Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy

• Verfasst von: Brietzke, Birger [VerfasserIn]
• Verfasst von: Knüpfer, Hans [VerfasserIn]
• Titel: Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy
• Verf.angabe: Birger Brietzke and Hans Knüpfer
• E-Jahr: 2022
• Jahr: 20 May 2022
• Umfang: 27 S.
• Fussnoten: Gesehen am 14.10.2022
• Titel Quelle: Enthalten in: Arxiv
• Ort Quelle: Ithaca, NY : Cornell University, 1991
• Jahr Quelle: 2022
• Band/Heft Quelle: (2022), Artikel-ID 2205.10061, Seite 1-27
• DOI: doi:10.48550/arXiv.2205.10061
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Mathematical Physics
• K10plus-PPN: 1818947625

Abstract

We consider the onset of pattern formation in an ultrathin ferromagnetic film of the form Ωt:=Ω×[0,t] for Ω⋐R2 with preferred perpendicular magnetization direction. The relative micromagnetic energy is given by E[M]=∫Ωtd2|∇M|2+Q∫Ωt(M21+M22)+∫R3|H(M)|2−∫R3|H(e3χΩt)|2, describing the energy difference for a given magnetization M:R3→R3 with |M|=χΩt and the uniform magnetization e3χΩt. For t≪d, we derive the scaling of the minimal energy and a BV-bound in the critical regime, where the base area of the film has size of order |Ω|12∼(Q−1)−12de2πdtQ−1√. We furthermore investigate the onset of non-trivial pattern formation in the critical regime depending on the size of the rescaled film.