Asymptotic shape of isolated magnetic domains

• Verfasst von: Knüpfer, Hans [VerfasserIn]
• Verfasst von: Stantejsky, Dominik [VerfasserIn]
• Titel: Asymptotic shape of isolated magnetic domains
• Verf.angabe: Hans Knüpfer and Dominik Stantejsky
• E-Jahr: 2022
• Jahr: 20 July 2022
• Fussnoten: Gesehen am 09.11.2022
• Titel Quelle: Enthalten in: Royal Society (London)Proceedings of the Royal Society of London / A
• Ort Quelle: London, 1905
• Jahr Quelle: 2022
• Band/Heft Quelle: 478(2022), 2263, Artikel-ID 20220018
• ISSN Quelle: 1471-2946
• DOI: doi:10.1098/rspa.2022.0018
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: approximation
• Sach-SW: calculus of variations
• Sach-SW: equilibrium
• Sach-SW: fluids
• Sach-SW: G-convergence
• Sach-SW: isoperimetric problem
• Sach-SW: limit
• Sach-SW: magnetism
• Sach-SW: microphase separation
• Sach-SW: minimizers
• Sach-SW: non-local isoperimetric problem
• Sach-SW: phases
• K10plus-PPN: 1821318811

Abstract

We investigate the energy of an isolated magnetized domain omega c Rn for n = 2, 3. In non-dimensionalized variables, the energy given by epsilon(omega) = integral(Rn) |& nabla;(chi omega)|dx + integral(Rn) |& nabla;h(omega)|(2)dx penalizes the interfacial area of the domain as well as the energy of the corresponding magnetostatic field. Here, the magnetostatic potential h(omega) is determined by h(omega) = & part;(1 chi omega), corresponding to uniform magnetization within the domain. We consider the macroscopic regime |omega| -> infinity, in which we derive compactness and gamma-limit which is formulated in terms of the cross-sectional area of the anisotropically rescaled configuration. We then give the solutions for the limit problems.