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.
