eprintid: 23797
rev_number: 20
eprint_status: archive
userid: 3062
dir: disk0/00/02/37/97
datestamp: 2018-01-03 14:37:16
lastmod: 2018-01-15 14:18:39
status_changed: 2018-01-03 14:37:16
type: doctoralThesis
metadata_visibility: show
creators_name: Nolte, Florian
title: Optimal scaling laws for domain patterns in thin ferromagnetic films with strong perpendicular anisotropy
subjects: 510
divisions: 110400
adv_faculty: af-11
cterms_swd: Variationsrechnung
cterms_swd: Skalierungsgesetz
cterms_swd: Mikromagnetismus
cterms_swd: Dipol-Dipol-Wechselwirkung
cterms_swd: Musterbildung
cterms_swd: Strukturbildung
abstract: 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
id_scheme: DOI
id_number: 10.11588/heidok.00023797
ppn_swb: 1658668979
own_urn: urn:nbn:de:bsz:16-heidok-237973
date_accepted: 2017-11-03
advisor: HASH(0x564e1c4c2718)
language: eng
bibsort: NOLTEFLORIOPTIMALSCA2017
full_text_status: public
citation:   Nolte, Florian  (2017) Optimal scaling laws for domain patterns in thin ferromagnetic films with strong perpendicular anisotropy.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/23797/1/Dissertation_Florian_Nolte_PDFA-1b.pdf