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 the recently detected compounds ${\mathrm{Ba}}_2{\mathrm{CuGe}}_2{\mathrm{O}}_7$ and ${\mathrm{K}}_2{\mathrm{V}}_3{\mathrm{O}}_8.$ Crystallographic symmetry and magnetic ordering in these systems allow the simultaneous occurrence of chiral inhomogeneous magnetic structures and weak ferromagnetism. Incommensurate magnetic structures, chiral helices, with a rotation of the staggered magnetization accompanied by oscillations of the total magnetization, are possible. 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 nonsingular line defects, are stabilized by inhomogeneous Dzyaloshinskii-Moriya interactions in uniaxial noncentrosymmetric antiferromagnets.

• Received 15 July 2002

DOI:https://doi.org/10.1103/PhysRevB.66.214410