Electric polarization reversal under high magnetic field in square lattice antiferromagnet Ba$_{2}$CoGe$_{2}$O$_{7}$

Recently, Ba$_{2}$CoGe$_{2}$O$_{7}$ was found to develop electric polarization ($P)$ below $T_{N}$=6.7 K [1]. Interestingly, $P$ along the $a$-axis increases linearly, crossing zero at $H$=0 when magnetic field ($H)$ is applied along the $c$-axis. To investigate the linear $H$-dependence of $P$ further, we measured $P$ dielectric constant (\textit{$\varepsilon $}), and magnetization ($M)$ under high $H$ up to 45 T. On application of high $H$, $P$ increases linearly up to $H\sim $15 T but suddenly decreases to a constant negative value. A peak in \textit{$\varepsilon $} is found at the $P$-reversal point which is suppressed with increasing $H$ to lower temperature with a concomitant sharpening up to $H\sim $36 T at $T$=0.6 K Furthermore, $M(H)$ curves below $T_{N}$ show saturation above the $P$-reversal magnetic field, indicating that the negative $P$ state is due to the fully ordered spin configuration. This phenomenon is similar to the case of multiferroic BiMn$_{2}$O$_{5}$, in which $P$reversal is driven by a spin-flop crossover [2]. However, in Ba$_{2}$CoGe$_{2}$O$_{7}$, $P$-reversal does not accompany a $H$ induced magnetic phase transition. We discuss possible mechanisms for this unique magnetoelectric behavior and suggest possible quantum phase transition behavior. [1] H. Yi \textit{et al.}, Appl. Phys. Lett. 91, 212904 (2008). [2] Jae Wook Kim \textit{et al.}, arXiv:0810.1907.