In a ferromagnetic material, the dynamics of the relaxation process is
affected by the presence of a strong shape or material anisotropy. In this
paper, we systematically explore this fact to derive the effective dynamical
equation for a soft ferromagnetic thin film. We show that as a consequence
of the interplay between shape anisotropy and damping, the gyromagnetic
term is effectively also a damping term for the in-plane components of
the magnetization distribution. We validate our result through numerical
simulation of the original Landau-Lifshitz equation and our effective equation.
Comparison of the full Landau-Lifshitz Dynamics and the Effective Dynamics:
The following are some of the simulations we have performed to assess the validity of our effective equation. We have performed numerical simulations of the full Landau-Lifshitz equation and our effective equation, with and without an appied field, and compared them for several different values of the aspect ratio.