Origin of Terahertz Soft-Mode Nonlinearities in Ferroelectric Perovskites

Abstract

Soft modes are intimately linked to structural instabilities and are key for the understanding of phase transitions. The soft modes in ferroelectrics, for example, map directly the polar order parameter of a crystal lattice. Driving these modes into the nonlinear, frequency-changing regime with intense terahertz (THz) light fields is an efficient way to alter the lattice and, with it, the physical properties. However, recent studies show that the THz electric-field amplitudes triggering a nonlinear soft-mode response are surprisingly low, which raises the question on the microscopic picture behind the origin of this nonlinear response. Here, we use linear and two-dimensional terahertz (2D THz) spectroscopy to unravel the origin of the soft-mode nonlinearities in a strain-engineered epitaxial ferroelectric SrTiO_{3} thin film. We find that the linear dielectric function of this mode is quantitatively incompatible with pure ionic or pure electronic motions. Instead, 2D THz spectroscopy reveals a pronounced coupling of electronic and ionic-displacement dipoles. Hence, the soft mode is a hybrid mode of lattice (ionic) motions and electronic interband transitions. We confirm this conclusion with model calculations based on a simplified pseudopotential concept of the electronic band structure. It reveals that the entire THz nonlinearity is caused by the off-resonant nonlinear response of the electronic interband transitions of the lattice-electronic hybrid mode. With this work, we provide fundamental insights into the microscopic processes that govern the softness that any material assumes near a ferroic phase transition. This knowledge will allow us to gain an efficient all-optical control over the associated large nonlinear effects.