Electric polarization reversal and nonlinear magnetoelectric coupling in the honeycomb antiferromagnet Fe4Nb2O9 single crystal

As a new magnetoelectric material, honeycomb-based antiferromagnet ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ has attracted a great deal of attention due to its prominent magnetoelectric (ME) coupling and high N\'eel temperature, while the physics of magnetoelectricity is far from understood. In the present study, we present our systematic investigations of the anisotropic ME effect, electric polarization reversal, and nonlinear ME effect of ${\mathrm{Fe}}_{4}{\mathrm{Nb}}_{2}{\mathrm{O}}_{9}$ single crystals, thus highlighting the phase diagram extended down to 10 K. Our results provide clear evidence for electric polarization reversal driven by magnetic field ($H$) along the [110] and [1-10] directions, respectively, while no such polarization reversal occurs as $H$ is applied along the [001] direction. The nonlinear ME effects and electric control of magnetism are unambiguously demonstrated. In addition, the angular-dependent probing reveals a 2\ensuremath{\theta} rotation of the induced electric polarization around the $c$ axis upon the rotation of magnetic field by an angle \ensuremath{\theta}. The electric polarization responses and concomitant ME coupling are well explained by means of the metal-ligand hybridization $p\text{\ensuremath{-}}d$ mechanism. This work represents an essential step forward in the understanding of ME coupling not only in this ${A}_{4}{M}_{2}{\mathrm{O}}_{9}$ honeycomb magnet.