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Recent experiments for linear magnetoelectric (ME) response in honeycombantiferromagnet Co$_4$Nb$_2$O$_9$ revealed that the electric polarization canbe manipulated by the in-plane rotating magnetic field in a systematic way. Wepropose the minimal model by extracting essential ingredients ofCo$_4$Nb$_2$O$_9$ to exhibit such ME response. It is the three-orbital modelwith $xy$-type atomic spin-orbit coupling (SOC) on the single-layer honeycombstructure, and it is shown to reproduce qualitatively the observed field-angledependence of the electric polarization. The obtained results can be understoodby the perturbative calculation with respect to the atomic SOC. These findingscould be useful to explore further ME materials having similar manipulabilityof the electric polarization.

Manipulating magnetoelectric effect -- Essence learned from Co$_4$Nb$_2$O$_9$