| Abstract: | We focus on a special type of domain wall appearing in the Landau–Lifshitz theory for soft ferromagnetic films. These domain walls are divergence-free ({mathbb{S}^2})-valued transition layers that connect two directions ({m_theta^pm in mathbb{S}^2}) (differing by an angle ({2theta})) and minimize the Dirichlet energy. Our main result is the rigorous derivation of the asymptotic structure and energy of such “asymmetric” domain walls in the limit ({theta downarrow 0}). As an application, we deduce that a supercritical bifurcation causes the transition from symmetric to asymmetric walls in the full micromagnetic model. |
