  TbMnO3 is an orthorhombic insulator where incommensurate spin order for
temperature T_N < 41K is accompanied by ferroelectric order for T < 28K. To
understand this, we establish the magnetic structure above and below the
ferroelectric transition using neutron diffraction. In the paraelectric phase,
the spin structure is incommensurate and longitudinally-modulated. In the
ferroelectric phase, however, there is a transverse incommensurate spiral. We
show that the spiral breaks spatial inversion symmetry and can account for
magnetoelectricity in TbMnO3.
