title: Optimal scaling laws for domain patterns in thin ferromagnetic films with strong perpendicular anisotropy
creator: Nolte, Florian
subject: 510
subject: 510 Mathematics
description: The topic of this thesis are magnetic domains in thin ferromagnetic films with strong perpendicular anisotropy. Our starting point is Micromagnetics, a continuum model based on the principle of minimal energy. At its core is the micromagnetic energy functional, whose local minimizer represent the stable magnetization configurations of the ferromagnetic body. Identifying a suitable thin film regime leads us to investigate a singular limit of the nonconvex and nonlocal micromagnetic energy functional. Our asymptotic analysis yields a scaling law for the typical domain size as a function of the film thickness and another material parameter. To prove an ansatz free lower bound of the energy, we extend an interpolation inequality first obtained in [26]. Moreover, we study a shape optimization problem that can be considered as a prototypical model for a single magnetic domain. We minimize the sum of the perimeter and the dipolar self-energy among subsets of R3 with prescribed volume. Upon proving that minimizers exist, we show that they are (L3-equivalent to) connected open sets with smooth boundary. We furthermore establish a scaling law for the minimal energy in terms of the prescribed volume which yields further information about the shape of minimizers.
date: 2017
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/23797/1/Dissertation_Florian_Nolte_PDFA-1b.pdf
identifier: DOI:10.11588/heidok.00023797
identifier: urn:nbn:de:bsz:16-heidok-237973
identifier:   Nolte, Florian  (2017) Optimal scaling laws for domain patterns in thin ferromagnetic films with strong perpendicular anisotropy.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/23797/
rights: info:eu-repo/semantics/openAccess
rights: Please see front page of the work (Sorry, Dublin Core plugin does not recognise license id)
language: eng