Analysis of thin ferromagnetic films
Project description
Magnetic materials can be described by a variational principle for the magnetisation vector, which is of fixed length in ferromagnetic materials. The micromagnetic energy also includes the stray field generated by the magnetisation. The resulting model is non-convex and non-local, which results in a simple model that yields extemely rich multi-scale pattern formation. The geometry of thin films sometimes allows reduced theories can be derived. In this project, we study some thin film scalings and determine the possible ground states and their range of validity (using Gamma-convergence or Gamma-expansions) as well as studying the magnetisation dynamics.
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Project published references
R. Ignat, Singularities of divergence-free vector fields with values into S1 or S2. Applications to micromagnetics, Confluentes Math., 4 (2012), pp. 1230001, 80. https://www.math.univ-toulouse.fr/~rignat/paperConfluentesMaths.pdf
A. DeSimone, R. V. Kohn, S. Müller, and F. Otto, Recent analytical developments in micromagnetics, in The Science of Hysteresis, G. Bertotti and I. Mayergoyz, eds., vol. 2, Elsevier Academic Press, 2005, ch. 4, pp. 269–381. https://www.mis.mpg.de/preprints/2004/preprint2004_80.pdf
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