Atomic-Scale Visualizations of Charge Order Phenomena

219 pagesIn materials where electrons strongly interact with other degrees of freedom, novel electronic patterns and properties emerge. One of the most fascinating manifestations is charge ordering, whereby electrons form superstructures which break the translational symmetry of the atomic lattice. Charge order is under intense scrutiny due to its relationship to unconventional superconductivity, the colossal magnetoresistance effect, metal-insulator transitions, and phase transitions in general. Often, these electronic states have complex spatial variations at the nanoscale and subtle microscopic details which are difficult to ascertain. The lattice response in these phases– how atoms move upon entering the charge-ordered state– is deeply entwined with the electronic behavior but has not been visualized at the atomic scale. In this thesis, we apply scanning transmission electron microscopy (STEM) to map the lattice behavior in charge-ordered materials. We develop a methodology to extract tiny atomic shifts, on the picometer scale, and reveal the underlying ground states of charge ordering in various systems. Many exotic electronic phases, including charge ordering, typically emerge at low temperatures, yet STEM measurements have been limited to room temperature due to stringent stage stability requirements. We demonstrate for the first time cryogenic STEM with sub-Angstrom resolution and picometer precision which enables novel studies of low temperature phenomena. We map topological defects and elastic deformations of stripes in a manganite material near its transition temperature and visualize emergent coherence upon cooling. These measurements also determine the nature of temperature-dependent incommensurate charge order in which the wavevector is an irrational fraction of the reciprocal lattice. We find that incommensuration reflects phase disorder and that locally charge ordering is commensurate with the lattice. Next we address the microscopic nature of charge and orbital order in a half-doped manganite, an ordered phase that occurs below 150 K and requires cryogenic STEM. Both site-centered (stripe) and bond-centered (bi-stripe, Zener polaron) orders have been proposed in the half-doped compounds. They differ by the charge and orbital arrangement within the superlattice and are expected to behave differently because they have distinct symmetries. By measuring picoscale periodic lattice distortions using cryogenic STEM, we find two distinct ground states coexisting over tens of nanometers. The first is consistent with site-centered order. The second represents bi-stripes which, unlike the proposed Zener polaron, are not purely bond-centered. Instead, the bi-stripes are intermediate between bond- and site-centered order and break inversion symmetry. We extend these microscopy techniques to the layered material TaTe2 which contains a complex stacking of distorted, trimerized tantalum clusters. This complicates interpretation of the modulated state since we cannot measure lattice displacements as was done for the manganites; the staggered arrangement of atoms in this material blurs structural information due to the projection nature of STEM. We develop new tools to extract structural information from contrast modulation in the atomic resolution STEM image and visualize an additional, orthogonal trimerization involving Ta sites and subtle distortions of Te sites at low temperature. Coupled with density functional theory calculations and image simulations, this approach overcomes limitations of projection imaging and opens the door for atomic-scale visualization of complex stacking order in a variety of layered systems. Together, these atomic-scale measurements and methodologies solve fundamental problems about the nature of electronic orders and their fluctuations. More broadly, the successful demonstration and application of low temperature STEM provides unprecedented access to exotic electronic phases