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This thesis addresses the tunnelling of charge carriers in different materials. First looking at the simplest case of electron tunnelling in metals at zero, then finite temperature, the current is obtained using the Fermi-Dirac golden rule and then the conductance is obtained. This is extended to take into account the spatial dependence of one of the metals being a tip since experimentally this is done by scanning tunnelling microscopy where a tip traces over the surface of a sample. The next step is to look at tunnelling between a metal and a semiconductor, again the current is found. Semiconductors can be doped and the effect this has on tunnelling is examined. Next superconductors are introduced. The purpose of my research has been to look at the tunnelling spectra of high-temperature superconducting cuprates for both extrinsic (metal-superconductor) and intrinsic (superconductor-superconductor) tunnelling. The main features seen experimentally with cuprate tunnelling are identified and then a theory capable of explaining these features is discussed. The theory is compared to experimental results and we find good agreement.

In this thesis results of x-ray scattering and neutron scattering experiments on several strongly correlated transition metal oxides are presented. The prototypical charge ordered cuprate La1.48Nd0.4Sr0.12CuO4 was investigated using polarised neutron scattering. The results show that several proposed schemes for the magnetic order in this class of materials may be ruled out, however the data are consistent with one-dimensional stripe-like magnetic order. X-ray diffraction was used to show that the charge order is insensitive to an applied magnetic field, but might be affected by the existence of superconductivity. The magnetic excitations were also studied, and at low energies a gap in the magnetic fluctuations was observed and there is tentative evidence that this is related to magnetic anisotropy. The spin state transition in LaCoO3 was investigated using neutron inelastic scattering, and excitations reminiscent of those observed in ferromagnets above their critical temperatures were observed. The debate surrounding the nature of the excited spin state, S=1 or S=2, could not be resolved, however. The nature of the spin excitations in La0.82Sr0.18CoO3 was investigated using polarised neutrons and it was found that at low energies the excitations take the form of spin-waves. At higher energies this mode becomes heavily damped, and several possible damping mechanisms for this are discussed. Finally, the multiferroic material DyMn2O5 was studied using x-ray resonant scattering. A complex, temperature dependent, magnetic structure was found using a Dy resonance, which reflects an underlying order of the Mn ions. The measurements were in agreement with a theory of multiferroics based on acentric spin-density waves.

This thesis describes inelastic neutron scattering (INS) experiments on several iron-based materials. The experiments were primarily designed to investigate the link between magnetic dynamics and superconductivity. The work contributes to evidence that magnetic fluctuations influence or are influenced by superconductivity. It is demonstrated that the INS response of a material, in conjunction with theoretical models, can provide valuable information about both superconductivity and magnetism. I measured the magnetically ordered parent-compound SrFe2As2 to investigate the nature of magnetism in iron-based systems. Comparison of the data to models based on both itinerant and localised magnetism showed that an itinerant model offers the best description of the data. LiFeAs is a superconductor that shows no magnetic order, however I was able to distinguish a magnetic signal in its INS spectrum. The signal is consistent with the magnetic resonance observed in several other iron-based superconductors. This indicates that LiFeAs likely hosts an s± gap symmetry. I investigated two iron-phosphide systems, LaFePO and Sr2ScO3FeP, and in this case I was unable to identify any magnetic scattering. Comparison to LiFeAs showed that any signal in LaFePO is at least 7 times weaker. These results suggest that magnetic fluctuations are not as influential to the electronic properties of iron-phosphide systems as they are in other iron-based superconductors. In CsxFe2−ySe2 I found two independent signals that appear to be related to phase-separated magnetic and superconducting regions of the sample. I showed that fluctuations associated with the magnetically ordered phase are consistent with localised magnetism, and do not respond to superconductivity. The second signal, however, increases in intensity below the superconducting transition temperature Tc = 27K, consistent with a magnetic resonance. This could be indicative of a pairing symmetry in CsxFe2−ySe2 that is distinct from most other iron-based superconductors. Finally, the molecular intercalated FeSe compound Li0.6(ND2)0.2(ND3)0.8Fe2Se2 revealed strong magnetic fluctuations. Again the signal was consistent with a magnetic resonance responding to Tc = 43 K. The results suggest that Lix(ND2)y(ND3)1−yFe2Se2 is similar to the superconducting phase of CsxFe2−ySe2, placing constraints on theoretical models to describe the molecular intercalated FeSe compounds.

It is increasingly being realised that localised deviations from the average structure can play an important role in a material's properties, and hence an understanding of these deviations is essential when constructing a coherent picture of a system. In this thesis, both neutron and X-ray total scattering data have been collected and used to reveal information on three canonical systems: the high-temperature superconductor YBa₂Cu₃O_7-x; the parent compound of the colossal magnetoresistive manganites, LaMnO₃; and the oldest known magnetic material, Fe₃O₄. Reverse Monte Carlo refinements-using the RMCProfile implementation of the algorithm-have been used as the principal analysis technique, and the functionality of the RMCProfile program has been extended to allow the refinement of magnetic systems involving substitutional disorder. For YBa₂Cu₃O_7-x, the focus of this thesis is on the apical Cu{O bond length. This is shown to have a bimodal distribution, but correlations in the displacements of both atoms disguise this fact in the average structure, thus resolving the apparent controversy that had existed between local- and average-structure probes. LaMnO₃ displays (what was thought to be) a simple order{disorder transition that results in the Jahn-Teller distortion becoming invisible in the average structure above ~ 750 K. Here it is shown that in fact the transition is more complicated, and involves a change in the symmetry of the Jahn-Teller distortion, whereby the long Mn-O bonds move from being opposite one another in the octahedra to being adjacent to one another. This new distortion still breaks the degeneracy of the system, and is consistent with a wide range of existing observations. Finally the low temperature structure of Fe₃O₄ is examined using the updated RMCProfile code. The refinements show sensitivity to local structure variations, producing a bimodal Fe atom bond valence distribution. In addition, the refined magnetic spin configuration is presented, providing the first detailed description of the low-temperature magnetic structure. It is found to be a canted ferrimagnet, and appears to be consistent with Cc symmetry.