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Repulsive interaction of Néel walls, and the internal length scale of the cross--tie wall
Antonio DeSimone, Robert V. Kohn, Stefan Müller and Felix Otto
Néel walls and cross--tie walls are two structures commonly seen in ferromagnetic thin films. They are interesting because their internal length scales are not determined by dimensional analysis alone. This paper studies (a) the repulsive interaction of one--dimensional Néel walls; and (b) the internal length scale of the cross--tie wall. Our analysis of (a) is mathematically rigorous; it provides, roughly speaking, the first two terms of an asymptotic expansion for the energy of a pair of interacting walls. Our analysis of (b) is heuristic, since it rests on an analogy between the cross--tie wall and an ensemble of Néel walls. This analogy, combined with our results on Néel walls and a judicous choice of parameter regime, yields a specific prediction for the internal length scale of a cross--tie wall. This prediction is consistent with the experimentally--observed trends.