Abstract
A ferroelectricity-magnetism-coexisting system, hexagonal $R{\mathrm{MnO}}_{3}(R=\mathrm{Y},$ Lu, and Sc), has been investigated by synchrotron x-ray and neutron powder diffraction measurements. It is found from x-ray diffraction measurements that the ferroelectric polarization originates from the tilting of ${\mathrm{MnO}}_{5}$ polyhedra and the buckling of R layers, which persists up to 1000 K. Neutron diffraction measurements have revealed the reduction of ordered moments from the expected value, as well as strong magnetic diffuse scattering existing far above ${T}_{\mathrm{N}},$ both of which are caused by geometrical frustration of the triangular lattice of Mn ions. We have also investigated the effects of Zr doping into the R site and have found that Zr doping drastically suppresses both ferroelectric distortion and magnetic ordering.
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