Driving strontium titanate ferroelectric Hidden phases are metastable collective states of matter that are typically not accessible on equilibrium phase diagrams. Nova et al. used infrared pulses to excite higher-frequency lattice modes that drive the crystal into a metastable ferroelectric phase, a phase that can persist for many hours. X. Li et al. used terahertz fields to drive the soft mode that moves the ions in the crystal into the positions they occupy in the new phase. The ferroelectric phase in this case was transient, lasting on the order of 10 picoseconds. Because these hidden phases can host exotic properties in otherwise conventional materials, the accessibility to and control of such hidden phases may broaden potential functionality and applications. Science, this issue p. 1075, p. 1079

Abstract “Hidden phases” are metastable collective states of matter that are typically not accessible on equilibrium phase diagrams. These phases can host exotic properties in otherwise conventional materials and hence may enable novel functionality and applications, but their discovery and access are still in early stages. Using intense terahertz electric field excitation, we found that an ultrafast phase transition into a hidden ferroelectric phase can be dynamically induced in quantum paraelectric strontium titanate (SrTiO 3 ). The induced lowering in crystal symmetry yields substantial changes in the phonon excitation spectra. Our results demonstrate collective coherent control over material structure, in which a single-cycle field drives ions along the microscopic pathway leading directly to their locations in a new crystalline phase on an ultrafast time scale.

In recent years, important advances have been made in the search for materials with complex multiphase landscapes that host photoinduced metastable collective states, or “hidden phases.” These phases are rarely accessible on equilibrium phase diagrams and may persist long after the external stimuli that induced them have ceased. Recent experiments (1–6) have illustrated some of the possibilities and expanded our understanding of nonequilibrium material properties and dynamics. In some cases, ultrafast resonant excitation of crystal lattice vibrations (phonons) has played the key role in reaching hidden metallic and superconducting phases (1, 2). Here, we extend this capability in the discovery of a hidden ferroelectric (FE) phase in the paradigmatic material SrTiO 3 (STO). We accessed the hidden phase by selectively exciting the “soft” phonon mode that serves as a collective reaction coordinate along which ions move from their initial positions toward their positions in the new phase (Fig. 1). The resulting ultrafast control over ferroelectricity may find rich applications in memory devices (7), STO-based heterostructures (8), and high-T c superconductivity (9, 10). In other recent experiments (11), ionic displacements along soft-mode coordinates have been driven through nonlinear coupling between the soft modes and other phonon modes that were excited by long-wavelength infrared pulses. In the present case, we excite the soft mode directly, using a terahertz (THz) light field to move the ions into their positions in the incipient crystalline phase. This case was foreshadowed by molecular dynamics (MD) simulations of THz field–induced switching between different FE domain orientations, a closely related type of “collective coherent control” (12).

Fig. 1 Hidden ferroelectric phase accessed through THz field excitation. (A) Collective coherent control over material structure. A single-cycle THz-frequency electric field moves all the ions it encounters toward their positions in a new crystalline phase. In STO, the initial high-symmetry configuration around each Ti4+ ion has no dipole moment and the crystal is paraelectric. The incident field drives the “soft” lattice vibrational mode, moving the ions along the directions indicated into a lower-symmetry geometry with a dipole moment. Long-range ordering of dipole moments in the same direction yields a FE crystalline phase. (B) Experimental setup. THz field–induced lowering of the STO crystal symmetry is observed using 800-nm probe pulses that are partially depolarized (terahertz Kerr effect, or TKE) and which are partially converted to the second harmonic frequency (THz field–induced second harmonic, or TFISH). STO crystal cut is (100). The 800-nm probe pulses are polarized at 45° relative to the vertical THz polarization in the TKE experiments and 0° in the TFISH experiments, respectively. The reflected 400-nm signal is not polarization-resolved. DM, dichroic mirror; PMT, photomultiplier tube.

STO is a widely used dielectric material that has a cubic perovskite structure at room temperature. Many members of this crystal family (e.g., PbTiO 3 ) undergo transitions into FE phases in which the transition metal ions occupy positions that are displaced from the unit cell center so that the material has a macroscopic electric polarization. The collective pathway between the cubic, paraelectric phase and the FE phase involves motions of the ions along the soft phonon coordinate illustrated in Fig. 1A. In contrast, upon reduction of the temperature to 105 K, STO undergoes an antiferrodistortive (AFD) structural phase transition into a second paraelectric phase of tetragonal symmetry (13, 14). Further cooling reveals mode softening (decrease in frequency ω) in the usual Curie-Weiss form ω ∝ (T – T c )1/2 with critical temperature T c = 36 K (15), but at such a low temperature, the zero-point quantum uncertainties in ion positions prevent long-range FE ordering of their locations. Thus, STO is a textbook example of a so-called quantum paraelectric (QPE) phase (15), in which dipole correlation lengths do not extend beyond nanometer length scales (16). Recently, studies have shown that the QPE state in STO is a result of a more complex competition among three driving forces (17, 18): quantum fluctuations, AFD structural distortions (rotations of neighboring oxygen octahedra in opposite directions), and ferroelectric ordering. As a result, even subtle perturbations such as 18O isotope substitution (19) are able to turn STO ferroelectric.

Here, we show that intense coherent THz excitation of the FE soft modes in STO can lead to highly nonlinear phonon responses that overcome the quantum fluctuations and yield clear signatures of an ultrafast QPE-to-FE phase transition. The observed signals reveal a substantial rise in ferroelectric ordering and restructuring of phonon spectra beyond a threshold THz field strength, indicating the emergence of the collective FE phase.

We carried out two complementary experiments with single-cycle THz pump pulses and time-delayed optical probe pulses (Fig. 1B). THz field–induced second harmonic (TFISH) generation spectroscopy (20) was conducted to observe signals that arise from inversion-symmetry breaking due to coherent soft-mode lattice vibrational motion away from the initially centrosymmetric structure of the QPE phase. THz field–induced optical birefringence (THz Kerr effect, or TKE) spectroscopy (21) was performed to characterize Raman-active phonon responses that were driven nonlinearly by the THz-initiated soft-mode lattice vibrations. Figure 2 shows TFISH measurement results from STO and their Fourier transforms at several temperatures and THz field amplitudes. At temperatures above 30 K, a single mode that softens with decreasing temperature, consistent with the FE soft mode, is observed (fig. S6) (14, 22). The coherent vibrational displacements in either direction break the symmetry, resulting in optical second harmonic signals that oscillate at twice the soft-mode frequency. There is also a nonoscillatory signal component due to THz-induced orientation of dipoles, whose decay becomes slower as T is reduced because of the increasing dipolar correlation (23). In the QPE phase at T < 36 K, two features in the signals change substantially at high THz field amplitudes: (i) The nonoscillatory signal component grows in a highly nonlinear fashion as a function of the field strength, which indicates a pronounced growth in the extent of steady-state (nonoscillatory) dipole ordering (24); (ii) additional phonon signatures appear with amplitudes that also increase in a highly nonlinear fashion with THz field strength. These features reveal additional ionic displacements that take place as the FE crystal structure is formed. At soft-mode amplitudes sufficient to reach the new phase, collective displacements of other phonon modes (coupled nonlinearly to the soft mode) are induced. The THz-induced ordered structure is noncentrosymmetric, so oscillations about this structure produce changes in the second harmonic signal level that oscillate at the phonon frequencies, not twice the frequencies. It is noteworthy that the three distinct low-frequency peaks in the TFISH response at high field strength harden gradually as T is reduced (fig. S9), as is known to occur for the soft modes in SrTi18O 3 below its FE phase transition temperature (19). It is likely that we are observing these modes, with frequencies altered slightly as a result of the nonequilibrium transient crystal structure in which we are observing them, and that their sharp onset at high fields indicates their displacements associated with the FE crystal structure. We also observe a broad phonon feature at 1.3 THz whose frequency does not appear to change with temperature and whose signal strength does not increase as sharply as the lower-frequency peaks. We believe this behavior to be consistent with a Raman-active A 1 g mode (we retain the “A 1 g ” label even though the crystal symmetry has been changed; fig. S1B shows the AFD mode coordinate) (25) that is coupled anharmonically to the soft mode. Similar nonlinear coupling has been observed in room-temperature STO using femtosecond x-ray diffraction (26).

Fig. 2 STO symmetry breaking measured by optical second harmonic generation (TFISH). (A and B) Temperature-dependent TFISH signals recorded at 550 kV/cm field amplitude from STO (A) and their Fourier transforms (B). The FE soft mode is observed above 30 K, and new phonon peaks as well as nonoscillatory signals appear at lower temperatures. (C and D) THz field strength–dependent TFISH signals measured at 5 K (C) and their Fourier transforms (D). Signals at low field strengths are magnified by the amounts indicated in (D) for better visibility. Pronounced changes in the nonoscillatory signal components and the phonon spectra occur when the THz field level is increased above 340 kV/cm. The numerical first derivatives of the time-domain signals were calculated before Fourier transformation to reduce the relative amplitude of the nonoscillatory components.

Figure 3 shows TKE data recorded at several sample temperatures and THz field strengths. Although the optical and THz pulses propagate with very different velocities in STO (21, 27), the strong THz absorption (28) ensures that this does not affect the time-dependent signals. At high temperatures (Fig. 3A), only nonoscillatory signals are observed. Unlike such signals in the TFISH data, these signals show only weakly T-dependent decay kinetics and they do not increase substantially as functions of either temperature or THz field amplitude (figs. S7 and S8). They are associated with dipole alignment rather than FE orientation or polarity (22). We also observe the A 1 g mode at 1.3 THz, which increases quadratically with THz field strength, indicating ordinary anharmonic coupling to the FE soft mode as suggested above. By far most striking is the emergence of several low-frequency phonon features whose strengths depend in a highly nonlinear fashion on the THz field strength, clearly similar to what we observed in TFISH measurements. We conclude from all the experimental evidence that at sufficiently large soft-mode amplitudes, an ultrafast FE phase transition is triggered. The strong nonoscillatory TFISH signals reveal the associated increase in FE ordering. The modes that grow in sharply as the THz field amplitude is increased reveal collective displacements of ions along multiple vibrational modes that are coupled nonlinearly to the soft mode and also reveal the change in lattice symmetry. It has been suggested that excitation of the Raman modes may provide constructive feedback to the FE soft mode that drives them by disrupting the balance between AFD and FE structural distortions (17, 18, 29), thereby dynamically destabilizing the paraelectric ground state on a multidimensional energy landscape.

Fig. 3 Strongly nonlinear phonon responses appear in the low-symmetry STO phase. (A and B) Temperature dependence of THz-induced optical depolarization (TKE) signals recorded with 630 kV/cm THz pump field amplitude (A) and their Fourier transforms (B). The numerical first derivatives of the time-domain signals were calculated before Fourier transformation to reduce the relative amplitude of the nonoscillatory components. At temperatures of 60 K and above (22), no oscillatory signal is observed after THz excitation. The 1.3-THz peak and additional low-frequency modes appear at low temperatures. (C) THz field strength dependence of the TKE spectra at 10 K. New peaks grow in sharply as the THz field level is increased from 470 to 630 kV/cm. Inset: Quadratic fit to the 1.3-THz A 1 g mode. The 0.8-THz mode shows faster than quadratic scaling in the THz field strength.

To reach a clearer understanding of THz-induced effects, we conducted classical MD simulations for a supercell of 20 × 20 × 20 unit cells in an isothermal-isobaric ensemble, with the interatomic interaction described by the bond valence model and with external pressure applied (22). For each MD simulation, the system was first relaxed for 100 ps to reach equilibrium at 5 K, and then a Gaussian-profile electric field pulse (duration 0.66 ps, full width at half maximum) was applied in either the z or x crystallographic direction. Trajectories of the system were collected for 50 ps, with the electric field reaching its maximum at 11.5 ps. To evaluate whether the electric field could induce ferroelectricity in STO, we performed simulations with different field amplitudes, and in each case we calculated the global polarization of the system from the collected trajectories. As shown in Fig. 4A, the induced polarization rises sharply over a narrow range of applied field amplitudes, saturating at around 300 kV/cm along both the x and z directions. The important result of the simulations is the confirmation that a single-cycle THz field can induce a substantial global FE polarization when the field is above a threshold level on the order of 200 kV/cm. By calculating the projections of the MD simulation trajectory along different lattice vibrational mode coordinates, we also confirmed that the key displacements occur along the FE soft mode and the coupled AFD mode coordinates [see (22) for details of the mode assignments], whose calculated time-dependent responses are shown in Fig. 4B. The soft-mode response is driven directly by the THz field and reaches its peak at the same time as the peak field. The AFD modes are driven indirectly through their anharmonic coupling to the FE soft mode, and their peak displacements are delayed as a result. The soft mode and the AFD modes show steady-state displacements that persist well after the THz field is gone, indicating relaxation of the coupled system into the FE structure.

Fig. 4 MD simulation of response to STO THz excitation. (A) The peak global polarization induced by excitation with a THz field along different crystallographic axes. A threshold electric field amplitude of about 300 kV/cm is needed in order to fully polarize the crystal. (B) MD simulation trajectory projection onto different vibrational mode coordinates. The FE soft-mode response is driven directly and peaks at the same time as the z-polarized THz field (dashed vertical line). The antiferrodistortive (AFD) modes are driven through coupling to the FE soft mode and reach their maximum displacements after a delay. A steady-state AFD mode displacement (dashed green line shows time-averaged value) as well as FE soft-mode displacement remain well after the THz driving field has ceased.

The experimental data and MD simulations together demonstrate a THz-induced ultrafast QPE-to-FE phase transition in STO. The THz field drives the soft mode, and additional coupled-mode displacements occur to reach the FE structure. Our results demonstrate collective coherent control of material structure that may be applicable to a wide range of classical and quantum phase transitions in which soft phonon modes play key roles in the collective structural transformations.

Supplementary Materials science.sciencemag.org/content/364/6445/1079/suppl/DC1 Materials and Methods Supplementary Text Figs. S1 to S13 Table S1 References (30–47)

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Acknowledgments: We thank T. Egami, A. Steinbacher, Y. Wang, and E. Demler for stimulating discussions. Funding: The work at MIT was supported in part by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, under award DE-SC0019126, and by Swiss National Science Foundation fellowship P2ELP2-172290 (E.B.). The work at Penn (T.Q., J.Z., and A.M.R.) was supported by the DOE, Office of Science, Office of Basic Energy Sciences, under grant DE-FG02-07ER46431. We acknowledge computational support from the NERSC of the DOE. Author contributions: K.A.N. conceived the project and the experiments together with X.L. and J.L.; the time-resolved THz setup was built by X.L., who performed the TFISH and TKE measurements and analyzed the data with support from E.B.; T.Q., J.Z., and A.M.R. provided MD calculations of the pump thresholds and mode displacements for the THz-driven ferroelectricity and the time- and mode-resolved responses; the manuscript was written by K.A.N., X.L., and E.B. with input from all authors. Competing interests: Authors declare no competing interests. Data and materials availability: All data are available in the manuscript or the supplementary materials.