Multiferroicity in the frustrated spinel cuprate GeCu$_2$O$_4$.

Different from other magnetically frustrated spinel systems, GeCu$_{2}$O$_{4}$ is a strongly tetragonal distorted spinel cuprate in which edge-sharing CuO$_{2}$ ribbons are running along alternating directions perpendicular to the $c$-axis. Here, GeCu$_{2}$O$_{4}$ samples of high quality were prepared via high pressure synthesis (at 4 GPa) and the corresponding magnetic and dielectric properties were investigated. For the first time, we observed a ferroelectric polarization emerging at T$_{N}$ $\sim$ 33~K. Although the ferroelectric polarization is weak in GeCu$_{2}$O$_{4}$ ($P$ $\sim$ 0.2$\mu$C/m$^{2}$), the existence of spin-induced multiferroicity provides a strong constraint on the possible ground state magnetic structures and/or the corresponding theoretical models of multiferroicity for GeCu$_{2}$O$_{4}$.