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.
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