One-dimensional in-plane edge domain walls in ultrathin ferromagnetic films

We study existence and properties of 1D 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 1D micromagnetic energy functional and show that they are classical solutions of the associated Euler-Lagrange equation with a Dirichlet boundary condition at the edge. We also perform a numerical study of these 1D domain walls and uncover further properties of these domain wall profiles.