  We present a detailed study of complex dielectric constant and ferroelectric
polarization in multiferroic LiCuVO4 as function of temperature and external
magnetic field. In zero external magnetic field, spiral spin order with an ab
helix and a propagation vector along the crystallographic b direction is
established, which induces ferroelectric order with spontaneous polarization
parallel to a. The direction of the helix can be reoriented by an external
magnetic field and allows switching of the spontaneous polarization. We find a
strong dependence of the absolute value of the polarization for different
orientations of the spiral plane. Above 7.5 T, LiCuVO4 reveals collinear spin
order and remains paraelectric for all field directions. Thus this system is
ideally suited to check the symmetry relations for spiral magnets as predicted
theoretically. The strong coupling of ferroelectric and magnetic order is
documented and the complex (B,T) phase diagram is fully explored.
