  Recent experiments for linear magnetoelectric (ME) response in honeycomb
antiferromagnet Co$_4$Nb$_2$O$_9$ revealed that the electric polarization can
be manipulated by the in-plane rotating magnetic field in a systematic way. We
propose the minimal model by extracting essential ingredients of
Co$_4$Nb$_2$O$_9$ to exhibit such ME response. It is the three-orbital model
with $xy$-type atomic spin-orbit coupling (SOC) on the single-layer honeycomb
structure, and it is shown to reproduce qualitatively the observed field-angle
dependence of the electric polarization. The obtained results can be understood
by the perturbative calculation with respect to the atomic SOC. These findings
could be useful to explore further ME materials having similar manipulability
of the electric polarization.
