Asymptotic shape of isolated magnetic domains - Knüpfer, Hans; Stantejsky, Dominik (Proceedings. Mathematical, physical and engineering sciences, 2022)
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.