Abstract
We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers, called Néel walls. We first establish compactness of \({\mathbb{S}^2}\) -valued magnetizations in the energetic regime of Néel walls and characterize the set of accumulation points. We then prove that Néel walls are asymptotically the unique energy-minimizing configurations. We finally study the corresponding dynamical issues, namely the compactness properties of the magnetizations under the flow of the Landau–Lifshitz–Gilbert equation.
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To our Professor Haïm Brezis on his 70th anniversary with esteem
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Côte, R., Ignat, R. & Miot, E. A thin-film limit in the Landau–Lifshitz–Gilbert equation relevant for the formation of Néel walls. J. Fixed Point Theory Appl. 15, 241–272 (2014). https://doi.org/10.1007/s11784-014-0183-2
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DOI: https://doi.org/10.1007/s11784-014-0183-2