Non-planar Dzyaloshinskii spirals and magnetic domain walls in non-centrosymmetric systems with orthorhombic anisotropy.

The basic micromagnetic models of Landau, Lifshitz, and Dzyaloshinskii, are extended by an anisotropy term with two independent parameters. The resulting ground states of the magnetic domains and the domain-wall profiles are discussed for crystal lattices with orthorhombic unit cells. In these simple geometries, the magnetization is not confined to a single plane. Depending on the relations between the spin-stiffness, anisotropy, and Dzyaloshinskii-Moriya interaction several different zero-temperature phases of the magnetic structure are found. The corresponding phase diagrams are obtained numerically. Analytical results are given for some special cases. The studied model is of particular relevance for magnetic wires, nanostripes and ultrathin magnetic films deposited on non-magnetic surfaces.