Symmetry Breaking, Order-by-Disorder, Fragmentation, and Spin-Liquids in the Magnetic Pyrochlore Lattice with Anisotropic Interactions

Abstract

Within the study of frustrated magnetism, the pyrochlore lattice is deemed a fruitful ground where phenomena such as quantum and thermal order-by-disorder, moment fragmentation, and spin-liquids, both quantum and classical, might be realized. In this thesis, we study a Heisenberg and Dzyaloshisnkii-Moriya nearest-neighbor Hamiltonian in this lattice which presents all the above phenomena, providing a quantitative description through the application of both analytical and numerical approaches. First, we obtain a phase diagram where three long-range ordered phases (two antiferromagnetic and one ferromagnetic), and two spin-liquid points, the well-known classical Coulomb phase and a new spin-liquid, that we dub “order-by-disorder selected spin liquid”, are identified. We then proceed to study the order-by-disorder selection in two of the long-range ordered phases (an antiferromagnetic and a ferromagnetic phase) and show that the quantum order-by-disorder selection mechanism in one of these phases is only produced at non-zero temperature, i.e. without zero-temperature quantum order-by-disorder. Then, we study the newly identified spin-liquid and the evolution of its correlation function as a function of temperature. The correlation function of this spin-liquid presents pinch-lines, twofold and fourfold pinch-points at high temperature, whereas at low temperature, these features are replaced by a spin-ice pattern. This effect is a consequence of the order-by-disorder selection of an extensive subset of ground-states (the spin-ice states) within the manifold. Finally, we study the phenomenon of fragmentation, commonly referred to as the observation of both sharp pinch-points and Bragg peaks in the correlation functions of an ordered phase. Specifically, we demonstrate how this effect is a consequence of a Helmholtz-Hodge decomposition of the spin mode excitations in an ordered phase, and is therefore expected to be observed especially for Hamiltonians whose interaction parameters are proximate to a spin-liquid point.