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Nonlinear Stability of Static N\'eel Walls in Ferromagnetic Thin Films

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arxiv 2309.04432 v2 pith:7Y2PTVMY submitted 2023-09-08 math.AP math.SP

A. Capella , C. Melcher , L. Morales , R. G. Plaza This is my paper · ORCID
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keywords staticwallferromagneticfilmsnonlinearstabilitywallsaround
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In this paper, the nonlinear (orbital) stability of static 180^\circ N\'eel walls in ferromagnetic films, under the reduced wave-type dynamics for the in-plane magnetization proposed by Capella, Melcher and Otto [CMO07], is established. It is proved that the spectrum of the linearized operator around the static N\'eel wall lies in the stable complex half plane with non-positive real part. This information is used to show that small perturbations of the static N\'eel wall converge to a translated orbit belonging to the manifold generated by the static wall.

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