Howson, Griffin2025-09-182025-09-182025-09-182025-09-16https://hdl.handle.net/10012/22478In the field frustrated magnetism, magnetic pyrochlore oxides are one of the most widely explored platforms for realizing exotic phenomena in three dimensions, including classical, fragmented and quantum spin liquids. In this thesis, we elaborate on the existing understanding of the low-temperature properties of a subclass of magnetic pyrochlore oxides -- the so-called dipolar-octupolar (DO) pyrochlores -- using various analytical and numerical techniques. To begin, we explore the `XZ' line of the DO phase diagram, which exhibits a strong competition between neighbouring quantum spin liquid and long-range ordered phases using large-scale quantum Monte Carlo (QMC). In particular, we examine how this competition can explain the low-temperature behaviours observed in moment fragmentation candidate Nd_2Zr_2O_7. We proceed by examining the thermodynamics and correlations exhibited by another DO pyrochlore Ce_2Sn_2O_7, arguing that it too harbours moment fragmentation in the T=0 ordered state by comparing and contrasting its behaviour with Nd_2Zr_2O_7. To further elaborate the extent of this phenomenon, we scan the XZ line discussing the evolution of fragmentation as one varies the microscopic exchange parameters between neighbouring ordered and disordered phases in the DO phase diagram. Extending beyond the nearest-neighbour (NN) model, we present a derivation of the symmetry-allowed exchange interactions for the DO model up to third nearest-neighbours. Taking a subset of these new exchange parameters, we construct a mean-field phase diagram centered at the NN exchange parameters presented for quantum spin ice candidate Ce_2Zr_2O_7. In particular, we identify the ordering wavevectors characterizing the long-range order stabilized by lifting the degeneracy exhibited by the NNx model. Further, we present estimates of the critical temperatures associated with the ordering transitions presented, defending the lack of order observed in experiments.enEmergenceFrustrated MagnetismQuantum MatterMaterials ScienceQuantum Many-Body PhysicsComputational PhysicsQuantum Monte CarloSpin LiquidsQuantum Spin IceMean-Field TheoryMaster Thesis