Chiral magnetic ordering in two-dimensional ferromagnets with competing Dzyaloshinsky-Moriya interactions

Chiral magnetic ordering due to Dzyaloshinsky-Moriya interaction on two-dimensional lattices is studied theoretically. Several competing Dzyaloshinsky-Moriya vectors are introduced on the basis of symmetry arguments. The role of the exchange interaction, magnetic anisotropy, and dipolar coupling for the ordering in chiral nanomagnets is investigated. It is demonstrated that the periodicity of the modulated structure, which is determined by all interactions involved, is lattice dependent; the direction of spiral propagation and orientation of magnetization is determined by the competition between different Dzyaloshinsky-Moriya vectors and anisotropy; the anisotropy can induce a domain formation or destroy the chiral ordering depending on its orientation. We show that the Dzyaloshinsky-Moriya coupling is responsible for the chiral magnetic ordering in Fe/W(110).