Nonlinear magnetoelectric effect in paraelectric state of Co4Nb2O9 single crystal.

We report the structural, magnetoelectric (ME), magnetic and electric control of magnetic properties in Co4Nb2O9 (CNO) single crystal. A detailed ME measurement reveals a nonlinear ME effect instead of a linear ME effect in CNO single crystal. By fitting the magnetization-electric field (M-E) curve, it can be found that the linear ([Formula: see text]) and quadratic (γ) coefficients equal to ~8.27 ps/m and ~-6.46 ps/MV for upper branch, as well as ~8.38 ps/m and ~6.75 ps/MV for the lower branch. More importantly, a pronounced response was observed under a small cooling magnetic field, which cannot even cause the spin flop. This suggests a magnetoelectric effect can occur at paraelectric state for CNO single crystal. Furthermore, we also found that the magnetization of every axis responds to electric field applied along a-axis, but fails to do so when the electric field is applied c-axis. Such findings supply a direct evidence to the magnetic structure and ME coupling mechanism indirectly reflected by our neutron experiment.