Terahertz-Driven Local Dipolar Correlation in a Quantum Paraelectric

Bing Cheng, Patrick L. Kramer, Zhi-Xun Shen, and Matthias C. Hoffmann

Phys. Rev. Lett. 130, 126902 – Published 24 March 2023

Abstract

Light-induced ferroelectricity in quantum paraelectrics is a new avenue of achieving dynamic stabilization of hidden orders in quantum materials. In this Letter, we explore the possibility of driving a transient ferroelectric phase in the quantum paraelectric ${KTaO}_{3}$ via intense terahertz excitation of the soft mode. We observe a long-lived relaxation in the terahertz-driven second harmonic generation (SHG) signal that lasts up to 20 ps at 10 K, which may be attributed to light-induced ferroelectricity. Through analyzing the terahertz-induced coherent soft-mode oscillation and finding its hardening with fluence well described by a single-well potential, we demonstrate that intense terahertz pulses up to $500 kV / cm$ cannot drive a global ferroelectric phase in ${KTaO}_{3}$ . Instead, we find the unusual long-lived relaxation of the SHG signal comes from a terahertz-driven moderate dipolar correlation between the defect-induced local polar structures. We discuss the impact of our findings on current investigations of the terahertz-induced ferroelectric phase in quantum paraelectrics.

Received 17 June 2022
Accepted 22 February 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.126902

Physics Subject Headings (PhySH)

Dynamical phase transitions Exotic phases of matter Ferroelectricity Lattice dynamics

Insulators

High-harmonic generation Laser techniques Photoexcitation Terahertz techniques

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bing Cheng^1,*, Patrick L. Kramer², Zhi-Xun Shen^1,3,4, and Matthias C. Hoffmann ^2,†

¹Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
²Laser Science and Technology, SLAC Linear Accelerator Laboratory, Menlo Park, California 94025, USA
³Geballe Laboratory for Advanced Materials, Stanford University, Stanford, California 94305, USA
⁴Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305, USA

^*chengbing986@gmail.com
^†hoffmann@slac.stanford.edu

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Issue

Vol. 130, Iss. 12 — 24 March 2023

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Images

Figure 1
(a) The cubic lattice structure and ferroelectric soft mode of ${KTaO}_{3}$ . (b) Schematic illustration of our terahertz pump SHG probe setup. PMT: photomultiplier tube, EF: effective focal length. (c) Illustration of the single-well lattice potential along the soft-mode coordinate $Q_{f}$ in paraelectric (PE) state. (d),(e) Illustration of terahertz-driven soft-mode displacement $Q_{f}$ and terahertz-induced SHG intensity $I_{SH}$ as a function of delay time in the lattice potential shown in (c). Note that $I_{SH} \propto Q_{f}^{2} (t)$ . Hence, the oscillating frequency of $I_{SH}$ is the double of the fundamental soft-mode frequency. (f) Illustration of the ultrafast deepening of the FE potential along the soft-mode coordinate $Q_{f}$ in a terahertz-driven transient FE phase. Note that the soft mode will be driven to oscillate in a new potential minimum. (g),(h) Illustration of possible soft-mode displacement $Q_{f}$ and terahertz-induced SHG signal as a function of delay time in a terahertz-driven transient FE phase. Because of being driven to a new potential minimum, $Q_{f}$ will include a nonoscillatory component. The oscillation of $I_{SH}$ follows the oscillation of $Q_{f}$ and will not show a simple frequency doubling.
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Figure 2
(a) Temperature-dependent time-resolved SHG signals recorded at maximum terahertz field strength. (b) Terahertz field strength-dependent time-resolved SHG signals at 10 K. The terahertz field is attenuated in 10% steps. (c),(d) Temperature-dependent Fourier transform of time-resolved SHG signal pumped with 10% and 100% of maximum terahertz field strength respectively. (e) A single exponential relaxation fit to the nonoscillatory SHG relaxation.
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Figure 3
(a) The pure oscillatory SHG signals recorded under various terahertz field strengths at 10 K. The maximum (100%) terahertz field strength is $500 kV / cm$ . (b) The Fourier transforms of oscillatory SHG signals in (a). The gray dashed curve indicates the hardening trend of the FE soft mode as increasing terahertz field strength. (c),(d) Numerical simulations of terahertz-driven soft-mode displacement squared $Q_{f}^{2}$ using Eq. (1) pumped by 100% and 10% of maximum terahertz field strength, respectively. Because of $I_{SH} \propto Q_{f}^{2} (t)$ , $I_{SH} (t)$ (left axis) and $Q_{f}^{2} (t)$ (right axis) have similar temporal waveform. (e) The experimentally reconstructed anharmonic potential of the FE soft mode plotted along with the harmonic potential.
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Figure 4
(a),(b) The pump-probe magnitude $I_{0}$ and relaxation time $τ_{0}$ of terahertz-induced nonoscillatory SHG component as a function of temperature under maximum terahertz excitation. (c),(d) The pump-probe magnitude $I_{0}$ and relaxation time $τ_{0}$ of terahertz-induced nonoscillatory SHG component as a function of terahertz field strength at different temperatures. (e) A qualitative phase diagram of PNR dynamics in the terahertz-pumped ${KTaO}_{3}$ . $T_{1} \sim 60 K$ is the onset temperature of PNRs. $T_{c} \sim 4 K$ is the FE Curie temperature. Above $T_{1}$ , as shown in region I, the pointlike dipoles are dominant. Below $T_{1}$ , PNRs start to appear. In region II, these PNRs behave like noninteracting dipolar entities, even if they are partially polarized by strong terahertz pulses. As temperature is further lowered, as shown in region III, strong terahertz pulses not only polarize PNRs, they also enhance the dipolar interaction between PNRs and induce longer depolarization relaxation.
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