Models of magnetism show complex collective behaviour which arises from simple interactions among microscopic degrees of freedom. Upon cooling from high temperatures conventional magnets typically undergo a phase transition to a magnetically ordered phase due to microscopic interactions which favour an ordered state. In frustrated magnets however, competing microscopic interactions place non-trivial constraints on the allowed configurations at low temperature, without selecting a unique ordered state. In this thesis, we investigate the collective behaviour of a paradigmatic frustrated magnet, the classical Heisenberg model on the pyrochlore lattice with antiferromagnetic nearest neighbour interactions. Within a self consistent Gaussian approximation, we derive analytic expressions for correlation functions which match Monte Carlo simulations extremely well at all temperatures. We study the precessional dynamics of the model and provide a comprehensive description of the dynamics by constructing an analytically tractable stochastic model by extending the self-consistent Gaussian approximation to include dynamics. We relate these results to other highly constrained models. Real experimental systems often have features that go beyond the phenomenology afforded by the simplest models; we investigate the effects of further neighbour interactions on paramagnetic spin correlations, and propose further neighbour interactions as the mechanism underlying experimentally observed patterns of scattering in frustrated spinel compounds. In the dynamics linearized around a ground-state, the macroscopic degeneracy of the classical model leads to modes with zero frequency. Small perturbations stabilize ordered states and lift such zero modes to finite frequency. The ordered state has two widely separated energy scales both of which affect the dynamics, the leading scale of nearest neighbour exchange coupling, and the much smaller scale of the perturbation which relieves the frustration. We investigate the interplay between these widely different energy scales in setting the mode frequencies in states ordered by weak interactions.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:589636 |
| Date | January 2010 |
| Creators | Conlon, Peter Hugh |
| Contributors | Chalker, John |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://ora.ox.ac.uk/objects/uuid:66d30c85-3ccf-4887-b0de-b3f2ee983ffe |
Page generated in 0.0019 seconds