Hidden domain boundary dynamics toward crystalline perfection

Abstract

A central paradigm of nonequilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which nonequilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous nonequilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single-shot X-ray photon correlation spectroscopy to resolve the nonequilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition in a (PbTiO₃)₁₆/(SrTiO₃)₁₆ superlattice. Such ferroelectric superlattice systems are a useful platform to study phase transitions and topological dynamics due to their high degree of tunability. This provides an approach for capturing the nucleation of the light-induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. We identify a nonequilibrium correlation response spanning >10 orders of magnitude in timescales, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We further show how the observed time-dependent long-time correlations can be understood in terms of stochastic and non-Markovian dynamics of domain walls, encoded in waiting-time distributions with power-law tails. This work defines possibilities for probing the nonequilibrium and correlated dynamics of disordered and heterogeneous media.

Keywords: X-ray photon correlation spectroscopy; domain walls; heterogeneous processes; non-equilibrium dynamics; phase transitions.

Fig. 1.

(A) Reciprocal space maps of pristine and transformed structures. The red box shows area of reciprocal space shown in B. (B) Single-shot XPCS setup showing the pulse-train sequence (Top) and sample diffraction images (Bottom) capturing pristine, transient intermediate (at ΔT = 1 μs), and final state speckle patterns corresponding to boxed area in A. Black boxes show the region of the satellite peak shown in C. (C) Representative single location 50 × 50-pixel regions (centered at the peak centers extracted by procedure detailed in Materials and Methods) at the center of the transient and final supercrystal satellite peak at selected ΔT values. Whereas the integrated intensity of the entire peak saturates after tens of microseconds, the correlations in the speckle patterns continue to evolve on millisecond timescales.

Fig. 2.

(A) Average two-time correlation plots at 500 ns (Top) and 3 ms (Bottom). The average was conducted across different sample locations pumped with the same pump–probe delay. (B) Comparison of the normalized integrated intensity (red) to evolution of correlation function $⟨C\left(t,f\right)⟩$ (black) (Top). Comparison of the normalized differential intensity (red) to differential correlation normalized to the final correlation value (black) (Bottom). Each time point was normalized to the average $C\left(f,f\right)$ at that time point. In both the Top and Bottom plots, the points after 3 ms were calculated by averaging selected n > 0 rows of the two-time plots and are included to show the asymptotic value of $⟨C\left(t,f\right)⟩$ and $⟨\mathrm{\Delta }C/C\left(f,f\right)⟩$. Insets show speckle correlation data at delays earlier than 1 µs.

Fig. 3.

(A) Real-space phase-field simulation results of the heterogeneous evolution of the supercrystal growth as a function of time showing the z-component of the polarization vector in a 308 nm × 308 nm area at selected simulated timesteps labeled in the top left corner (Inset: corresponding computed diffraction pattern). (B) Comparison of the first supercrystal satellite peak intensity (purple) to correlation function (yellow) as defined by Eq. 2 from data in (A), over the entire first supercrystal satellite peak.

Fig. 4.

(A) (Top row) Simulated nucleation and growth model snapshots showing isolated domains growing and impinging upon each other to form defect regions at the boundary between nuclei, followed by defect annihilation. (Bottom row) The corresponding diffraction pattern for each image in the Top row. Animations of these simulations can be found in Movies S2 and S3. (B) Average over 100 simulations of the correlation function between the transient and final computed speckle pattern in an annular region of interest. The generated defects are annihilated using two different waiting time distributions overlayed on the experimental raw correlation data. Inset is the computed integrated intensity with negligible difference for the two waiting time distributions (C) Overlayed average simulation and experimental normalized differential correlation data. Both (B) and (C) show the sensitivity in the long-time data to the waiting time distribution governing the annihilation of boundary defects.