In a thin-film ferromagnet, the leading-order behaviour of the magnetostatic energy is a strong shape anisotropy, penalizing the out-of-plane component of the magnetization distribution. We study the thin-film limit of Landau-Lifshitz-Gilbert dynamics, when the magnetostatic term is replaced by this local approximation. The limiting two-dimensional effective equation is overdamped, i.e. it has no precession term. Moreover, if the damping coefficient of three-dimensional micromagnetics is alpha, then the damping coefficient of the two-dimensional effective equation is alpha + 1/alpha; thus reducing the damping in three dimensions can actually increase the damping of the effective equation. This result was previously shown by Garcia-Cervera and E using asymptotic analysis; our contribution is a mathematically rigorous justification.
|Number of pages||12|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 8 Jan 2005|
- thin film
- effective dynamics
- GINZBURG-LANDAU EQUATIONS