Thermal and Size Effects in Ferroelastic Domains by Machine Learning

Ferroelastic domain walls (DWs) underpin key functionalities in complex oxides. In free-standing ferroic thin films, where elastic interactions are highly thickness dependent, understanding DW behaviour across length scales and external stimuli is crucial. A thickness-dependent monopolar-to-dipolar crossover in elastic DW behaviour has been reported; however, how temperature influences this regime remains unexplored. Here, LaAlO3 thin films spanning the dipolar ($<200$ nm) and crossover (200-300 nm) regimes are investigated using in situ heating scanning transmission electron microscopy (STEM) and a machine-learning-driven image analysis approach. By tracking DW curvature and density from above $T_C$ (approximately $550,^\circ$C) to room temperature (RT), a distinct interplay between temperature and thickness is identified. In the dipolar regime, DWs are mobile and curved near $T_C$ and gradually freeze upon cooling, consistent with the well-known temperature freezing regime. In contrast, within the crossover regime, DWs are nearly static, with minimal reconfiguration through cooling and curvature an order of magnitude lower at RT. These results map the evolution of DWs across the thermally driven super-elastic to freezing regimes, revealing how thickness and temperature govern DW morphology and dynamics, and providing insight relevant for domain engineering in free-standing oxide thin films.

💡 Research Summary

The authors investigate how the combined effects of film thickness and temperature govern the morphology and dynamics of ferroelastic domain walls (DWs) in free‑standing LaAlO₃ membranes. Samples with four distinct thicknesses—160 nm, 180 nm, 200 nm, and 300 nm—were fabricated by focused ion beam lift‑out and mounted on a DENSsolution Climat MEMS heating chip. In‑situ scanning transmission electron microscopy (STEM) dark‑field images were recorded while the specimens were heated from room temperature to 600 °C (≈TC + 50 °C) and then cooled back at a rate of 0.33 °C s⁻¹, with images taken every 50 °C.

To handle the large image dataset, a convolutional neural network based on the U‑Net architecture with a ResNet‑34 encoder was trained on 33 manually annotated images (75 % of the data) and validated on 9 images. The model performed semantic segmentation of each pixel into DW, domain, or background. From the binary DW masks, the authors extracted two quantitative metrics: (i) DW area fraction (as a proxy for DW density) and (ii) local curvature, obtained by fitting splines to contiguous DW pixel chains. Averaged values for each thickness and temperature step were calculated, and uncertainties were estimated via bootstrapping.

The results reveal a clear thickness‑dependent crossover. In the thin, dipolar regime (≤180 nm), DW area fraction rises sharply just below TC, reaching a maximum between 300 °C and 400 °C, then gradually declines to a plateau near 200 °C. Simultaneously, the curvature is high (≈1–1.5 µm⁻¹) near TC, decreasing continuously during cooling to ≈0.3–0.5 µm⁻¹ below 250 °C. This behavior mirrors the “super‑elastic” regime known from bulk LaAlO₃, where DWs are highly mobile at elevated temperature and become progressively pinned as the temperature falls, entering a freezing regime.

In contrast, samples in the crossover thickness range (200–300 nm) display a nearly constant, low DW area fraction across the entire temperature range, with only modest, discrete increases corresponding to the nucleation of isolated walls. Their curvature remains an order of magnitude smaller (≈0.05–0.1 µm⁻¹) even at room temperature, indicating that DWs are essentially static throughout the thermal cycle. This static behavior is consistent with a monopolar‑dominated elastic interaction (∝ d⁻¹) that exerts strong long‑range restoring forces, suppressing wall bending and mobility.

Finite‑element COMSOL simulations of the MEMS heating geometry show temperature gradients of only 5–12 °C across the sample, confirming that the observed shift in the apparent transition temperature for the thicker films is intrinsic and not an artefact of thermal non‑uniformity.

The authors discuss the functional implications of DW curvature: prior work on BiFeO₃ and ErMnO₃ has shown that curved DWs can host enhanced charge accumulation and altered local electric fields, affecting conductivity. By analogy, curvature‑controlled strain fields in ferroelastic LaAlO₃ could modulate ionic or phonon transport, offering a route to engineer thermal or electromechanical properties via thickness and temperature.

Overall, the study demonstrates that (1) a thickness‑dependent monopole‑dipole crossover exists in free‑standing LaAlO₃, (2) temperature drives a super‑elastic to freezing transition that is strongly modulated by film thickness, and (3) machine‑learning‑based image segmentation provides rapid, reliable quantification of DW density and curvature in large STEM datasets. The findings establish a framework for domain‑wall engineering in oxide membranes, suggesting that precise control of thickness and thermal history can be used to tailor DW morphology, mobility, and associated functional properties. Future work combining time‑resolved diffraction, acoustic spectroscopy, and phase‑field modeling is proposed to further elucidate the interplay of elastic softening, defect pinning, and DW dynamics at the nanoscale.