  Non-resonant X-ray magnetic scattering has been used to study the magnetic
structure of multiferroic TbMnO3 in its ferroelectric phase. Circularly
polarized X-rays were combined with a full polarization analysis of the
scattered beam to reveal important new information on the magnetic structure of
this canonical multiferroic. An applied electric field is shown to create a
magnetic nearly mono-domain state in which the cylcoidal order on the Mn
sublattice rotates either clockwise or counter-clockwise depending on the sign
of the field. It is demonstrated how this technique provides sensitivity to the
absolute sense of rotation of the Mn moments, and to components of the ordering
on the Tb sublattice and phase shifts that earlier neutron diffraction
experiments could not resolve.
