Winding domain walls in thin ferromagnetic films

MuratovDMS-0908279 薄膜铁磁材料是现代数字技术的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的磁化状态的形式保留信息，而不需要供电，并且可以以快速可靠的方式读取和写入信息。 铁磁薄膜中的磁化反转通常是由畴壁的出现和运动所介导的，畴壁可以被认为是分隔不同磁畴的线缺陷。 本计画研究一种特殊的磁畴壁，它具有内在的拓扑性质--缠绕磁畴壁。 最简单的绕组畴壁是360度壁，其中磁化矢量在膜平面中穿过壁旋转360度角。 调查员进行了系统的研究的存在，稳定性和运动的绕组畴壁和调查他们的作用，在磁化反转过程。 这个问题提出了许多数学挑战，因为弯曲畴壁的存在和性质是由不同的非线性和非局部力的微妙平衡决定的。 研究人员开发了新的分析，渐近，数值和随机工具来应对这些挑战。 该项目的强烈动机是努力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，该项目的成果对计算机行业和社会的潜在影响总体上是很大的。 为此，研究人员解决了利用铁磁纳米环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，研究员开发应用科学课程，并参加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促进应用数学研究人员和实验科学家之间更好的互动。 研究人员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.