Florida Polytechnic University

Applied Mathematics & Science Seminar

Tues 2/24 in IST 1068 12:00-1:00pm

Speaker: Dr. Bradford Barker - Physics

Title: Magnetic Anisotropy Energy Constants for any crystalline or chemical environment via simple group theoretic considerations

Abstract: During work for a project as a postdoctoral scholar, I investigated the impact of the local crystalline environment on the magnetic properties of a transition metal ion substitutional defect in a ferroelectric oxide. The scientific and industrial significance of such a nanoscale material system will be discussed in this talk, but the focus is on a surprising gap in the literature. During this project, I needed to describe the spatial variations of the magnetism of an Fe 3+ ion within an ``orthorhombic" crystalline environment, to compare and contrast with the well-known equations for rhombohedral and tetragonal environments. I found, at best, somewhat misleading or over-complete descriptions of this geometry, and I failed to find any systematic cataloging of the equations for the so-called magnetic anisotropy energy (MAE) surfaces for all but a handful of typical geometries. Instead, the best I found was a comment from a textbook about a completely general procedure, beginning with a basis set of spherical harmonics. I pursued this advice to its conclusion, deriving the equations for MAE surfaces for all 32 crystallographic groups, as well as determining the rules to construct the appropriate MAE surface equation for any arbitrary space group, to arbitrary order, based on relatively simple arguments from representation theory, a topic accessible to students after taking a first course in Abstract Algebra, or self-study. Some implications for technologically significant materials is discussed.