Frustration driven emergent phenomena in quantum and classical magnets

2021 Spring.Includes bibliographical references.Frustrated and quantum magnets remain a fascinating and broad area of physics with applications ranging from information science to commercial applications. The wide breadth of possible behavior, caused through the combination of frustration, anisotropy, and many-body physics allow for a large number of exotic phenomena to be realized within these systems. In this dissertation, I cover work on three compounds which all exhibit unusual properties in their low temperature magnetic phases. For Fe3PO4O3, the low temperature static magnetic structure shows partial magnetic ordering, where the system orders commensurately along the c-axis and retains a well-defined ordering wavevector in magnitude but not direction within the ab-plane. Within a simple Heisenberg J1-J2 model, Luttinger-Tisa ground state calculations show the existence of a quasi-degenerate well of lowest energy states coinciding with the rings of scattering observed in neutron diffraction. Taken with polycrystalline data, a small correlation size in the ab-plane suggests a large number of topological defects present in Fe3PO4O3. A few possible magnetic textures which could produce the observed behavior in Fe3PO4O3 are discussed. In the antiferromagnetic pyrochlore Yb2Ge2O7, continuum excitations were previously found through neutron scattering below this material's long range magnetic ordering temperature. By comparing field polarized inelastic neutron scattering data to linear spin wave theory we extract the four unique exchange parameters and place Yb2Ge2O7 within a classical phase diagram. We find Yb2Ge2O7 lies in close proximity to the boundary between an antiferromagnetic and ferromagnetic state leads to a phenomenon known as phase competition, where the excitations are poorly defined because of the influence of the neighboring state. Finally non-equilibrium dynamics in CoNb2O6 show the existence of a frozen state existing within its commensurate antiferromagnetic long range ordered state. This frozen state introduce aging effects at low temperatures in CoNb2O6, complicating its behavior. Following quenches of a magnetic field transverse to all moments in this material, we observe a relaxation below its field-induced phase transition into the commensurate antiferromagnetic state. Quenches of a transverse field exhibit a scaling behavior as a function of quench rate remarkably similar to a Kibble Zurek mechanism, although in our experiments, this behavior can be traced back to systematic effects. Each of these materials exemplify distinct unusual behaviors possible in low temperature quantum and frustrated magnetism