This work is a theoretical study of fronts propagating into an uniaxial ferromagnetic medium with velocity v, when the magnetization, M, is driven by a DC applied magnetic field, H0, from the demagnetized to the magnetized state. It is assumed that the dynamics of M is govern by the LandauâLifshitzâGilbert equation (LLGE). We also consider an effective field that includes in-plane uniaxial, HU, and shape anisotropy fields, HD. We show that, in the particular case of uniformly translating profiles, this equation reduces to a damped-forced Duffing's equation, with a family of solutions that describe periodic oscillating (PO), damped oscillating (DO) or exponential front profiles (EF). Of particular interest is the existence of a critical speed, v0, below which there are no stable states for the magnetization. When the velocity of the profile exactly equals vosc, the only stable states are the PO profiles. Above vosc, there is an asymptotic speed, v*, that separates the DO profiles from EF profiles. This velocity (v*) is connected with the existence of a non-linear marginal stability point for front propagation. Both v0 and v* depend on the applied field and on the anisotropy constants of the material. A stability diagram for front propagation and magnetization curves are also calculated.
Fronts, magnetic waves, Duffing's equation, non-linear dynamics
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