  Charged domain walls are a type of domain walls in thin ferromagnetic films
which appear due to global topological constraints. The non-dimensionalized
micromagnetic energy for a uniaxial thin ferromagnetic film with in-plane
magnetization $m \in \mathbb{S}^1$ is given by
  \begin{align*}
  E_\epsilon[m] \ = \
  \epsilon\|\nabla m\|_{L^2}^2 + \frac {1}{\epsilon} \|m \cdot e_2\|_{L^2}^2
  + \frac{\pi\lambda}{2|\ln\epsilon|} \|\nabla \cdot (m-M)\|_{\dot
H^{-\frac{1}{2}}}^2,
  \end{align*} where magnetization in $e_1$-direction is globally preferred and
where $M$ is an arbitrary fixed background field to ensure global neutrality of
magnetic charges. We consider a material in the form a thin strip and enforce a
charged domain wall by suitable boundary conditions on $m$. In the limit
$\epsilon \to 0$ and for fixed $\lambda> 0$, corresponding to the macroscopic
limit, we show that the energy $\Gamma$-converges to a limit energy where jump
discontinuities of the magnetization are penalized anisotropically. In
particular, in the subcritical regime $\lambda \leq 1$ one-dimensional charged
domain walls are favorable, in the supercritical regime $\lambda > 1$ the limit
model allows for zigzaging two-dimensional domain walls.
