  A phenomenological theory of magnetic states in noncentrosymmetric tetragonal
antiferromagnets is developed, which has to include homogeneous and
inhomogeneous terms (Lifshitz-invariants) derived from Dzyaloshinskii-Moriya
couplings. Magnetic properties of this class of antiferromagnets with low
crystal symmetry are discussed in relation to its first known members, the
recently detected compounds Ba2CuGe2O7 and K2V3O8. Crystallographic symmetry
and magnetic ordering in these systems allow the simultaneous occurrence of
chiral inhomogeneous magnetic structures and weak ferromagnetism. New types of
incommensurate magnetic structures are possible, namely, chiral helices with
rotation of staggered magnetization and oscillations of the total
magnetization. Field-induced reorientation transitions into modulated states
have been studied and corresponding phase diagrams are constructed. Structures
of magnetic defects (domain-walls and vortices) are discussed. In particular,
vortices, i.e. localized non-singular line defects, are stabilized by the
inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric
antiferromagnets.
