  We present a characterization of the domain wall solutions arising as
minimizers of an energy functional obtained in a suitable asymptotic regime of
micromagnetics for infinitely long thin film ferromagnetic strips in which the
magnetization is forced to lie in the film plane. For the considered energy, we
provide existence, uniqueness, monotonicity, and symmetry of the magnetization
profiles in the form of 180$^\circ$ and 360$^\circ$ walls. We also demonstrate
how this energy arises as a $\Gamma$-limit of the reduced two-dimensional thin
film micromagnetic energy that captures the non-local effects associated with
the stray field, and characterize its respective energy minimizers.
