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
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Submission date: 19. Feb. 2002
published in: Multiscale modeling and simulation, 1 (2003) 1, p. 57-104
DOI number (of the published article): 10.1137/S1540345902402734
MSC-Numbers: 82D40, 49J05, 47G30
Keywords and phrases: multiscale, magnetic materials, néel walls, thin films, nonlocal problems
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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.