Correlation between spin helicity and electric polarization vector in quantum chain magnet LiCu$_2$O$_2$

Measurements of polarized neutron scattering were performed on the multiferroic quantum chain magnet LiCu$_2$O$_2$. In the ferroelectric ground phase, the existence of transverse spiral spin component in the $bc$-plane was confirmed. When the direction of electric polarization is reversed, the vector spin chirality as defined as ${\bf C}_{ij} = {\bf S}_i \times {\bf S} _j$ is also reversed. This directly proves that the spin- current model ${\bf P}_{ij} \propto {\bf e}_{ij} \times {\bf C}_ {ij}$ is applicable even to this $e_{\mathrm{g}}$-electron quantum $S$=1/2 system. Differential scattering intensity of polarized neutrons shows a large discrepancy from that expected for the classical $bc$-cycloidal spin structure, implying either the complexity of magnetic structure or the effect of quantum fluctuation.