Charged domain walls are a type of domain wall 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

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 \(\varepsilon \rightarrow 0\) 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 \(\lambda \leqq 1\), one-dimensional charged domain walls are favorable, in the supercritical regime \(\lambda > 1\), the limit model allows for zigzaging two-dimensional domain walls.

带电畴壁是铁磁薄膜中的一种畴壁，由于整体拓扑约束而出现。具有面内磁化\（m \ in {\ mathbb {S}} ^ 1 \）的单轴铁磁薄膜的无量纲微磁能由下式给出

其中M是任意固定的背景场，以确保磁性的全局中性。我们认为材料是细条状，并通过在m上的适当边界条件来强制带电畴壁。在极限\（\ varepsilon \ rightarrow 0 \）中，对于固定的\（\ lambda> 0 \），对应于宏观极限，我们显示出能量\（\ Gamma \）-收敛到极限能量，其中跳跃不连续磁化强度各向异性地受到惩罚。特别地，在亚临界状态\（\ lambda \ leqq 1 \）中，一维带电畴壁是有利的，在超临界状态\（\ lambda> 1 \），极限模型可以使二维畴壁成Z字形。