Influence of magnetic on ferroelectric ordering in LuMnO₃

We have studied the influence of antiferromagnetic ordering on the local dielectric moments of the MnO₅ and LuO₇ polyhedra by measuring neutron powder-diffraction patterns of LuMnO₃ at temperatures near TN. We show that the coupling is weak, because the magnetic exchange coupling is predominantly in the ab plane of the MnO₅ trigonal bipyramids, and the electric dipole moments, originating in the LuO₇ 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 MnO₅ and the LuO₇ polyhedra.