Abstract
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 isa, then the damping coefficient of the two–dimensional effective equation isa+ 1/a; thus reducing the damping in three dimensions can actually increase the damping of the effective equation. This result was previously shown by García–Cervera and E using asymptotic analysis; our contribution is a mathematically rigorous justification.
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