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

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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).