We present an analysis of edge domain walls in exchange-biased ferromagnetic films appearing as a result of a competition between the stray field at the film edges and the exchange bias field in the bulk. We introduce an effective two-dimensional micromagnetic energy that governs the magnetization behavior in exchange-biased materials and investigate its energy minimizers in the strip geometry. In a periodic setting, we provide a complete characterization of global energy minimizers corresponding to edge domain walls. In particular, we show that energy minimizers are one-dimensional and do not exhibit winding. We then consider a particular thin-film regime for large samples and relatively strong exchange bias and derive a simple and comprehensive algebraic model describing the limiting magnetization behavior in the interior and at the boundary of the sample. Finally, we demonstrate that the asymptotic results obtained in the periodic setting remain true in the case of finite rectangular samples.

中文翻译：

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超薄交换偏置膜的边缘畴壁

我们提出了对交换偏置铁磁膜中的边缘畴壁的分析，这是由于膜边缘处的杂散场与整体中的交换偏置场之间的竞争导致的。我们介绍了一种有效的二维微磁能，该能控制交换偏置材料中的磁化行为，并研究其在带钢几何形状中的能量最小化器。在周期性设置中，我们提供了与边域壁相对应的全局能量最小化器的完整表征。特别是，我们显示出能量最小化器是一维的，并且没有缠绕。然后，我们考虑大样本和相对较强的交换偏差的特定薄膜状态，并得出一个简单而全面的代数模型，该模型描述了样本内部和边界处的极限磁化行为。最后，我们证明在有限矩形样本的情况下，在周期设置中获得的渐近结果仍然正确。