  We study existence and properties of one-dimensional edge domain walls in
ultrathin ferromagnetic films with uniaxial in-plane magnetic anisotropy. In
these materials, the magnetization vector is constrained to lie entirely in the
film plane, with the preferred directions dictated by the magnetocrystalline
easy axis. We consider magnetization profiles in the vicinity of a straight
film edge oriented at an arbitrary angle with respect to the easy axis. To
minimize the micromagnetic energy, these profiles form transition layers in
which the magnetization vector rotates away from the direction of the easy axis
to align with the film edge. We prove existence of edge domain walls as
minimizers of the appropriate one-dimensional micromagnetic energy functional
and show that they are classical solutions of the associated Euler-Lagrange
equation with Dirichlet boundary condition at the edge. We also perform a
numerical study of these one-dimensional domain walls and uncover further
properties of these domain wall profiles.
