Magnetization Dynamics At Nanoscale

This research project investigates questions in the area of magnetic materials, emphasizing modeling, analysis, and numerical explorations of nanoscale systems. Magnetic materials have been an indispensable ingredient for information storage since the advent of the computer age and presently hold great promise for the development of revolutionary new computer and information technologies. Recent advances in nanofabrication allow an unprecedented precision in building magnetic multilayer structures, using ultrathin films with thickness down to a single atomic layer and a lateral extent down to ten nanometers. At these very small scales, new physical effects become prominent, driving interesting new phenomena such as spin traNational Science Foundation er torque, chiral domain walls, magnetic skyrmions, spin, inverse spin, and topological Hall effects. This new physics needs to be incorporated into the micromagnetic modeling framework that proved very successful in the previous studies of magnetic systems at larger scales. This research project explores the multiscale, nonlinear, nonlocal, and often stochastic nature of the new models, which represents a significant challenge to understanding and predicting the behavior of such systems. A key component of the project is the involvement of a new generation of applied mathematicians in this highly interdisciplinary area of research.This project aims to formulate and analyze models of ultrathin ferromagnetic films in the presence of antisymmetric exchange interaction, which produces a non-trivial interplay with the topological characteristics of the magnetization. Particular care will be taken to incorporate into the models the non-local effects of the stray field via rigorous analysis of the appropriate asymptotic thin film limits arising from the full three-dimensional treatment. Within the obtained reduced thin film models, the properties of charged domain walls, chiral domain walls, and magnetic skyrmions will be investigated, using a combination of analytical, formal asymptotic, and numerical tools. The questions of existence and asymptotic properties of these coherent structures give rise to challenging problems of energy-driven pattern formation and calculus of variations. The research is strongly motivated by the rapidly expanding field of spintronics. All the special magnetization configurations that will be considered in the project are currently targets for potential applications in spintronics devices and, in particular, for the development of non-volatile sequential and random access computer memories.