Front propagation in anisotropic magnetic media

The purpose of this work is to investigate on the phenomenon of front propagation into magnetic media. Here, we study the case when the magnetization, M, is driven by a dc applied magnetic field, H (0), from the demagnetized to the magnetized state. A theoretical model is presented for solving the Landau-Lifshitz-Gilbert equation (LLGE) in the framework of an effective field that includes first order cubic, H-1, in-plane uniaxial, H-u, and shape anisotropy fields, H-D. It is shown that the dynamics of the magnetization is governed by a diffusion-reaction equation, and in the important case of uniformly translating profiles, this equation gives a family of solutions that describe harmonic oscillating (HO), damped oscillating (DO), exponential (EF), amplified oscillating (AO), and dual front profiles (DF), depending on the relative value of the anisotropy fields. Also of interest is the existence of a critical front speed, nu*, connected to a transition point from a region of pulled fronts (nu < nu*) into a region of pushed fronts (nu > nu*). This transition shows a strong dependence on the relative value of the anisotropy constants of the medium, and characterizes the magnetization dynamics.