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Title: Classical and quantum spin liquids on the pyrochlore lattice
Author: Benton, John Owen
ISNI:       0000 0004 5920 5684
Awarding Body: University of Bristol
Current Institution: University of Bristol
Date of Award: 2015
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The study of frustrated magnetism sits at the frontier of modern condensed matter physics, offering the possibility to discover new states of matter with exotic excitations. A textbook example of this is seen in the rare earth pyrochlore oxides H02Ti20 7 and DY2Ti207, better known as "spin ice". These magnets exhibit a classical spin liquid state with emergent magnetic monopole excitations. Inspired by this, we explore in this thesis a wide landscape of possibilities for novel magnetic behaviour on the pyrochlore lattice. Starting from the most general model for anisotropic nearest neighbour exchange interactions we show that the full zero temperature classical phase diagram can be obtained simply by considering the symmetries of a tetralledron. In the process of doing this we obtain an exact rewriting of the model in terms of a set of local order parameter fields defined on tetrahedra. After classifying and describing the ordered phases of this model we turn to give consideration to the novel physics which may be found near the boundaries where phases with different symmetry meet. We find that interesting properties of several materials can be traced back to the "accidental" degeneracies which arise on these boundaries. These include the "order by disorder" in Er2Ti207, the "dimensional-reduction" observed in Yb2Ti207, and the suppression of The observation that the physics of the phase boundaries manifests itself throughout the nearby regions of the phase diagram leads us to a systematic analysis of all of the phase boundaries of the model. In several cases dipole order persists at the phase boundary, stabilised by fluctuations. By constructing the ground state manifolds in each case we identify those configurations which are favoured by fluctuations. We also identify two limits of the phase diagram in which dipolar order vanishes to be replaced by spin nematic order. At certain phase boundaries we find that magnetic order vanishes entirely. This leads to the discovery of a new classical spin liquid on the pyrochlore lattice- the anisotropic Coulomb liquid. This spin liquid, like the Coulomb phase observed in spin ice, possesses algebraic correlations and conserved fluxes but also presents several new features including an anisotropic Coulomb interaction between its excitations. A long-wavelength theory of this spin liquid is derived from the microscopic model by coarse graining the fluctuations of the local order-parameter fields. Homing in on a different limit of the phase diagram, we move on to consider the effects of quantum fluctuations on a spin ice material and in particular how these effects would manifest themselves in neutron scattering experiments. We explore the correlations of the U(I) spin liquid which arises in this limit by explicitly constructing a basis of photon operators on the pyrochlore lattice and calculating the associated dispersion relation and correlation functions. This enables us to quantitatively describe how these unusual excitations would manifest themselves in neutron scattering experiments. We find that "pinch points," which are the signal feature of a classical spin ice, fade away as a quantum ice is cooled to its quantum spin liquid ground state.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available