A phenomenological theory of magnetic states in noncentrosymmetric tetragonalantiferromagnets is developed, which has to include homogeneous andinhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriyacouplings. Magnetic properties of this class of antiferromagnets with lowcrystal symmetry are discussed in relation to its first known members, therecently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetryand magnetic ordering in these systems allow the simultaneous occurrence ofchiral inhomogeneous magnetic structures and weak ferromagnetism. New types ofincommensurate magnetic structures are possible, namely, chiral helices withrotation of staggered magnetization and oscillations of the totalmagnetization. Field-induced reorientation transitions into modulated stateshave been studied and corresponding phase diagrams are constructed. Structuresof magnetic defects (domain-walls and vortices) are discussed. In particular,vortices, i.e. localized non-singular line defects, are stabilized by theinhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetricantiferromagnets.
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