### Abstract or Additional Information

Abstract: In the continuum theory, the magnetization of a ferromagnetic sample $\Omega \subset \R^3$ is described by a unit vector field $m \in H^1(\Omega,S^2)$. The minimization of the underlying micromagnetic energy leads to the formation of extended magnetic domains with uniform magnetization, separated by thin transition layers. One type of such transition layers, observed in thin ferromagnetic films are the so called zigzag walls. We consider the family of energies$$E_\varepsilon[m] \ = \ \frac{\epsilon}{2}\|\nabla m\|_{L^2(\Omega)}^2 + \frac 1{2\varepsilon} \|m \cdot e_2\|_{L^2(\Omega)}^2 %+ \frac{\pi\lambda}{2|\ln \varepsilon|} \|\nabla \cdot (m-M)\|_{\dot H^{-\frac 12}}^2,$$valid for thin ferromagnetic films. We consider a material in the form a thin strip andenforce a charged domain wall by suitable boundary conditions on $m$. Here, $M$ is an arbitrary fixed background field to ensure global neutrality of magnetic charges. In thelimit $\varepsilon \to 0$ and for fixed $\lambda > 0$, corresponding to the macroscopiclimit, we show that the energy $\Gamma$--converges to a limit energy where jumpdiscontinuities of the magnetization are penalized anisotropically. Inparticular, in the subcritical regime $\lambda \leq 1$ one--dimensional chargeddomain walls are favorable, in the supercritical regime $\lambda > 1$ the limitmodel allows for zigzaging two--dimensional domain walls.