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.

Atomic-resolution cryogenic scanning transmission electron microscopy (cryo-STEM) has provided a path to probing the microscopic nature of select low-temperature phases in quantum materials. Expanding cryo-STEM techniques to broadly tunable temperatures will give access to the rich temperature-dependent phase diagrams of these materials. With existing cryo-holders, however, variations in sample temperature significantly disrupt the thermal equilibrium of the system, resulting in large-scale sample drift. The ability to tune the temperature without negative impact on the overall instrument stability is crucial, particularly for high-resolution experiments. Here, we test a new side-entry continuously variable temperature dual-tilt cryo-holder which integrates liquid nitrogen cooling with a 6-pin micro-electromechanical system (MEMS) sample heater to overcome some of these experimental challenges. We measure consistently low drift rates of 0.3–0.4 Å/s and demonstrate atomic-resolution cryo-STEM imaging across a continuously variable temperature range from ~100 K to well above room temperature. We conduct additional drift stability measurements across several commercial sample stages and discuss implications for further developments of ultra-stable, flexible cryo-stages.