Charge order textures induced by non-linear couplings in a half-doped manganite

Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data

As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 μm2) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.

In Situ Cryogenic HAADF-STEM Observation of Spontaneous Transition of Ferroelectric Polarization Domain Structures at Low Temperatures

Precise determination of atomic structures in ferroelectric thin films and their evolution with temperature is crucial for fundamental study and design of functional materials. However, this has been impeded by the lack of techniques applicable to a thin-film geometry. Here we use cryogenic scanning transmission electron microscopy (STEM) to observe the atomic structure of a BaTiO₃ film on a (111)-SrTiO₃ substrate under varying temperatures. Our study explicitly proves a structure transition from a complex polymorphic nanodomain configuration at room temperature transitioning to a homogeneous ground-state rhombohedral structure of BaTiO₃ below ∼250 K, which was predicted by phase-field simulation. More importantly, another unexpected transition is revealed, a transition to complex nanodomains below ∼105 K caused by an altered mechanical boundary condition due to the antiferrodistortive phase transition of the SrTiO₃ substrate. This study demonstrates the power of cryogenic STEM in elucidating structure-property relationships in numerous functional materials at low temperatures.

Atomic-Resolution Cryogenic Scanning Transmission Electron Microscopy for Quantum Materials

ConspectusThe rich physics permeating the phase diagrams of quantum materials have commanded the attention of the solid-state chemistry, materials science, and condensed-matter physics communities, sparking immense research into quantum phase transitions including superconducting, ferroic, and charge-order transitions. Many of these transitions occur at low temperatures and involve electronic, magnetic, or lattice order, which emerges on the atomic to mesoscopic scales. The complex interplay of these states and the heterogeneity that arises due to competition and intertwining of phases, however, is not fully understood and requires probes that capture ordering over multiple length scales down to the local atomic symmetries. Advances in scanning transmission electron microscopy (STEM) have enabled atomic-resolution imaging as well as mapping of functional picometer-scale atomic displacements inside materials. In this Account, we discuss our group's work to expand the reach of atomic-resolution STEM to cryogenic temperatures (cryo-STEM) to study quantum materials with focus on charge-ordered systems.Charge-ordered phases, in which electrons as well as the atomic lattice form periodic patterns that lift the translational symmetries of the crystal, are not only intertwined with superconductivity but also underlie other exotic electronic phenomena such as colossal magnetoresistance and metal-insulator transitions. The periodic lattice distortions (PLDs) modulate the positions of the crystal's nuclei, which can be readily probed by electron microscopy. In a set of examples, we demonstrate cryo-STEM as a powerful technique for probing local order, nanometer-scale heterogeneities, and topological defects in charge-ordered manganites and in transition metal dichalcogenide charge density wave (CDW) systems.With the nearly commensurate-to-commensurate CDW transition upon cooling in 1T-TaS₂, we show that nanoscale lattice textures in CDW phases can be revealed through direct imaging. These early atomic-resolution results, however, also highlighted the need for improvements in cryo-STEM imaging, which led to a push to advance data collection and analysis for direct spatial mapping and quantification of PLDs. By introducing an image registration algorithm developed specifically to accommodate fast, low signal-to-noise image acquisitions of crystalline lattices, we address previous limitations due to sample drift in cryo-STEM experiments. This has enabled subangstrom cryo-STEM imaging with sufficient signal-to-noise to reveal the low temperature structure of 1T'-TaTe₂. Furthermore, it allows mapping and quantification of PLD atomic displacements in the charge-ordered manganites Bi_0.35Sr_0.18Ca_0.47MnO₃ and Nd_0.5Sr_0.5MnO₃ with picometer precision at ∼95 K to resolve not only distinct ordered phases (i.e., site- and bond-centered charge order) but also their nanoscale coexistence within the same sample.Atomic-resolution cryo-STEM opens new opportunities for understanding the microscopic underpinnings of quantum phases. In this Account, we focus on spatial mapping of lattice degrees of freedom in phases that are present at temperatures down to liquid nitrogen. Further advances in instrumentation are needed to expand the temperature range and to also enable atomic-resolution measurements that rely on weaker signals such as electron energy loss spectroscopy (EELS) for probing of electronic structure or 4D-STEM approaches to map electric and magnetic fields.