Onset of pattern formation in thin ferromagnetic films with perpendicular anisotropy - Brietzke, Birger; Knüpfer, Hans (Calculus of variations and partial differential equations, 2023)
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.
Gesehen am 16.05.2023