Influence of antiferromagnetic ordering on ferroelectric ordering in   LuMnO3
  We have studied the influence of antiferromagnetic ordering on the local dielectric moments of the MnO_5 and LuO_7 polyhedra by measuring neutron powder diffraction patterns of LuMnO_3 at temperatures near T_N. We show that the coupling is weak, because the magnetic exchange coupling is predominantly in the ab-plane of the MnO_5 trigonal bipyramids, and the electric dipole moments, originating in the LuO_7 polyhedra, are oriented along the hexagonal c-axis. Anomalies in the dielectric properties near T_N are thus caused by the geometric constraints between the MnO_5 and the LuO_7 polyhedra. 
Bas B. Van Aken, Thomas T. M. Palstra