  By combining neutron four-circle diffraction and polarized neutron
diffraction techniques we have determined the complex spin structures of a
multiferroic, YMn2O5, that exhibits two ferroelectric phases at low
temperatures. The obtained magnetic structure has spiral components in both the
low temperature ferroelectric phases that are magnetically commensurate and
incommensurate, respectively. Among proposed microscopic theories for the
magneto-electric coupling, our results are consistent with both the
spin-current model that requires a magnetic transverse (cycloidal) spiral
structure in order to induce a spontaneous electric polarization and the
magneto-restriction model. Our results also explain why the electric
polarization changes at the commensurate-to-incommensurate phase transition.
