Understanding Magnetic Hysteresis in Cubic Materials

Abstract

Hysteresis is the limiting criterion in many applications of functional materials. Recent understanding and development in shape memory alloys have lead to very low hysteresis materials. Low hysteresis shape memory alloys with unusual magnetoelectric properties have found new and interesting applications. In this thesis, we try to understand magnetic hysteresis in cubic ferromagnets using the framework of micromagnetics. We look at two cubic materials: Galfenol (Fe$_{74}$Ga$_{26}$ and Fe$_{83}$Ga$_{17}$) and Permalloy (Fe$_{21.5}$Ni$_{78.5}$). The material parameters of Galfenol show that it belongs to a new parameter regime in micromagnetics that has not been explored before. We study the macroscopic properties and try to understand its magnetic microstructure. The main tools used to study the macroscopic properties are: Weak convergence and Young measures. Theoretical predictions of the macroscopic properties match well with results obtained from experiments. By including the exchange energy and minimizing the total micromagnetic energy of Galfenol we show that its magnetic microstructure has lower energy than other commonly observed magnetic microstructures. This paves the way for obtaining optimal energy scaling laws for cubic ferromagnets in general. We also touch upon the well known Permalloy problem in this thesis. Permalloy has very low coercivity at a puzzling material composition. We make few interesting observations about the magnetic microstructure of the Permalloy. Finally, we shall report the results of some novel experiments that were aimed to synthesize an elusive hard ferromagnet known as Tetrataenite.