  Neutron diffraction on a triple-axis spectrometer and a small-angle neutron
scattering instrument is used to study the magnetic phase transition in
tetragonal Ba$_2$CuGe$_2$O$_7$ at zero magnetic field. In addition to the
incommensurate cycloidal antiferromagnetic (AFM) long-range order, we establish
that weak incommensurate ferromagnetism (FM) also arises below the transition
temperature $T_N$ identified by sharp Bragg peaks close to the $\Gamma$ point.
The intensities of both the incommensurate AFM and FM Bragg peaks vanish
abruptly 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 by
the incommensurate wavevector of the cycloidal order. We speculate that the
associated soft fluctuations are at the origin of the weak first-order
transition in the spirit of a scenario proposed by Brazovskii.
