Real-space Imaging of Periodic Nano-Textures in Epitaxial Ca­₂RuO₄ Thin Films via Inversion of Diffraction Data

Coherent X-ray diffraction imaging (CXDI) is a lensless imaging technique by directly inverting the oversampled diffraction pattern into real-space images. Because of its non-destructive nature and ability to image sub-picometer atomic-lattice displacements with nanometer resolutions, CXDI has been applied to visualize biological cells, strain in nanocrystals, and recently operando changes in energy materials. Yet, it is limited to objects spatially confined in all three dimensions. Here, we will demonstrate the extension of CXDI to mapping periodic lattice distortions in an extended object. By combining the conventional CXDI iterative computation and an unsupervised machine learning clustering algorithm, we imaged the periodic nanotextures in epitaxially strained Ca₂RuO₄ thin films grown on LaAlO₃ substrate via the inversion of its diffraction pattern. The result reveals the formation of striped periodic nanodomains during the Ca₂RuO₄ structural L-Pbca to S-Pbca phase transition upon cooling, which is confirmed by cryogenic scanning transmission electron microscopy. Our model-independent imaging approach promises to facilitate the understanding of low-dimensional quantum materials where periodic nano-textures are ubiquitous.