IMF2017

Ferroelectric materials display spontaneous and switchable electric polarization (P) emerging from breaking inversion symmetry upon cooling below the ferroelectric transition temperature, T_FE. In proper geometric ferroelectrics, P is driven by a soft zone-center polar phonon mode, but in improper ferroelectrics the anharmonic coupling between a stable zone-center polar phonon mode and unstable zone-boundary non-polar modes triggers the ferroelectricity. While the soft mode transition in proper ferroelectrics has been thoroughly investigated using both experimental and theoretical techniques, the exact mechanism of the transition driven by non-polar modes in improper ferroelectrics remains less well understood. This knowledge gap results from limitations of experimental studies with Raman and infra-red spectroscopy, intrinsically limited to q ≃ 0 (Γ-point), as well as from the failure of the often-used quasi-harmonic approximation in lattice dynamics simulations using density functional theory, for strongly anharmonic systems. These difficulties have precluded the direct observation and realistic modeling of unstable zone-boundary q~=0 modes and their anharmonic coupling with the zone-center polar mode. To bridge this gap, we have performed comprehensive T-dependent, momentum-resolved phonon dispersion measurements in the archetypal improper ferroelectric, YMnO₃, including the behavior across T_FE, using inelastic neutron scattering, as well as single-crystal x-ray diffraction. In addition, we performed both 0 K and finite temperature first-principles lattice dynamics simulations, including anharmonic renormalization effects, directly revealing the zone-boundary soft-mode, which condenses at T_FE. Our results are compared with proposed models of improper ferroelectric transitions and previous experimental observations.