Ducatman, Samuel2017-10-092017-10-092017-07https://hdl.handle.net/11299/190442University of Minnesota Ph.D. dissertation. July 2017. Major: Physics. Advisor: Natalia Perkins. 1 computer file (PDF); ix, 103 pages.The central aim of my research is to explain the connection between the macroscopic behavior and the microscopic physics of strongly correlated electron systems with orbital degrees of freedom through the use of effective models. My dissertation focuses on the sub-class of these materials where electrons appear to be localized by interactions, and magnetic ions have well measured magnetic moments. This suggests that we can capture the low-energy physics of the material by employing a minimal model featuring localized spins which interact with each other through exchange couplings. I describe Fe$_{1+y}$Te and $\beta$-Li$_2$IrO$_3$ with effective models primarily focusing on the spins of the magnetic ions, in this case Fe and Ir, respectively. The goal with both materials is to gain insight and make predictions for experimentalists. In chapter 2, I focus on Fe$_{1+y}$Te. I describe why we believe the magnetic ground state of this material, with an observed Bragg peak at $\mathbf{Q}=(\pm \frac{\pi}{2}, \frac{\pi}{2})$, can be described by a Heisenberg model with 1st, 2nd, and 3rd neighbor interactions. I present two possible ground states of this model in the small $J_1$ limit, the bicollinear and plaquette states. In order to predict which ground state the model prefers, I calculate the spin wave spectrum with $1/S$ corrections, and I find the model naturally selects the ``plaquette state." I give a brief description of the ways this result could be tested using experimental techniques such as polarized neutron scattering. In chapter 3, I extend the model used in chapter 2. This is necessary because the Heisenberg model we employed cannot explain why Fe$_{1+y}$Te undergoes a phase transition as $y$ is increased. We add an additional elements to our calculation; we assume that electrons in some of the Fe 3D orbitals have selectively localized while others remain itinerant. We write a new Hamiltonian, where localized moments acquire a new long-range RKKY-like interaction from interactions with the itinerant electrons. We are able to reproduce the phase diagram found from experimentalists, and make predictions about how Fe$_{1+y}$Te could potentially be driven into a ``stripe" magnetic ground state. In chapter 4, I examine another strongly correlated material, $\beta$-Li$_2$IrO$_3$, which exhibits Kitaev physics. I begin with a minimal model employing nearest neighbor isotropic and anisotropic exchange couplings between neighboring Iridium ions. I calculate the phase diagram, and find two states. I characterize both states in terms of spins along the zigzag chains of the hyperhoneycomb lattice, and calculate linear spin waves for both states. I find that, besides for special points in our phase diagram, the excitations are gapped. As the spectrum has many branches, I calculate the dynamic structure factor to find which branches of the spin wave spectrum have the highest intensity. It will be interesting to compare my dynamic structure factor results to single crystal inelastic neutron scattering, which to this point has not been performed for $\beta$-Li$_2$IrO$_3$.enIron TellurideLithium IridateSpin WavesStrongly Correlated MagnetismThesis or Dissertation