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.

The main goal of the project was to develop new experimental techniques to further investigate the phase diagram of the ferromagnetic superconductor UGe2 at high pressures. Of particular interest is the metamagnetic transition (FM1-FM2) which is thought to play the key role in the unconventional superconductivity in UGe2. The project attempted to detect experimentally the critical ferromagnetic fluctuations associated with the FM1-FM2 transition. The development of the experimental equipment constitutes a substantial part of the project and includes: (1) a 2-axis Rotation Stage for High Pressures, (2) an Ultrasonic Sapphire Anvil Cell and (3) a High Pressure Pulse Echo Setup. (1) allows transport measurement on single crystal samples with simultaneous two-axis rotation at temperatures down to 2 K, magnetic fields up to 9T and pressures up to 5GPa to be made. (2) employs Resonant Ultrasound Spectroscopy on a sample in the anvil type cell with an optical access at cryogenic temperatures. (3) uses the Pulse Echo Technique inside a cylinder type cell allowing for ultrasonic measurements on samples with a well-defined orientation. The design, technical challenges and tests results are presented and discussed. The existing techniques, used in the project, included Inelastic Neutron Scattering. A single crystal of UGe2 was studied at 12 kbar with a large volume two-layered piston-cylinder cell. No critical fluctuations were detected at Tx associated with the FM1-FM2 transition. Instead, a small inelastic signal below this transition temperature was observed at the threshold of the instrument sensitivity. The fluctuations at TC associated with the paramagnetic-to-ferromagnetic transition (PM-FM) were detected and the energy scale of these fluctuations was found to have decreased, as compared to the ambient pressure case, in proportion to the resistivity - a result supporting recent theory. The elastic constant c11 of a single crystal of UGe2 was measured as a function of temperature using (3) at ambient pressure as well as pressures up to 11 kbar. The elastic constant exhibits clear features associated with the two transitions, PM-FM and FM1-FM2. The temperature dependence of the elastic constant at ambient pressure was modelled with two main contributions (Schottky-like and Wiess-like) to the magnetic heat capacity coming from the two energy scales, Tx and TC, as well as two corresponding Gruneisen parameters, Ωx and ΩC. The values of Gruneisen parameters obtained from the data fitting were in good agreement with the values determined from the slope of the phase transition lines on the phase diagram. The temperature dependence of the elastic constant at high pressures was modelled according to the two-component system with coupled moments. The behaviour of the fitting parameters (including the Ωx and ΩT ) was consistent with the phase diagram of UGe2 and captured important features of c11 temperature evolution. The way forward would be to continue the measurements of c11 at higher pressures but also to repeat the measurements at different ultrasonic frequencies in order to obtain the temperature dependence of the ultrasonic attenuation which will provide more insight on the FM1-FM2 transition.

Here a temperature stable optical fiber current sensor based on the Sagnac loop interferometer and a cavity formed from two Faraday rotation mirrors is developed and tested. To the best of the author's knowledge a cavity composed of two Faraday rotation mirrors has never been used for the measurement of alternating currents. For the first time, it is shown that the maximum Faraday rotation angle for a long, static optical fiber is input polarization insensitive. Also, linear birefringence is shown to quench this angle in long optical fiber. The polarization dynamics in an optical ground wire network, for a summer period and a fall period, are reported for the first time. The highest-speed polarization changes are attributed to the high-voltage power line, i.e., the electrical current. A novel spectral analysis polarization optical time domain reflectometry method, that uses an induced birefringent event, is shown to work in long optical fiber.

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Weakly electric fish use a unique sensory modality in order to help them communicate, navigate and find prey. These fish emit electric discharges that are monitored by electroreceptors located in the fish's skin. Surrounding objects perturb these baseline transdermal potentials and create electric images. The study of these images has led to a better understanding of general sensory processing principles; however, many aspects of these fish's natural electrosensory environment remain unknown. To this end, a two-dimensional finite element model of Apteronotus leptorhynchus was created. Using this model, we suggest new ways by which electric fish are able to locate objects and propose that it is possible for these fish to extract useful information from their environment using their natural scanning behaviour. Our results also reveal important limitations in standard experimental paradigms that aim to mimic the effects of conspecifics. Alternative paradigms that will enable more realistic stimulation are suggested.

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