Deterministic and stochastic magnetization dynamics in thin ferromagnetic films and devices

铁磁薄膜中的磁化反转通常是由畴壁的出现和运动介导的，畴壁是分隔不同磁畴的狭窄过渡区。在之前的NSF资助下，研究者对任意应用场中的尼尔壁和单轴材料中没有应用场的360度壁进行了基本的数学理解，并研究了它们在没有和存在小热噪声的情况下在铁磁纳米结构中的磁化反转中的作用。在这个项目中，他进一步研究了具有四重磁晶各向异性的材料（如钴）的畴壁特性，并对磁化动力学进行了更详细的建模、计算和分析研究。特别地，新模型考虑了自旋进动、自旋力矩、随机效应以及生长铁磁薄膜中薄膜形貌和多晶结构的影响。研究者开发了新的数值和渐近工具来解决来自这些建模新方面的挑战。作为培训过程的一部分，他开发了应用科学课程，并参与了数学和工程研究生、本科生和博士后的跨学科培训。该项目有助于促进应用数学研究人员和实验科学家之间更密切的互动。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。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，磁阻随机存取存储器（MRAM）。研究者解决可行性和可靠性的问题，设计使用铁磁纳米片作为存储元件。这些问题的进展对计算机行业具有很大的潜在影响。此外，该项目的一个关键方面是在这个高度跨学科的研究领域培养新一代应用数学家。

Muratov1313687 Magnetization reversal in thin ferromagnetic films is often mediated by the appearance and motion of domain walls, which are narrow transition regions separating different magnetic domains. Under previous NSF funding, the investigator developed a basic mathematical understanding of Neel walls in arbitrary applied fields and 360-degree walls in the absence of the applied fields in uniaxial materials and studied their role in magnetization reversal in ferromagnetic nanorings, both in the absence and in the presence of small thermal noise. In this project, he further investigates the properties of the domain walls in materials with four-fold magnetocrystalline anisotropy characteristic of materials of technological interest, such as cobalt, and undertakes more detailed modeling, computational, and analytical studies of the magnetization dynamics. In particular, the new models incorporate spin precession, spin torque, and stochastic effects, as well as the effect of the film topography and polycrystalline structure in as-grown ferromagnetic films. The investigator develops new numerical and asymptotic tools to tackle the challenges coming from these new aspects of modeling. As part of the training process, he develops courses in applied sciences and takes part in interdisciplinary training of mathematics and engineering graduate and undergraduate students and postdocs. The project helps foster closer interactions between researchers in applied mathematics and experimental scientists. 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. This project is strongly motivated by the efforts to develop a new, universal computer memory based on thin film ferromagnetic materials, the Magnetoresistive Random Access Memory (MRAM). The investigator addresses the questions of feasibility and reliability of the designs that use ferromagnetic nanorings as storage elements. Progress on these problems has high potential impact for the computer industry. In addition, a key aspect of the project is the training of a new generation of applied mathematicians in this highly interdisciplinary area of research.