Magnetic inversion symmetry breaking and ferroelectricity in TbMnO3
  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. 
M. Kenzelmann, A.B. Harris, S. Jonas, C. Broholm, J. Schefer, S.B.   Kim, C.L. Zhang, S.-W. Cheong, O.P. Vajk and J.W. Lynn