We present macroscopic and neutron diffraction data on multiferroic lightly Co-doped Ni$_3$V$_2$O$_8$. Doping Co into the parent compound suppresses the sequence of four magnetic phase transitions and only two magnetically ordered phases, the paraelectric high temperature incommensurate (HTI) and ferroelectric low temperature incommensurate (LTI), can be observed. Interestingly, the LTI multiferroic phase with a spiral (cycloidal) magnetic structure is stabilized down to at least 1.8 K, which could be revealed by measurements of the electric polarization and confirmed by neutron diffraction on single crystal samples. The extracted magnetic moments of the LTI phase contain besides the main exchange also fine components of the cycloid allowed by symmetry which result in a small amplitude variation of the magnetic moments along the cycloid propagation due to the site-dependent symmetry properties of the mixed representations. In the HTI phase a finite imaginary part of the spine magnetic moment could be deduced yielding a spin cycloid instead of a purely sinusoidal structure with an opposite spin chirality for different spine spin chains. The magnetic ordering of the cross-tie sites in both phases is different in comparison to the respective ones in the pure Ni compound. A wider temperature stability range of the HTI phase has been observed in comparison to Ni$_3$V$_2$O$_8$ which can be explained by an additional single-ion easy-axis anisotropy due to Co-doping. The larger incommensurability of the Co-doped compounds yields a larger ratio between the competing next-nearest neighbour and nearest neighbour interaction, which is $J_2/J_1$=0.43 (0.47) for a doping level of 7% (10%) Co compared to 0.39 in the parent compound.
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