Coherent Structures in Nanomagnetism

在过去的5-10年里，先进磁性材料的纳米制造已经发生了真正的革命。自旋电子学是一门新兴学科，旨在利用电子除电荷外的固有自旋进行计算和数据存储。自旋电子学领域的迅速发展为这些材料的数学建模、分析和模拟提出了新的挑战，这些挑战需要与材料设计的进展保持同步。该项目的目的是在一般微磁建模框架内提供下一代磁性材料的有效理论处理，直到纳米级。受生物神经网络启发，特别适合深度学习的神经形态计算的新型自旋电子硬件正在不断发展，这强烈推动了它对磁性skyrmions和其他连贯结构的关注。该问题的非线性、非局部和多尺度特性使其成为21世纪应用数学的一大难题。然而，开发新的数学和计算工具来解决这些系统的真正复杂性的需求，以及它们对计算机技术革命的潜力，使这些基本挑战非常令人兴奋。研究者对层状铁磁材料进行了建模、分析、渐近和计算研究，这些材料目前对自旋电子应用很感兴趣。由于界面效应在纳米尺度上占主导地位的增加，三维微磁建模框架必须包含新型的边界项。这种新的物理特性通常会在材料边界附近产生令人惊讶的效应，并产生新型的边缘磁化结构，如边缘卷曲壁、边缘涡流和手性振荡。研究人员计划建立具有界面磁各向异性和Dzyaloshinskii-Moriya相互作用的铁磁薄膜的微磁模型，推导适用于薄膜的简化二维模型，并开发有效的计算工具来模拟电流和随机驱动系统。接下来，在获得的简化模型类别中，研究者计划对这些材料支持的几种类型的相干结构进行研究，例如扩展和图案化超薄膜中的磁性skyrmions，纳米线中的自旋纹理以及各种边缘结构。这些相干结构的存在性和渐近性质问题引起了能量驱动模式形成和变分演算等具有挑战性的问题。该项目的一个关键组成部分是新一代应用数学家参与这一高度跨学科的研究领域。作为这一过程的一部分，研究者开发应用科学课程，并参与数学和工程研究生、本科生和博士后的跨学科培训。希望该项目也将有助于促进应用数学家和实验学家之间更好的互动。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

There has been a genuine revolution in nanofabrication of advanced magnetic materials in the last 5-10 years. Swift advances in the field of spintronics - an emergent discipline that aims to take advantage of the intrinsic spin of electron in addition to its electric charge for computing and data storage - present new challenges for mathematical modeling, analysis and simulations of these materials, which need to keep pace with the progress in material design. The aim of this project is to provide efficient theoretical treatments of the next generation of magnetic materials within the general micromagnetic modeling framework down to nanoscale. Its focus on magnetic skyrmions and other coherent structures is strongly motivated by the ongoing development of new spintronic hardware for neuromorphic computing inspired by biological neural networks and particularly suited for deep learning. The nonlinear, nonlocal and multiscale nature of the problems make it into a formidable problem of the 21st century applied mathematics. Nevertheless, both the need to develop new mathematical and computational tools to tackle the genuine complexity of these systems and their potential to revolutionize computer technologies make these fundamental challenges very exciting. The investigator undertakes a combination of modeling, analytical, asymptotic and computational studies of layered ferromagnetic materials of current interest to spintronic applications. Due to the increased dominance of interfacial effects at nanoscale, the three-dimensional micromagnetic modeling framework must incorporate new types of boundary terms. This new physics often results in surprising effects near the material boundaries and gives rise to novel types of edge magnetization structures such as edge-curling walls, edge vortices and chiral bobbers. The investigator plans to formulate micromagnetic models of ferromagnetic films that exhibit interfacial magnetic anisotropy and Dzyaloshinskii-Moriya interaction, derive the reduced two-dimensional models appropriate for thin films and develop efficient computational tools to simulate current and stochastically driven systems. Next, within the obtained class of the reduced models, the investigator plans to undertake a study of several types of coherent structures supported by these materials, such as magnetic skyrmions in extended and patterned ultrathin films, spin textures in nanowires, and various edge structures. 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. 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 and postdocs. It is hoped that the project will also help foster better interactions between applied mathematicians and experimentalists.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.