Yang, Yang2024-01-052024-01-052023-10https://hdl.handle.net/11299/259682University of Minnesota Ph.D. dissertation. October 2023. Major: Physics. Advisor: Natalia Perkins. 1 computer file (PDF); viii, 123 pages.This dissertation presents an overview of my research works on studying magnetism emerging from bond-directional interactions in spin-orbit coupled Mott insulators. The study encompasses two primary activities: the examination of superexchange spin models and the comprehension of magnetic excitations observed in real materials. The first activity includes the study of theoretical Kitaev-Heisenberg model on the kagome lattice, where we identify nontrivial local symmetry of the system. We find the classical and quantum phase diagrams of the model. Our findings reveal striking similarities of the physics between the classical and quantum regimes. The second activity mainly focuses on understanding of Raman responses (inelastic light scattering) from different materials. We first employ the Loudon-Fleury form of the Raman operator to elucidate magnetic excitations in the pyrochlore compound Nd2Ir2O7. Then we extend the Raman operator beyond the conventional Loudon- Fleury formalism, and apply it to understand magnetic excitations observed in the hyperhoneycomb material β-Li2IrO3.enFrustrated magnetismRaman spectroscopyThesis or Dissertation