Origins of enhanced electromechanical coupling in ferroelectric BaTiO$_{3}$

The origins of enhanced piezoelectric coupling along non-polar crystallographic directions in ferroelectric BaTiO$_3$ are investigated using in situ neutron spectroscopy. It is observed that an electric field applied away from the equilibrium polarization direction causes a stiffening of the transverse acoustic (TA) phonon branch and consequently increases interaction between the TA and the transverse optic (TO) soft mode for a range of wave vectors extending from the Brillouin zone center. This provides a direct lattice dynamics mechanism for enhanced electromechanical coupling, and could act as a guide for designing improved piezoelectric materials.