Dynamic nanoscale spatial heterogeneity in a perovskite to brownmillerite topotactic phase transformation

Phase transitions are omnipresent in modern condensed matter physics and its applications. In solids, phase transformations typically occur by nucleation and growth under non-equilibrium conditions. Under constant external conditions, $\textit{e.g.}$, constant heating temperature and pressure, the nucleation and growth dynamics are often thought of as spatially and temporally independent. Here, $\textit{in-situ}$ Bragg X-ray photon correlation spectroscopy (XPCS) reveals nanoscale spatial and dynamical heterogeneity in the perovskite to brownmillerite topotactic phase transformation in La$_{0.7}$Sr$_{0.3}$CoO$_3$ (LSCO) thin films under constant reducing conditions over a time-span of multiple hours. Specifically, a timescale associated with domain growth remains stable, with a corresponding domain wall speed of $v_d = 6 \pm 0.5 \times10^{-4}$ nm/s ($2 \pm 0.2$ nm/h), while a slower timescale, associated with temperature driven de-pinning of domains, leads to accelerating dynamics with timescales following an aging power law with exponent $-2.2 \pm 0.5$. The experiment demonstrates that Bragg XPCS is a powerful tool to study nanoscale dynamics in phase transformations. The results are relevant for phase engineering of phase-change devices, as they show that nanoscale dynamics, linked to domain and domain-wall motion, can continuously evolve and speed up with time, even hours after the initiation of the phase transformation, with potential repercussions on electrical performance.