In the theory of micromagnetics, the magnetization of a ferromagnetic sample has an energy that is the sum of four components. We study the asymptotic behaviour of this functional when a parameter (the so-called exchange length) tends to 0. The interaction of two of the components of the energy permits the use of well-known methods from the theory of phase transitions. In the limit this gives rise to a division of the sample into domains of constant magnetization, separated by domain walls. We examine the contribution of a third energy (the energy of the stray ﬁeld) to the limiting problem. In particular, we derive an estimate for the energy density on the domain walls.
|Number of pages||21|
|Journal||Interfaces and Free Boundaries|
|Publication status||Published - 2009|