The incommensurate magnetic structure of a tetragonal antiferromagnet with antisymmetric exchange

Analysis of the incommensurate magnetic structure that emerges for two coexisting types of the antisymmetric Dzyaloshinski-Moriya exchange interaction (the weakly ferromagnetic component of vector D along the tetragonal axis and the helicoidal component distributed in the tetragonal plane) is carried out for the first time for a tetragonal antiferromagnet. The helicoidal component for each pair of interacting spins has a 2D distribution; its direction in the tetragonal plane depends on the direction of the exchange bond in each pair. The Lifshits invariant of the Ginzburg-Landau functional is obtained, which is responsible for the formation of an incommensurate magnetic structure for such a distribution. It is shown in the mean field approximation that the incommensurate magnetic structure that forms in this case is a nonlinear double helicoid with a modulation vector lying in the tetragonal plane and with a varying angle between the polarization planes of quasi-antiferromagnetic sublattices. The ground state of the magnet is degenerate in the orientation of the modulation vector in the tetragonal plane. The rate of variation in the orientations of moments in the polarization planes passing through the tetragonal axis is controlled by the angle between the directions of the moments and the tetragonal axis. The local weakly ferromagnetic moment remaining in the polarization plane varies in magnitude and sign. The relation between the orientations of the modulation and polarization vectors is derived for the cases of simple and inversion tetragonal axes in the space symmetry group of the crystal.