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 SrTiO3 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.Received 14 September 2020Revised 20 January 2021Accepted 12 March 2021DOI:https://doi.org/10.1103/PhysRevX.11.021023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDielectric propertiesElectric polarizationElectronic excitation & ionizationElectronic transitionsFerroelectricityLight-matter interactionNonlinear opticsPhononsStrong electromagnetic field effectsUltrafast phenomenaTechniquesTerahertz time-domain spectroscopyUltrafast pump-probe spectroscopyCondensed Matter, Materials & Applied PhysicsNonlinear DynamicsAtomic, Molecular & Optical
Highlights
Soft modes are excitations that are intrinsically linked to a phase instability and mediate the phase transition, where they approach zero frequency [1,2]
Some of the rare attempts towards this goal reveal that the nonlinear response of THz soft modes in ferroelectrics [8] or molecular crystals [9] occurs at surprisingly low THz electric-field amplitudes of approximately 50 kV=cm
We have presented a comprehensive study on the origin of THz nonlinearities of a polar soft mode in a strain-engineered epitaxial ferroelectric thin film
Summary
Soft modes are excitations that are intrinsically linked to a phase instability and mediate the phase transition, where they approach zero frequency [1,2]. When the coupling to the electromagnetic field is included, the purely phononic approach to the soft-mode dynamics gives unphysical values to certain parameters These include non-natural Born effective charges [12] on the ions [8,13] and large zero-point motions [8]. Close to the phase transition, the soft-mode frequency gradually approaches zero, leading to an instability of the entire crystal With this softening, the electronic contribution to the oscillator strength of the soft mode grows to values much larger than the contribution from its pure ionic motion. With classical equations for the electronic motion, this picture can reproduce soft-mode nonlinearities associated with slow collective motions, i.e., with frequencies far below the THz range, such as during thermal phase transitions [20,21]. The role of electronic degrees of freedom for low-frequency modes in condensed matter has been underestimated so far, and our work can stimulate future research in this direction
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