Magnetic field induced transitions in multiferroic TbMnO3 probed by   resonant and non-resonant X-ray diffraction
  Multiferroic TbMnO3 is investigated using x-ray diffraction in high magnetic fields. Measurements on first and second harmonic structural reflections due to modulations induced by the Mn and Tb magnetic order are presented as function of temperature and field oriented along the a and b-directions of the crystal. The relation to changes in ordering of the rare earth moments in applied field is discussed. Observations below T_N(Tb) without and with applied magnetic field point to a strong interaction of the rare earth order, the Mn moments and the lattice. Also, the incommensurate to commensurate transition of the wave vector at the critical fields is discussed with respect to the Tb and Mn magnetic order and a phase diagram on basis of these observations for magnetic fields H||a and H||b is presented. The observations point to a complicated and delicate magneto-elastic interaction as function of temperature and field. 
J. Strempfer, B. Bohnenbuck, I. Zegkinoglou, N. Aliouane, S.   Landsgesell, M. v. Zimmermann and D.N. Argyriou