Grant Details

The digital revolution and the explosion of the amount of digital data pose drastic challenges for continuing sustainable development of computer and information technologies. New physical principles and materials are urgently needed to improve the energy efficiency, information density and the data processing speed in the future devices to continue the trends of Moore's scaling law in the coming 20 year period. Spintronics, a branch of microelectronics that aims to harness the spin of the electron for information storage and processing is an emerging discipline that offers potentially unprecedented improvements in energy efficiency for data storage and processing. It also holds a great promise for novel hardware implementations of neuromorphic, probabilistic and reservoir computing, going beyond the classical von Neumann architecture and suitable for the development of the next generation of artificial intelligence systems. Developing spintronic applications requires a thorough theoretical understanding of the behavior of complex magnetic systems. These are described by systems of nonlinear and nonlocal partial differential equations subject to topological constraints. Our team combines a diverse applied mathematics expertise in modeling, analysis and simulation of energy-driven phenomena in a variety of physical systems and is ideally suited to carry out an interdisciplinary study of the coherent magnetization structures of strong interest to spintronics. Specifically, we will focus our efforts on the three types of magnetization configurations currently pursued experimentally in ultrathin ferromagnetic nanostructures: magnetic skyrmions, skyrmionic bubbles and domain walls. Skyrmions are the magnetization configurations that are endowed with non-trivial topological characteristics that make them robust against thermal noise and therefore offer an exciting possibility of their use to encode bits of information. In this project, we will carry out a comprehensive analysis of existence, stability, creation and manipulation of magnetic skyrmions under realistic conditions encountered in device-driven applications. It will require developing the analytically and numerically tractable mathematical models that will properly account for the effect of confinement in the device geometries and describe the highly non-trivial interactions of skyrmions there. This will involve an extensive use of the tools of the calculus of variations and PDE analysis, together with the use of existing and in-house software. The obtained mathematical results will be validated in close collaboration with our international experimental physicist partners. The potential impact of the results of the proposed research on the computer industry and society in general is high. An important component of the proposed research is the involvement of a new generation of applied mathematicians into this highly interdisciplinary area of research.