Direct evidence of phonon instability driving geometric improper ferroelectricity in multiferroic YMnO3*

In improper ferroelectrics, the anharmonic coupling between a stable zone-center polar phonon mode and unstable zone-boundary non-polar modes is theoretically proposed to drive the spontaneous polarization. However, the exact mechanism of the transition driven by the coupling between two phonon modes remains to be observed. We have performed comprehensive T-dependent phonon dispersion measurements in the archetypal improper ferroelectric, YMnO₃, including the behavior across the ferroelectric transition, using inelastic neutron scattering and single-crystal x-ray diffraction. In addition, we performed both 0K and finite temperature first-principles lattice dynamics simulations, including anharmonic renormalization effects. Both experiments and simulations reveal the zone-boundary soft-mode, and its temperature dependent anharmonic coupling to the zone-center polar mode, providing direct evidence for the previously proposed mechanism of geometric improper ferroelectricity.