Abstract
Ultrafast stimuli can stabilize metastable states of matter inaccessible by equilibrium means. Establishing the spatiotemporal link between ultrafast excitation and metastability is crucial to understand these phenomena. Here we utilize single-shot optical pump–X-ray probe measurements to capture snapshots of the emergence of a persistent polar vortex supercrystal in a heterostructure that hosts a fine balance between built-in electrostatic and elastic frustrations by design. By perturbing this balance with photoinduced charges, an initially heterogeneous mixture of polar phase disorders within a few picoseconds, leading to a state composed of disordered ferroelectric and suppressed vortex orders. On the picosecond–nanosecond timescales, transient labyrinthine fluctuations develop, accompanied by the recovery of the vortex order. On longer timescales, these fluctuations are progressively quenched by dynamical strain modulations, which drive the collective emergence of a single vortex supercrystal phase. Our results, corroborated by dynamical phase-field modelling, reveal non-equilibrium pathways following the ultrafast excitation of designer systems to persistent metastability.
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Data availability
The data shown in the main figures are available at https://doi.org/10.17605/OSF.IO/JPCRB. Any additional data and Python codes of interest are available from the corresponding authors upon request.
Change history
14 October 2024
A Correction to this paper has been published: https://doi.org/10.1038/s41563-024-02044-2
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Acknowledgements
This work is primarily supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award no. DE-SC-0012375 for diffraction and simulation-based study of the materials. R.R. and S.D. acknowledge support from the Office of Basic Energy Sciences, US Department of Energy (DE-AC02-05CH11231). L.W.M. and R.R. also acknowledge partial support from the Army Research Office under the ETHOS MURI via cooperative agreement W911NF-21-2-0162 for the development of SL structures. T.Y. and L.-Q.C. also acknowledge partial support as part of the Computational Materials Sciences Program funded by the US Department of Energy, Office of Science, Basic Energy Sciences, under award no. DE-SC0020145. Q.L.N. acknowledges support from the Bloch Fellowship in Quantum Science and Engineering by the Stanford-SLAC Quantum Fundamentals, Architectures and Machines Initiative. Y.C. and H. Wen acknowledge support from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. S.D. also acknowledges the Scheme for Transformational and Advanced Research in Sciences (MoE-STARS/STARS-2/2023-0048) and the Indian Institute of Science start-up grant for financial support. Y.C. and H. Wen also acknowledge the support for data reduction and analysis from the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory, is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under contract no. DE-AC02-76SF00515. The XFEL experiments were also performed at the BL3-EH2 of SACLA with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (proposal no. 2019B8019). Work performed at the Center for Nanoscale Materials and Advanced Photon Source, both US Department of Energy Office of Science User Facilities, was supported by the US Department of Energy, Office of Basic Energy Sciences, under contract no. DE-AC02-06CH11357. The Advanced Photon Source data were collected at the X-ray Science Division beamlines 7ID-C and 33-ID-D.
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V.A.S., J.W.F., H. Wen and Y.C. conceived the experimental design in consultation with Y.K., I.M., A.M.L. and D.Z. V.A.S., J.W.F., V.G. and H. Wen developed the central concepts of the research. V.A.S., A.D.D., H. Wen, D.A.W., H.P. and D.T. demonstrated the experimental proof of concept at the synchrotron. S.D. synthesized the samples and performed the basic laboratory X-ray diffraction with support from R.R. and L.W.M. V.A.S., Z.Z., H. Wen, D.A.W., H.P., D.T. and M.E.Z. conducted the sample screening using synchrotron X-ray diffraction. V.A.S. carried out the reciprocal-space map analysis of these samples with support from J.W.F., H. Wen and Z.Z. T.Y. and L.-Q.C. developed the phase-field modelling platform and carried out the simulations with assistance from C.D. T.Y. analysed the phase-field modelling results under guidance from L.-Q.C. and C.D., in close collaboration with V.A.S., V.G. and J.W.F. V.A.S., J.W.F., H. Wen, Y.K., D.Z., S.O., K.M., K.T., T.S., Q.L.N., J.W.F., V.E., S.N. and M.C.H. developed the single-shot pump–probe scheme at the X-ray free electron laser facilities. V.A.S., Y.C., H. Wang, Y.K., H.P., Y.S., A.M., Q.L.N., S.O., K.M., K.T., T.S., J.M.G., V.E., S.N., M.C.H., A.M.L., I.M., D.Z., H. Wen, V.G. and J.W.F. conducted the X-ray free electron laser experiments. J.W.F., Y.C., H. Wen and V.A.S. developed the standard Python-based scripts for the experimental data analysis at LCLS and SACLA. R.D.S. conducted the TA (optical) spectroscopy measurements. V.A.S. conducted the experimental data analysis in close collaboration with J.W.F., V.G., T.Y., H. Wen, L.-Q.C., Y.C., A.M.L., L.W.M., H. Wang, C.D. and R.D.S. V.A.S., J.W.F., V.G., L.W.M. and T.Y. wrote the manuscript with suggestions from the other authors. All authors contributed to the discussion and the final version of the manuscript.
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Extended data
Extended Data Fig. 1 Diffraction conditions and single-shot measurement protocol at X-ray free electron laser.
a. Selected detector planar projections relative to the diffraction pattern around the 002 Bragg peak measured at synchrotron in a [(SrTiO3)16/(PbTiO3)16]7.5 superlattice sample. The VSC detector projection intersects the position of the emerging VSC satellite peaks and a V satellite peak, which is used in Fig. 1a,b for time-dependent measurements. The V detector projection intersects the V satellite peaks, which is used in Fig. 3a for time-dependent measurements. b. The detector planar projection relative to the diffraction pattern around the 013 Bragg peak measured at synchrotron in a [(SrTiO3)16/(PbTiO3)16]7.5 superlattice sample. The V+FE detector projection intersects the position of emerging VSC satellite peaks and a V satellite peak, which is used in Fig. 2a for time-dependent measurements. c. Measurement geometry for [(SrTiO3)16/(PbTiO3)16]7.5 superlattice samples. Each sample is translated to expose fresh regions, while a selected diffraction condition is captured by an area detector using the diffraction geometry shown in a. d. The single-shot time resolved measurement protocol involves recording diffraction patterns from 20–30 shots at 30 Hz rate before and after the laser pulse arrival, which are the initial and final states of the system, respectively. The single-shot transient diffraction pattern (“on” shot) is captured on sub-ps to ms timescales after the laser pulse at the diffraction condition shown in a. The image measured at 1 ns is compared to initial and final images.
Extended Data Fig. 2 Single-shot dynamics of vortex supercrystal formation measured near the 002 Bragg peak.
The detector planar surface, intersecting the V satellite peak (marked in the inset and shown in Extended Data Fig. 1a) and VSC satellite peaks, probes a detailed temporal evolution of the nonvolatile phase transformation in a [(SrTiO3)16/(PbTiO3)16]7.5 superlattice sample. The diffraction geometry probes an extended time dependence of VSC growth, where selected time delays are marked in the inset for changes in the dynamical behavior. The logarithmic scale (false color) is kept the same in all individual detector images after photon count rate normalization to the X-ray beam intensity monitor. The vertical position in the images shows qy values relative to the image center, where the latter intersects the crystal truncation rod. The horizontal position in the images mixes the qx and qz components of the peaks. Different regimes captured during the dynamical evolution of phase transformations are marked in the inset.
Extended Data Fig. 3 Single-shot dynamics near the 013 Bragg peak.
Complementary to Fig. 2a, the dynamics at successive time delays are shown for two [(SrTiO3)16/(PbTiO3)16]7.5 superlattice samples in a. and b., respectively. The detector planar surface intersects V and FE satellite peaks (marked in the inset) allowing for a direct comparison of their dynamics. Superlattice peaks (SL) linked with the vertical periodicity of PTO-STO are marked in the inset for n = 0 and n = −1 index of SL reflections. The logarithmic false color scale is the same in all individual detector images after photon count rate normalization to the X-ray beam intensity monitor. The diffraction geometry is the same as in Fig. 1b and Extended Data Fig. 1b, monitoring the extended time dependence of V and FE satellite peaks. The relative intensity changes of different peaks versus time are marked in the inset. The horizontal position in the images is calibrated against the qx values relative to the crystal truncation rod. The vertical position in the images mixes the qy and qz components of the peaks.
Extended Data Fig. 4 Capturing the picosecond strain reconfiguration in the FE phase and the formation of labyrinthine phase.
a. False color maps of scattering X-ray intensities include line profiles along qz projection on the detector at a few representative values for incidence angle near the 002 Bragg diffraction condition. The comparison of the map collected before laser excitation and the corresponding map at 1 ps shows that the FE-phase peak position does not change on this timescale. On the other hand, the map recorded at 10 ps shows that the FE peak moved to substantially smaller qz, which is consistent with a tetragonality increase in this region of the sample. At 10 ps, the satellites of FE vanished (not shown), and the “soup” emerged. The shifted superlattice peak shows that the polarization disorder persists throughout all layers of the superlattice. b. False color maps of detector images capturing the dynamics of diffuse scattering pattern near the 013 Bragg diffraction condition. Data is averaged over the marked time intervals to improve photon statistics of weak features in the pattern. The satellites along a streak corresponding to spatially modulated structure of V-phase is marked with a dashed rectangle. The dashed ellipsoid monitors the position of diffuse scattering of the L-phase, which develops after 10 ps.
Extended Data Fig. 5 Charge carrier and strain relaxation dynamics measured with stroboscopic pump-probe in a [(SrTiO3)16/(PbTiO3)16]7.5 superlattice sample.
a. Transient absorption spectroscopy at a few representative time delays; two characteristic peaks (described in the text) are marked by the vertical lines. b. The temporal dynamics measured at the indicated energies (probe energy) provide the charge carrier recombination rate used in DPFM simulations. c. The reversible temporal dynamics and fluence dependence measured at synchrotron for the FE peak using rocking scans and peak profile fitting. Time-dependent peak position is used to estimate the maximum temperature jump (~300 K) and thermal relaxation rate used in DPFM simulations. The error bar represents typical standard deviation from peak profile fitting.
Extended Data Fig. 6 Calculated spatially dependent charge-carrier dynamics and effect on simulated diffraction on a few ps timescale.
a. In-plane spatially averaged electron (n, continuous lines) and hole (p, dotted lines) concentrations are plotted as function of vertical direction of the superlattice revealing a larger n in SrTiO3 layers near interfaces, while the larger p is found in PbTiO3 near the interfaces. b. The calculated dynamics of electrons in the two spatial regions of the sample are plotted against the experimental TA measurement. c. Calculated line cuts through the diffraction pattern of V-phase satellite peaks near the 002 Bragg diffraction condition, on a few ps timescale (red curve) compared to before laser excitation (black curve), where the later corresponds to the development of the “soup” state (marked in the inset) as described in Fig. 1.
Extended Data Fig. 7 Transient phases captured in single-shot dynamics near the 002 Bragg peak.
The detector planar surface probes the dynamics at successive time delays as indicated in a [(SrTiO3)16/(PbTiO3)16]7.5 superlattice sample, intersecting the first and second order satellite peaks of the V-phase, which are indicated by arrows. The diffraction geometry is the same as in Fig. 3a & Extended Data Fig. 1a. A transient labyrinthine (L) phase is observed and marked at time delays of 0.1–10 ns. The appearance of second-order peaks after 20 ns signals the simultaneous conversion of L- and V- phases to the VSC-phase. The vertical position in the images mixes the qy and qz components of the peaks.
Extended Data Fig. 8 Simulated dynamical evolution of polarization and polarization vorticity during the vortex supercrystal formation.
a. Spatiotemporal snapshots of polarization and polarization vorticity evolving inside the DPFM simulated volumes containing two PTO layers and two STO layers. The L- and V- phases are observed at 5 ns, and VSC phase is observed at 50 ns. b. The spatially averaged polarization components on extended timescales from DPFM simulations show the abrupt reduction of Pz and Py polarization components on a few ps timescale. The Pz recovery starts after 3 ns, while the Py recovery initiates after 10 ns and correlates with the nucleation and growth of VSC.
Extended Data Fig. 9 Model for dynamics of phase transformation when starting from pure FE-phase and exploring the role of strain anisotropy.
Spatiotemporal snapshots of polarization evolving inside the simulated volume with DPFM (containing two PTO layers separated by an STO layer) after single-shot optical excitation of a pure FE phase. The relative normal strain, Δε22, is varied comparatively in simulations as indicated. For Δε22 = 0.0%, the short-range periodic ordering vanishes at 2 ns, while the polarization is dominantly oriented out-of-plane. Labyrinthine (L) fluctuations form at ~10 ns, while a transition to VSC is not observed. For Δε22 = 0.4%, up and down polarized domains coexist at 2 ns and convert to a mixture between vortices and in-plane polarized regions at 10 ns, while a transition to VSC is not observed at longer time.
Extended Data Fig. 10 Model for dynamics of phase transformation starting from phase mixture and exploring the role of strain anisotropy in VSC formation.
Simulated volumes with DPFM (containing two PTO layers separated by an STO layer) provide spatiotemporal snapshots of polarization evolution after single-shot optical excitation. Initial state comprises of coexisting FE- and V- phases, while the normal strain, e22, is varied comparatively (relative Δe22 values are marked above the grey arrows). For Δε22 = 0.06–0.14%, coexisting labyrinthine (L) fluctuations and c+/c- like stripes are observed between 2 and 20 ns, which are transformed to VSC-phase at 50 ns. In contrast, for Δε22 = 0.2% case, a transition to VSC is not observed, demonstrating that VSC formation is sensitive to static and dynamic boundary conditions with anisotropic strain origin.
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Stoica, V.A., Yang, T., Das, S. et al. Non-equilibrium pathways to emergent polar supertextures. Nat. Mater. 23, 1394–1401 (2024). https://doi.org/10.1038/s41563-024-01981-2
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DOI: https://doi.org/10.1038/s41563-024-01981-2
