Multiferroicity in the spin-1/2 quantum matter of LiCu$_{2}$O$_{2}$

Multiferroicity in LiCu$_{2}$O$_{2}$ single crystals is studied using resonant soft x-ray magnetic scattering, hard x-ray diffraction, heat capacity, magnetic susceptibility, and electrical polarization. Two magnetic transitions are found at 24.6 K (\textit{T}$_{1}$ and 23.2 K (\textit{T}$_{2}$. Our data are consistent with a sinusoidal spin structure at \textit{T}$_{2}$ $<$ \textit{T} $<$ \textit{T}$_{1}$ and with a helicoidal spin structure at \textit{T} $<$ \textit{T}$_{2}$ giving rise to ferroelectricity. Surprisingly, above \textit{T}$_{2}$ the correlation lengths of the spin structures increase as the temperature increases with dramatic changes of $\sim $42{\%} occurring along the \textit{c} -axis. Our results demonstrate the intimate connection between frustration and coupling between electronic and magnetic polarizations in LiCu$_{2}$O$_{2}$.