Title: Local Structural Insights into Exotic Electronic States in 𝓭- and 𝑓-Electron Oxides with Joint Neutron and X-ray Pair Distribution Function Analysis
Description: Quantum materials have strong electron correlation effects. According to the “structure-property” relationship, it is crucial to study the structure of quantum materials to better understand and manipulate the physical properties. The quantum effects are significant at the atomic microscopic length scale, which is not feasible to be studied by the average long-range structure measurement from conventional diffraction methods. Instead the local structure probe, pair distribution function (PDF) analysis, can effectively reveal the mystery of local structure, which is sensitive to the local behavior rather than the bulk average properties. In this thesis, the joint neutron and x-ray PDF (NXPDF) method is implemented. Because of their different interactions with matters, a combination of neutron and x-ray scattering can help comprehensively understand the atomic structures of some strongly correlated d- and f-electron systems that are difficult to be studied alone. Though powerful for understanding the structure of complex materials, performing the PDF modeling and structure refinement usually requires a lot of work on model selection for candidate structures.

To address this problem, a new approach is developed to obtain candidate atomic structures from NXPDF, called structure-mining, in a highly automated way. It fetches, from open structural databases, all the structures meeting the experimenter's search criteria and performs structure refinements on them without human intervention. Tests on various material systems show the effectiveness and robustness of the algorithm in finding the correct atomic crystal structure. It works on crystalline and nanocrystalline materials including complex oxide nanoparticles and nanowires, low-symmetry and locally distorted structures, and complicated doped and magnetic materials. The examples of applying structure-mining method to identify the local structures of Pr₆O₁₁, BaFeₓTi₁−ₓO₃, and MgTi₂O₄ materials, which have strongly correlated 𝓭- and 𝑓-orbital electronic states under study in the thesis, are shown as well. This approach could greatly reduce the traditional structure searching work for quantum materials as well as other systems.

The NXPDF method is first applied to the praseodymium oxide semiconductor nanoparticles to investigate the local structure behavior accompanied by the loss of electrical conductivity when temperature changes. The Pr and O sublattices can be determined precisely by x-ray and neutron PDF, respectively, because of their distinct x-ray atomic form factors and neutron scattering lengths. A combination of a highly ordered structure motif and a locally distorted oxygen deficient structure environment can describe the measured NXPDFs reasonably well. The iron doped barium titanate BaFeₓTi₁−ₓO₃ system is also investigated using PDF methods for studying the multiferroic behavior in the nanocrystals, which are synthesized near room temperature. The perovskite structure is established to be non-centrosymmetric, consistent with predictions of the pseudo-Jahn-Teller effect being the underlying cause of off-center displacements of B-site (Ti and doped Fe) atom, lowering the symmetry in order to make additional overlap between the 3d orbital of Ti and neighboring O atoms to create π molecular orbitals.

This triggers the spontaneous polarization of the crystal. The PDF results establish that Fe is successfully doped into the ferroelectric BaTiO₃ phase, and the measured dielectric and magnetic properties also validate the multiferroic behavior of the synthesized BaFeₓTi₁−ₓO₃ nanocrystals. In addition, the NXPDF analysis is also conducted on the MgTi₂O₄ system to track the evolution of the local atomic structure across the temperature-dependent metal-insulator transition, and the results reveal that local tetragonality is persistent, preformed with reduced magnitude, deep in the metallic and on average cubic regime. Significantly, the high temperature local state revealed by PDF is not continuously connected to the orbitally ordered band insulator ground state and the transition cannot be characterized as a trivial order-disorder type. The shortest Ti-Ti bond lengths corresponding to spin singlet dimers shift to longer distances on warming but are still shorter than those seen in the cubic average structure.

These seemingly conflicting observations could be reconciled within the model of a local fluctuating t₂g orbital-degeneracy-lifted (ODL) precursor state. These results undoubtedly establish the effectiveness of the joint neutron and x-ray PDF analysis to investigate the structure-property relationship on the sub-nanometer length scale of strongly correlated electron materials, utilizing the complementary structure information obtained from neutron and x-ray scattering.