Oxygen displacements and magnetoelectric coupling in LuMnO ₃

The hexagonal multiferroic LuMnO ₃ transforms to the P6 ₃cm symmetry upon entering the ferroelectric phase. Using neutron diffraction and the pair density function analysis, it is shown that short-range local atomic distortions are present, calling for a lower symmetry, such as the P6 ₃, for the following reasons. With cooling, the MnO ₅ bipyramid tilting becomes more enhanced than previously determined. This splits the in-plane Mn-O-Mn angles especially below T _N, leading to inequivalent magnetic coupling constants J between the in-plane Mn ions. Additionally, below T _N, several weak incommensurate magnetic phases appear in response to the reminiscent frustration from the triangular Mn lattice. The complex magnetic structure may be the driving mechanism for the lower crystal symmetry.