Developing relationships between crystal structure and magnetic and electronic properties can clarify the origins of functional properties in materials with a complex array of interactions, including correlated electron behavior, magnetic ordering, and structural instabilities. Insight into the factors that underly materials properties can be used to both predict new functional materials as well as develop understanding of fundamental solid state physics phenomena. Through a combination of computational techniques like density functional theory and machine learning, as well as experimental techniques such as X-ray and neutron scattering, magnetic and physical properties measurements, and single crystal growth, it is possible to gain a detailed understanding of inorganic oxide and chalcogenide materials for use in a wide array of electronic and magnetic applications.

Crystal structure distortions in magnetic materials can drive the formation of chiral spin textures by breaking centrosymmetry and enabling the Dzyaloshinskii-Moriya interaction. A special type of chiral spin texture, known as a skyrmion lattice, is made up of vortices of magnetic spin that behave like particles and can be manipulated through an applied voltage, making them promising for computer memory applications. Understanding how crystal structure and magnetic behavior couple in skyrmion host materials can help us predict new skyrmion hosts with skyrmions stable over wider temperature and magnetic field ranges. Symmetry-breaking can also contribute to insulator-metal transitions, a phenomenon where the electronic behavior of a material transitions from insulating to metallic, typically as a response to an external stimulus like temperature, pressure, or composition. In many insulator-metal transition materials, structural transitions like Jahn-Teller distortions or dimer formation localize electrons, leading to a change in electronic behavior.

Chapters 2 and 3 of this dissertation focus on the lacunar spinel family of materials, with a unique crystal structure consisting of tetrahedral clusters of transition metal atoms. We study two members of the family, GaV₄Se₈, a known skyrmion host, and GaMo₄Se₈, which we report as a novel skyrmion host. Through density functional theory and experiment, it is shown that in both materials small changes to the symmetry of a tetrahedral cluster have significant impacts on the magnetic behavior. Chapter 4 examines how local structure displacements of S atoms in BaCo_1-xNi_xS₂ can be thought of as dynamic Jahn-Teller distortions and are related to the composition-driven insulator-metal transition in this solid solution. Chapter 5 reports on a combined machine learning and DFT pipeline to predict new trirutile materials as well as understand what factors determine whether a given AB₂(O/F)₆ material will crystallize in the trirutile structure in order to develop insight into the mechanisms of crystal structure formation in ternary materials. Appendix A examines the crystal structure evolution of two hybrid perovskite materials to understand the origins of high photovoltaic performance in this material family.