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.
Cite this article
Roger Moser, On the energy of domain walls in ferromagnetism. Interfaces Free Bound. 11 (2009), no. 3, pp. 399–419