁的出现和运动是导致磁化逆转的主要原因，磁畴壁的出现和运动可以看作是分离不同磁畴的线缺陷。本项目研究了一种特殊类型的磁畴壁，它具有内在的拓扑性质——绕组畴壁。最简单的绕畴壁是360度壁，其中磁化矢量在膜平面上绕壁旋转360度角。研究者系统地研究了缠绕畴壁的存在、稳定性和运动，并研究了它们在磁化逆转过程中的作用。这个问题提出了许多数学上的挑战，因为缠绕畴壁的存在和性质是由各种非线性和非局部力的微妙平衡决定的。研究者开发新的分析，渐近，数值和随机工具来解决这些挑战。这个项目的动机是开发一种基于薄膜铁磁材料的新型通用计算机存储器：MRAM（磁阻随机存取存储器）。因此，总体而言，项目成果对计算机行业和社会的潜在影响是很高的。为此，研究者解决了利用铁磁纳米片作为存储元件的设计的可行性和可靠性问题。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跨学科的研究领域。作为这一过程的一部分，研究者开发应用科学课程，并参与数学和工程研究生和本科生的跨学科培训。这些努力的目的是帮助培养应用数学研究人员和实验科学家之间更好的互动。研究者开发的工具也有望对能量驱动模式形成的许多其他问题有用。

MuratovDMS-0908279 Thin film ferromagnetic materials are at the core of a large array of data storage applications of modern digital technology. The widespread use of these materials is due to their ability to retain information in the form of distinct magnetization states, without the need of being powered, and the possibility to read and write information in a fast and reliable way. Magnetization reversal in thin ferromagnetic films is often mediated by appearance and motion of domain walls, which can be considered as line defects separating different magnetic domains. This project studies one particular type of magnetic domain wall, which is of intrinsically topological nature -- winding domain walls. The simplest winding domain wall is a 360-degree wall, in which the magnetization vector rotates by a 360-degree angle in the film plane across the wall. The investigator undertakes a systematic study of existence, stability, and motion of winding domain walls and investigates their role in magnetization reversal processes. This problem presents many mathematical challenges, because existence and properties of winding domain walls are determined by a delicate balance of different nonlinear and nonlocal forces. The investigator develops new analytical, asymptotic, numerical and stochastic tools to tackle these challenges. This project is strongly motivated by the efforts to develop a new, universal computer memory based on thin film ferromagnetic materials: MRAM (Magnetoresistive Random Access Memory). Therefore, the potential impact of the results of the project on the computer industry and society, in general, is high. To this end, the investigator addresses the questions of feasibility and reliability of the designs that utilize ferromagnetic nanorings as storage elements. A key component of the project is the involvement of a new generation of applied mathematicians into this highly interdisciplinary area of research. As part of this process, the investigator develops courses in applied sciences and takes part in interdisciplinary training of mathematics and engineering graduate and undergraduate students. The aim of these efforts is to help foster better interactions between researchers in applied mathematics and experimental scientists. The tools developed by the investigator are also expected to be useful for many other problems of energy-driven pattern formation.