2001/01/09 by Jiang, J. Samuel, Kaper, Hans G., Leaf, Gary K.
#34C23 #49S05 #58C07 #82D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.math/0101077
This article addresses a problem of micromagnetics: the reversal of magnetic moments in layered spring magnets. A one-dimensional model is used of a film consisting of several atomic layers of a soft material on top of several atomic layers of a hard material. Each atomic layer is taken to be uniformly magnetized, and spatial inhomogeneities within an atomic layer are neglected. The state of such a system is described by a chain of magnetic spin vectors. Each spin vector behaves like a spinning top driven locally by the effective magnetic field and subject to damping (Landau-Lifshitz-Gilbert equation). A numerical integration scheme for the LLG equation is presented that is unconditionally stable and preserves the magnitude of the magnetization vector at all times. The results of numerical investigations for a bilayer in a rotating in-plane magnetic field show hysteresis with a basic period of 2π at moderate fields and hysteresis with a basic period of π at strong fields.