Magnetoelectric coupling in the honeycomb antiferromagnet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Co</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>Nb</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>9</mml:mn></mml:msub></mml:mrow></mml:math>

The magnetic structure and magnetoelectric effect have been investigated for single crystals of the antiferromagnet ${\mathrm{Co}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$. Single-crystal neutron diffraction and magnetic susceptibility measurement have revealed that the magnetic structure is different from a collinear arrangement with spin parallel to the trigonal axis as proposed previously. ${\mathrm{Co}}^{2+}$ magnetic moments are found to be almost lying in the basal plane, which lowers the magnetic symmetry to $C2/{c}^{\ensuremath{'}}$ with the propagation vector $\mathbit{k}=0$. Associated with the magnetic phase transition, a sharp anomaly in the dielectric constant and displacement current indicate the appearance of the magnetoelectric below N\'eel temperature ${T}_{N}$ with a large coupling constant up to 30 ps/m. The existence of off-diagonal components in a magnetoelectric tensor indicate the formation of ferrotoroidic order in ${\mathrm{Co}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$. Such a magnetoelectric effect can be ascribed to the reduction of symmetry caused by simple antiferromagnetic order in a honeycomb network.