  We report results of joint experimental and theoretical studies on
magnetoelectric (ME) compounds Co4Nb2O9 and Co4Ta2O9. On the experimental side,
we present results of the magnetization and dielectric permittivity
measurements in the magnetic field. On the theoretical side, we construct the
low-energy Hubbard-type model for the magnetically active Co 3d bands in the
Wannier basis, using the input of first-principles electronic structure
calculations, solve this model in the mean-field Hartree-Fock approximation,
and evaluate the electric polarization in terms of the Berry phase theory. Both
experimental and theoretical results suggest that Co4Ta2O9 is magnetically
softer than Co4Nb2O9. Therefore, it is reasonable to expect that the
antiferromagnetic structure of Co4Ta2O9 can be easier deformed by the external
magnetic field, yielding larger polarization. This trend is indeed reproduced
by our theoretical calculations, but does not seem to be consistent with the
experimental behavior of the polarization and dielectric permittivity. Thus, we
suggest that there should be a hidden mechanism controlling the ME coupling in
these compounds, probably related to the magnetic striction or a spontaneous
change of the magnetic structure, which breaks the inversion symmetry.
Furthermore, we argue that unlike in other ME systems (e.g. Cr2O3), in Co4Nb2O9
and Co4Ta2O9 there are two crystallographic sublattices, which contribute to
the ME effect. These contributions are found to be of the opposite sign and
tend to compensate each other. The latter mechanism can be also used to control
and reverse the electric polarization in these compounds.
