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Neutron diffraction on a triple-axis spectrometer and a small-angle neutronscattering instrument is used to study the magnetic phase transition intetragonal Ba$_2$CuGe$_2$O$_7$ at zero magnetic field. In addition to theincommensurate cycloidal antiferromagnetic (AFM) long-range order, we establishthat weak incommensurate ferromagnetism (FM) also arises below the transitiontemperature $T_N$ identified by sharp Bragg peaks close to the $\Gamma$ point.The intensities of both the incommensurate AFM and FM Bragg peaks vanishabruptly at $T_N$ indicative of a weak first-order transition. Above $T_N$,evidence is presented that the magnetic intensity within the tetragonal $(a,b)$plane is distributed on a ring in momentum space whose radius is determined bythe incommensurate wavevector of the cycloidal order. We speculate that theassociated soft fluctuations are at the origin of the weak first-ordertransition in the spirit of a scenario proposed by Brazovskii.

physical review. b./physical review. b

Formation of incommensurate long-range magnetic order in the  Dzyaloshinskii-Moriya antiferromagnet Ba$_2$CuGe$_2$O$_7$ studied by neutron  diffraction