Enhanced local lattice distortions with the antiferromagnetic transition in the multiferroic LuMnO$_{3}$

The ferroelectric hexagonal manganite, LuMnO$_{3}$, has been investigated via neutron scattering and the pair density function analysis to determine the nature of the local atomic distortions with the antiferromagnetic transition, T$_{N}$, of the Mn ions. While in previously reported neutron diffraction data, it was shown that all atomic coordinates changed based on symmetry considerations with T$_{N}$, we hereby show that it is the ferroelectric motion of the Lu ions coupled with O distortions that exhibits a strong temperature dependence below T$_{N}$ as reflected in the Lu-O bonds. This suggests an enhancement of the net electric polarization below T$_{N}$. At the same time, the motion of the apical O1 and O2 ions distorts the MnO$_{5}$ bipyramids, leading to more buckling of the ab-layers. However, the Mn ions do not appear to distort significantly away from their equilibrium position. The oxygen distortions induced with the spin reorientations below T$_{N}$ may be the cause for the Lu ion displacements through electrostatic interactions and this in turn produces coupling to the electric dipole moments.