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.
