  By combining single crystal x-ray and neutron diffraction, and the
magnetodielectric measurements on single crystal Fe4Nb2O9, we present the
magnetic structure and the symmetry-allowed magnetoelectric coupling in
Fe4Nb2O9. It undergoes an antiferromagnetic transition at TN=93 K, followed by
a displacive transition at TS=70 K. The temperature-dependent dielectric
constant of Fe4Nb2O9 is strongly anisotropic with the first anomaly at 93 K due
to the exchange striction as a result of the long range spin order, and the
second one at 70 K emanating from the structural phase transition primarily
driven by the O atomic displacements. Magneticfield induced magnetoelectric
coupling was observed in single crystal Fe4Nb2O9 and is compatible with the
solved magnetic structure that is characteristic of antiferromagnetically
arranged ferromagnetic chains in the honeycomb plane. We propose that such
magnetic symmetry should be immune to external magnetic fields to some extent
favored by the freedom of rotation of moments in the honeycomb plane, laying
out a promising system to control the magnetoelectric properties by magnetic
fields.
