Soft phonon driven orbital order in CaMn7O12
  We use variable-temperature x-ray thermal diffuse scattering and inelastic scattering to investigate the lattice dynamics in single crystals of multiferroic CaMn7O12 which undergo a series of orbital and magnetic transitions at low temperatures. Upon approaching the charge and orbital ordering temperature To=250 K from above, we observe intense diffuse scattering features and a pronounced optical phonon softening centered around the superstructure reflections of the incommensurately modulated structure. The phonon anomaly appears well above To and continuously increases upon cooling, following a canonical power-law temperature dependence that confirms the transition at To to be of second order and related to a soft-phonon lattice instability. Microscopic mechanisms for the incommensurate charge and orbital ordering based on competing interactions and on momentum dependent electron-phonon coupling could both account for the observed extended momentum width of the phonon softening. Our results highlight the importance of the lattice interactions in the physics of this magnetically induced ferroelectric system. 
S. M. Souliou, Y. Li, X. Du, M. Le Tacon, and A. Bosak
cond-mat.str-el