Orientation and internal structure of domain walls in ferromagnetic films with anisotropic Dzyaloshinskii-Moriya interaction

•Anisotrpic interfacial Dzyaloshinskii-Moriya interaction leads to formation of oriented domain wall in thin magnetic films.•Internal structure of the domain wall in magnetic thin film with anisotropic Dzyaloshinskii-Moriya is intimately related to the domain wall propagation direction.•Bloch, Neel or mixed domain wall appears in thin magnetic films depending on the interfacial Dzyaloshinskii-Moria interaction anisotropy. We present an analytical study of domain-wall internal structure and orientation in a ferromagnetic film with out-of-plane anisotropy and the anisotropic interfacial Dzyaloshinskii-Moriya interaction (iDMI). The term “anisotropic” means that the iDMI constant is different for different in-plane directions. The interplay between the magnetostatic interaction and the iDMI in a domain wall defines both its structure and orientation. In the case of the isotropic iDMI there is no preferable orientation of the DW in the film plane leading to formation of labyrinth domain structure with random shapes of the domains. In the case of the anisotropic iDMI an oriented domain stripe structure and zigzag domains appear. Depending on system parameters, either the Bloch domain walls, or the Néel ones or the hybrid canted walls realize in the magnetic film. The spatial orientation of the DW and the orientation of the magnetization rotation plane in the DW are intimately related by a simple linear ratio. The analytical results are corroborated by micromagnetic simulations.