  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.

Analysis of PDEs;Mesoscale and Nanoscale Physics;Pattern Formation and Solitons