Graduate Seminar Analysis
Tuesday, January 19, 2016, 2:15pm
Domains in ferromagnetic films with perpendicular anisotrophy
Florian Nolte, Universität Heidelberg
Abstract: We consider a regime of ultra-thin ferromagnetic films with strong anisotropy and easy axis pointing out of the film plane. Experiments show the formation of various domain patterns such as so-called bubble or maze domains. We aim to explain some of these patterns using an energy minimization approach - starting from the full three-dimensional micromagnetic model, we identify a reduced regime and derive the asymptotic behavior of the energy in the framework of Γ Γ-convergence. Our analysis indicates that the typical length scale of domains grows exponentially as a function of the inverse thickness of the plate.
When the ferromagnetic film is exposed to a critical external field, Knüpfer and Muratov have shown that a branching domain pattern consisting of long and slender domains is (in terms of scaling) energetically optimal. We study a single of those long and slender domains using a toy model: the perimeter functional with an additional nonlocal term modelling dipole interaction. We show existence, regularity and connectedness of minimizers as well as the scaling of the minimal energy in terms of the prescribed volume of the domain.
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Ort: Seminarraum 001, Erdgeschoss, Pontdriesch 14-16 , 52062 Aachen