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Strontium titanate is a classic quantum paraelectric oxide material that has been widely studied in bulk and thin films. It exhibits a well-known cubic-to-tetragonal antiferrodistortive phase transition at 105 K, characterized by the rotation of oxygen octahedra. A possible second phase transition at lower temperature is suppressed by quantum fluctuations, preventing the onset of ferroelectric order. However, recent studies have shown that ferroelectric order can be established at low temperatures by inducing strain and other means. Here, we used in situ multi-reflection Bragg coherent X-ray diffraction imaging to measure the strain and rotation tensors for two strontium titanate microcrystals at low temperature. We observe strains induced by dislocations and inclusion-like impurities in the microcrystals. Based on radial magnitude plots, these strains increase in magnitude and spread as the temperature decreases. Pearson's correlation heatmaps show a structural transition at 50 K, which we associate with the formation of a low-temperature ferroelectric phase in the presence of strain. We do not observe any change in local strains associated with the tetragonal phase transition at 105 K., Comment: 15 pages, 19 figures. Zenodo link will be active once published in a peer-reviewed journal

Ptychography, as a powerful lensless imaging method, has become a popular member of the coherent diffractive imaging family over decades of development. The ability to utilize low-dose X-rays and/or fast scans offers a big advantage in a ptychographic measurement (for example, when measuring radiation-sensitive samples), but results in low-photon statistics, making the subsequent phase retrieval challenging. Here, we demonstrate a dose-efficient automatic differentiation framework for ptychographic reconstruction (DAP) at low-photon statistics and low overlap ratio. As no reciprocal space constraint is required in this DAP framework, the framework, based on various forward models, shows superior performance under these conditions. It effectively suppresses potential artifacts in the reconstructed images, especially for the inherent periodic artifact in a raster scan. We validate the effectiveness and robustness of this method using both simulated and measured datasets., Comment: 26 pages, 5 figures

The temperature-dependent behavior of magnetic domains plays an essential role in the magnetic properties of materials, leading to widespread applications. However, experimental methods to access the three-dimensional (3D) magnetic domain structures are very limited, especially for antiferromagnets. Over the past decades, the spin-orbit Mott insulator iridate $Sr_2IrO_4$ has attracted particular attention because of its interesting magnetic structure and analogy to superconducting cuprates. Here, we apply resonant x-ray magnetic Bragg coherent diffraction imaging to track the real-space 3D evolution of antiferromagnetic ordering inside a $Sr_2IrO_4$ single crystal as a function of temperature, finding that the antiferromagnetic domain shows anisotropic changes. The anisotropy of the domain shape reveals the underlying anisotropy of the antiferromagnetic coupling strength within $Sr_2IrO_4$. These results demonstrate the high potential significance of 3D domain imaging in magnetism research.

In recent years, halide perovskite materials have been used to make high performance solar cell and light-emitting devices. However, material defects still limit device performance and stability. Here, we use synchrotron-based Bragg Coherent Diffraction Imaging to visualise nanoscale strain fields, such as those local to defects, in halide perovskite microcrystals. We find significant strain heterogeneity within MAPbBr$_{3}$ (MA = CH$_{3}$NH$_{3}^{+}$) crystals in spite of their high optoelectronic quality, and identify both $\langle$100$\rangle$ and $\langle$110$\rangle$ edge dislocations through analysis of their local strain fields. By imaging these defects and strain fields in situ under continuous illumination, we uncover dramatic light-induced dislocation migration across hundreds of nanometres. Further, by selectively studying crystals that are damaged by the X-ray beam, we correlate large dislocation densities and increased nanoscale strains with material degradation and substantially altered optoelectronic properties assessed using photoluminescence microscopy measurements. Our results demonstrate the dynamic nature of extended defects and strain in halide perovskites and their direct impact on device performance and operational stability., Comment: Main text and Supplementary Information. Main text: 15 pages, 4 figures. Supplementary Information: 16 pages, 27 figures, 1 table

The Verwey transition in magnetite (Fe3O4 ) is the prototypical metal-insulator transition and has eluded a comprehensive explanation for decades. A major element of the challenge is the complex interplay between charge order and lattice distortions. Here we use ultrafast electron diffraction (UED) to disentangle the roles of charge order and lattice distortions by tracking the transient structural evolution after charge order is melted via ultrafast photoexcitation. A dual stage response is observed in which X3, X1, and Delta5 type structural distortions occur on markedly different timescales of 0.7 to 3.2 ps and longer than 3.2 ps. We propose that these distinct timescales arise because X3 type distortions strongly couple to the trimeron charge order, whereas the Delta5-distortions are more strongly associated with monoclinic to cubic distortions of the overall lattice. Our work aids in clarifying the charge lattice interplay using UED method and illustrates the disentanglement of the complex phases in magnetite., Comment: 7 figures and 7 tables

Understanding the driving mechanisms behind metal-insulator transitions (MITs) is a critical step towards controlling material's properties. Since the proposal of charge-order-induced MIT in magnetite Fe3O4 in 1939 by Verwey, the nature of the charge order and its role in the transition have remained elusive-a longstanding challenge in the studies of complex oxides. Recently, a trimeron order was discovered in the low-temperature monoclinic structure of Fe3O4; however, the expected transition entropy change in forming trimeron at the Verwey transition is greater than the observed value, which arises a reexamination of the ground state in the high-temperature phase. Here we use electron diffraction to unveil that a nematic charge order on particular Fe sites emerges in the high-temperature cubic structure of bulk Fe3O4, and that upon cooling, a competitive intertwining of charge and lattice orders leads to the emergence of the Verwey transition. Moreover, MeV ultrafast electron diffraction (UED) provides a dynamic measure of the strong coupling between photoexcited electrons and the X3 phonon modes. Our findings discover a new type of electronic nematicity in correlated materials and offer novel insights into the Verwey transition mechanism in Fe3O4 via the electron-phonon coupling., Comment: Supplementary materials are added

As a critical component of coherent X-ray diffraction imaging (CDI), phase retrieval has been extensively applied in X-ray structural science to recover the 3D morphological information inside measured particles. Despite meeting all the oversampling requirements of Sayre and Shannon, current phase retrieval approaches still have trouble achieving a unique inversion of experimental data in the presence of noise. Here, we propose to overcome this limitation by incorporating a 3D Machine Learning (ML) model combining (optional) supervised learning with transfer learning. The trained ML model can rapidly provide an immediate result with high accuracy which could benefit real-time experiments, and the predicted result can be further refined with transfer learning. More significantly, the proposed ML model can be used without any prior training to learn the missing phases of an image based on minimization of an appropriate 'loss function' alone. We demonstrate significantly improved performance with experimental Bragg CDI data over traditional iterative phase retrieval algorithms.

In contrast to bulk materials, nanoscale crystal growth is critically influenced by size- and shape-dependent properties. However, it is challenging to decipher how stoichiometry, in the realm of mixed-valence elements, can act to control physical properties, especially when complex bonding is implicated by short and long-range ordering of structural defects. Here, solution-grown iron-oxide nanocrystals (NCs) of the pilot wustite system are found to convert into iron-deficient rock-salt and ferro-spinel sub-domains, but attain a surprising tetragonally distorted local structure. Cationic vacancies within chemically uniform NCs are portrayed as the parameter to tweak the underlying properties. These lattice imperfections are shown to produce local exchange-anisotropy fields that reinforce the nanoparticles magnetization and overcome the influence of finite-size effects. The concept of atomic-scale defect control in subcritical size NCs, aspires to become a pathway to tailor-made properties with improved performance for hyperthermia heating over defect-free NCs., Comment: 20 pages, 9 figures, Supplemental Material

It has been technically challenging to concurrently probe the electrons and the lattices in materials during non-equilibrium processes, allowing their correlations to be determined. Here, in a single set of ultrafast electron diffraction patterns taken on the charge-density-wave (CDW) material 1T-TaSeTe, we discover a temporal shift in the diffraction intensity measurements as a function of scattering angle. With the help of dynamic models and theoretical calculations, we show that the ultrafast electrons probe both the valence-electron and lattice dynamic processes, resulting in the temporal shift measurements. Our results demonstrate unambiguously that the CDW is not merely a result of the periodic lattice deformation ever-present in 1T-TaSeTe but has significant electronic origin. This method demonstrates a novel approach for studying many quantum effects that arise from electron-lattice dephasing in molecules and crystals for next-generation devices., Comment: 13 pages and 4 figures in main text

Quasi-two-dimensional (quasi-2D) materials hold promise for future electronics because of their unique band structures that result in electronic and mechanical properties sensitive to crystal strains in all three dimensions. Quantifying crystal strain is a prerequisite to correlating it with the performance of the device, and calls for high resolution but spatially resolved rapid characterization methods. Here we show that using fly-scan nano X-ray diffraction we can accomplish a tensile strain sensitivity below 0.001% with a spatial resolution of better than 80 nm over a spatial extent of 100 $\mu$m on quasi 2D flakes of 1T-TaS2. Coherent diffraction patterns were collected from a $\sim$ 100 nm thick sheet of 1T-TaS2 by scanning 12keV focused X-ray beam across and rotating the sample. We demonstrate that the strain distribution around micron and sub-micron sized 'bubbles' that are present in the sample may be reconstructed from these images. The experiments use state of the art synchrotron instrumentation, and will allow rapid and non-intrusive strain mapping of thin film samples and electronic devices based on quasi 2D materials.

Atomic rearrangements within crystals lie at the foundation of electron-phonon-coupled phenomena such as metal-insulator transition and superconductivity. Advanced laser-pump-probe studies have recently focused on various charge-density-wave (CDW) materials to sharpen our understanding of the charge-lattice entanglement, where non-thermal melting of the CDW state is evident from the enhanced Bragg diffraction peak intensities - attributed to the dominance of the metal-atom dynamics over the nonmetal-anion one. Here using ultrafast MeV electron diffraction on the prototypical CDW material 1T-TaSeTe, we observe an unusual coexistence of systematically enhanced and suppressed Bragg peak intensities upon the CDW suppression, indicating a dominance of nonmetal-anion dynamics during photoexcitation. By tracking these atomic trajectories quantitatively through the ultrafast process, we identify a transient state that manifests itself as an unexpected decoupling of the Ta and Se/Te sublattices. These findings unambiguously unveil a new kind of laser manipulations of lattice order parameters, which has potentials in creating new quantum states and discerning hidden phases such as intra-unit-cell orders., Comment: Main text has 11 pages with 4 figures. Supplementary Information has 19 pages with 9 figures and 2 tables

This study presents a detailed examination of the lattice distortions introduced by glancing incidence Focussed Ion Beam (FIB) milling. Using non-destructive multi-reflection Bragg coherent X-ray diffraction we probe damage formation in an initially pristine gold micro-crystal following several stages of FIB milling. These experiments allow access to the full lattice strain tensor in the micro-crystal with ~25 nm 3D spatial resolution, enabling a nano-scale analysis of residual lattice strains and defects formed. Our results show that 30 keV glancing incidence milling produces fewer large defects than normal incidence milling at the same energy. However the resulting residual lattice strains have similar magnitude and extend up to ~50 nm into the sample. At the edges of the milled surface, where the ion-beam tails impact the sample at near-normal incidence, large dislocation loops with a range of burgers vectors are formed. Further glancing incidence FIB polishing with 5 keV ion energy removes these dislocation loops and reduces the lattice strains caused by higher energy FIB milling. However, even at the lower ion energy, damage-induced lattice strains are present within a ~20 nm thick surface layer. These results highlight the need for careful consideration and management of FIB damage. They also show that low-energy FIB-milling is an effective tool for removing FIB-milling induced lattice strains. This is important for the preparation of micro-mechanical test specimens and strain microscopy samples., Comment: 21 pages, 9 figures

Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga+), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale has revolutionised sample preparation across the life-, earth- and materials sciences. For example FIB is central to microchip prototyping, 3D material analysis, targeted electron microscopy sample extraction and the nanotechnology behind size-dependent material properties. Despite its widespread usage, detailed understanding of the functional consequences of FIB-induced structural damage, intrinsic to the technique, remains elusive. Here, we present nano-scale measurements of three-dimensional, FIB-induced lattice strains, probed using Bragg Coherent X-ray Diffraction Imaging (BCDI). We observe that even low gallium ion doses, typical of FIB imaging, cause substantial lattice distortions. At higher doses, extended self-organised defect structures appear, giving rise to stresses far in excess of the bulk yield limit. Combined with detailed numerical calculations, these observations provide fundamental insight into the nature of the damage created and the structural instabilities that lead to a surprisingly inhomogeneous morphology., Comment: 35 pages total, 12 figures total. Main text 16 pages 3 figures. Supplementary information 19 pages 9 figures

Atomic level defects such as dislocations play key roles in determining the macroscopic properties of crystalline materials. Their effects are important and wide-reaching, and range from increased chemical reactivity to enhanced mechanical properties to vastly increased rates of crystal growth. Dislocations have therefore been widely studied using traditional techniques such as X-ray diffraction (XRD) and optical imaging. More recently, advances in microscopy have allowed their direct visualization. Atomic force microscopy (AFM) has enabled the 2D study of single dislocations while transmission electron microscopy (TEM), which was initially limited to 2D projections of thin specimens, can now visualize strain fields in 3D with near atomic resolution. However, these techniques can- not offer in situ, 3D imaging of the formation or movement of dislocations during dynamic processes such as crystal growth and dissolution. Here, we describe how Bragg Coherent Diffraction Imaging (BCDI) can be used to visualize in 3D the entire network of dislocations present within an individual crystal. Using calcite (CaCO3) single crystals, we also use BCDI to monitor the propagation of the dislocation network during repeated growth and dissolution cycles, and show how this is intimately linked to the growth and dissolution mechanisms. These investigations demonstrate the potential of BCDI for studying the mechanisms underlying the response of crystalline materials to external stimuli.

We have recently shown that normal-metal/superconductor (N/S) bilayer TESs (superconducting Transition-Edge Sensors) exhibit weak-link behavior.1 Here we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We find TESs with added Au structures also exhibit weak-link behavior as evidenced by exponential temperature dependence of the critical current and Josephson-like oscillations of the critical current with applied magnetic field. We explain our results in terms of an effect converse to the longitudinal proximity effect (LoPE)1, the lateral inverse proximity effect (LaiPE), for which the order parameter in the N/S bilayer is reduced due to the neighboring N structures. Resistance and critical current measurements are presented as a function of temperature and magnetic field taken on square Mo/Au bilayer TESs with lengths ranging from 8 to 130 {\mu}m with and without added N structures. We observe the inverse proximity effect on the bilayer over in-plane distances many tens of microns and find the transition shifts to lower temperatures scale approximately as the inverse square of the in- plane N-structure separation distance, without appreciable broadening of the transition width. We also present evidence for nonequilbrium superconductivity and estimate a quasiparticle lifetime of 1.8 \times 10-10 s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayer's steep resistive transition., Comment: 10 pages, 8 figures