  Strongly correlated materials with multiple order parameters provide unique
insights into the fundamental interactions in condensed matter systems and
present opportunities for innovative technological applications. A class of
antiferromagnetic honeycomb lattices compounds, A4B2O9 (A = Co, Fe, Mn; B = Nb,
Ta), have been explored owing to the occurrence of linear magnetoelectricity.
We observe a highly nonlinear magnetoelectric effect on single crystals of
Co4Ta2O9 (CTO), distinctive from the linear behavior in the isostructural
Co4Nb2O9. Ferroelectricity emerges primarily along the [110] direction under
magnetic fields, with the onset of antiferromagnetic order at TN = 20.5 K. For
in-plane magnetic field, a spin-flop occurs at HC ~ 0.3 T, above which the
ferroelectric polarization gradually becomes negative and reaches a broad
minimum. Upon increasing magnetic field further, the polarization crosses zero
and increases continuously to ~60 uC/m2 at 9 T. In contrast, the polarization
for a magnetic field perpendicular to the hexagonal plane increases
monotonously and reaches ~80 uC/m2 at 9 T. This observation of a strongly
nonlinear magnetoelectricity suggests that two types of inequivalent Co2+
sublattices generate magnetic field-dependent ferroelectric polarization with
opposite signs. These results motivate fundamental and applied research on the
intriguing magnetoelectric characteristics of these honeycomb lattice
materials.
