Integrating Physics and Numerical Mathematics for Characterizing Magnetic Sensor Materials and Analyzing Magnetic Force Microscope Images

近几十年来，磁性材料科学在信息技术领域的积极研究对磁性数据存储系统的快速发展起着至关重要的作用。PI计划在一年的时间里，在这一重要领域进行相当广泛的学习和研究，以一种重要的方式利用数学科学。传统上，这一研究领域属于物理、化学、电气工程、冶金和材料工程方面的研究人员。对于应用数学家来说，这是一个相对未触及的前沿。这个为期一年的项目包括对磁性和磁记录的基础物理进行广泛的研究，并随后开发几个数值模型和方法，以帮助解决磁性材料研究中两个重要但困难的问题：(1)确定未来用于超高密度磁记录和非易失性磁随机存储器的铁磁和反铁磁耦合薄膜的未知磁参数；(2)分析磁性薄膜的磁力显微镜图像，揭示有用信息。除了PI和至少一名数学学生外，这个跨学科项目还将包括物理系的两位教授作为主持人。它还在至少另一位物理教员和一些物理学生的协助下使用了几种仪器。该项目为PI提供了与物理学研究人员进行有效合作的难得机会。数学方法的主要组成部分将是最优化。设计并实现了具有或不具有目标函数梯度信息的优化方法。研究了表示所提出的物理系统的近似数学模型。物理，数学模型和数值方法的整合将从不同的角度揭示这两个难题的新见解，这将为使用现有仪器解决这两个问题提供新的方法。该项目还有助于促进整个数学界对磁性材料的研究兴趣，丰富数学和物理专业学生的教育经验，拓宽他们的职业选择。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学司（DMS）联合支持。

Aggressive research in magnetic materials science for information technology has been playing an essential role in rapid advancement of magnetic data storage systems for over a couple of decades. The PI proposes to engage rather extensively for a period of one year in study and research in this important area that makes use of the mathematical sciences in a significant way. Traditionally, this area of research belongs to researchers in physics, chemistry, electrical engineering, and metallurgical and materials engineering. It has been a relatively untouched frontier for applied mathematicians. The one-year project involves extensive study of basic physics of magnetism and magnetic recording, and subsequent development of several numerical models and methods to help solve two important but difficult problems in magnetic materials research: (1) identification of unknown magnetic parameters of ferromagnetic and anti-ferromagnetic coupled thin films that are used for future ultra-high density magnetic recording and nonvolatile magnetic random access memories, and (2) analysis of magnetic force microscope images of magnetic films for revealing useful information. In addition to the PI and at least one math student, this interdisciplinary project will involve two professors as hosts from department of physics. It also utilizes several instruments with assistance from at least another physics faculty and some physics students. The project provides the PI with rare opportunity to engage in effective collaboration with researchers in physics. The major component of mathematical methods will be on optimization. Optimization methods with or without gradient information of the objective function will be designed and implemented. Approximate mathematical models for representing the proposed physical systems are investigated. Integration of physics, mathematical models, and numerical methods will reveal new insights into those two difficult issues from a different perspective that would offer new ways to help solve the two proposed problems using currently available instruments. The project also helps promote research interests on magnetic materials in the mathematics community in general, enriches the educational experiences and broadens the career options for students majoring in mathematics as well as in physics.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).