Ye, Mengxing2019-12-112019-12-112019-08https://hdl.handle.net/11299/209029University of Minnesota Ph.D. dissertation. August 2019. Major: Physics. Advisor: Andrey Chubukov. 1 computer file (PDF); xiv, 147 pages.This dissertation covers several aspects of magnetism in correlated electron systems. The rapid progress in understanding the origins and consequences of emergent quantum phenomena in correlated electron systems is pushed by the advances in theoretical developments, quantum material realizations and experiment probes. Magnetism has been found to be a driving force in many examples. We start with analysis of frustrated magnetic systems with localized spins. We first show the phase diagram of the triangular lattice Heisenberg $J_1$-$J_2$ model in a magnetic field, which exhibit a cascade of field induced magnetic phase transitions. We next critically examine the quantized thermal Hall measurement in Kitaev material and emphasize the importance the spin-lattice coupling in the observation of the quantization. We then study the spin-density-wave state in a compensated metal on a triangular lattice in the weak coupling limit, which develops the same ordering pattern as in the localized spin picture. While the system is not sensitive to the frustration as in a localized spin system, the magnetic field triggers a time-reversal-invariant bond order, unique in a compensated metal. Finally, we study the pseudogap physics, which describes the anomalies in the electronic properties of the system in transition between a Mott insulator with magnetic order and a normal metal by varying certain external parameter, such as temperature or the doping level away from half-filling. We analyze within the magnetic precursor scenario, and show that a coplanar magnetic order, which can be realized in the Hubbard model on a triangular lattice, introduces a knob that controls the strength of the pseudogap behavior. We find a transition between normal Fermi liquid like behavior and pseudogap behavior by varying the value of the knob.enCorrelated ElectronMagnetismThesis or Dissertation