In this reply to S. Durbin's comment on our original paper "Ultrafast terahertz-field-driven ionic response in ferroelectric BaTiO3," we concur that his final equations 8 and 9 more accurately describe the change in diffracted intensity as a function of Ti displacement. We also provide an alternative derivation based on an ensemble average over unit cells. The conclusions of the paper are unaffected by this correction.

The dynamical processes associated with electric field manipulation of the polarization in a ferroelectric remain largely unknown but fundamentally determine the speed and functionality of ferroelectric materials and devices. Here we apply subpicosecond duration, single-cycle terahertz pulses as an ultrafast electric field bias to prototypical BaTiO3 ferroelectric thin films with the atomic-scale response probed by femtosecond x-ray-scattering techniques. We show that electric fields applied perpendicular to the ferroelectric polarization drive large-amplitude displacements of the titanium atoms along the ferroelectric polarization axis, comparable to that of the built-in displacements associated with the intrinsic polarization and incoherent across unit cells. This effect is associated with a dynamic rotation of the ferroelectric polarization switching on and then off on picosecond time scales. These transient polarization modulations are followed by long-lived vibrational heating effects driven by resonant excitation of the ferroelectric soft mode, as reflected in changes in the c-axis tetragonality. The ultrafast structural characterization described here enables a direct comparison with first-principles-based molecular-dynamics simulations, with good agreement obtained.