This thesis describes studies of graphene, single walled carbon nanotubes (SWNTs) and InSb. Optical and electronic measurements probe the effects of high magnetic fields on these low-dimensional systems. Chapter 1 introduces a theoretical description and background behind the materials and physical phenomena studied in this work. The structure and unique properties of carbon nano-materials are described. The experimental methods used in this thesis are described in Chapter 2. Chapter 3 describes magnetotransport measurements on InSb/AlInSb heterostructures revealing that the large energy gaps, and extremely high mobility, associated with this system leads to exceptionally well defined quantum Hall plateaux for both even (Landau level) and odd (spin-split) filling factors. Even higher cyclotron energy gaps are expected in graphene. Chapter 4 reveals that due to a combination of large cyclotron energy gaps and fast electron-phonon energy loss rates, the quantum Hall effect (QHE) in graphene can be observed to unprecedented current densities (43 A/m) and temperatures (> 45 K). The behaviour of epitaxial graphene grown on silicon carbide in the quantum Hall regime is shown to be characterised by a strongly magnetic field dependent carrier density due to charge transfer from surface donor states in the substrate. Chapter 5 shows that polymer wrapping of SWNTs can achieve high quality purified samples. Individual SWNTs were probed using micro-photoluminescence measurements in magnetic fields up to 30 T. The combination of high magnetic fields and high spectral and spatial resolution allowed a detailed study of exciton fine structure. High intensity laser irradiation is shown to induce bound excitons in pristine tubes. The optical properties of a number of tubes are dominated by defect sites which may be imaged along the tube using the magnetic brightening of dark excitons associated with such defects.

Developing a greater understanding of multiferroic materials, particularly those in which a strong coupling is exhibited between magnetic and electrical orderings, is of great importance if potential applications are to be realised. This thesis reports new experimental findings on several multiferroics using the techniques of X-ray and neutron diffraction together with nonlinear optical experiments. Spherical neutron polarimetry measurements on RbFe(MoO<sub<4</sub>)₂ show how this system's chiral magnetic structure can be controlled by an external electric field. Consideration is given to the axial distortion that the crystal structure makes, and the effect that this has on the stabilised magnetic structures. A ferroaxial coupling is invoked to explain, from a symmetry point of view, the spin driven multiferroicity in this proper screw system. The charge ordering in YbFe₂O₄ is examined by a detailed imaging of reciprocal space measured by elastic X-ray diffraction. Continuous helices of scattering are observed above the three-dimensional ordering transition temperature, whereas the intensity is concentrated onto separated maxima below this. The low temperature data are modelled using a simple oxygen displacement pattern, generalised to an incommensurate structure. The observed incommensurability implies that YbFe₂O₄ cannot be truly ferroelectric. The low field magnetic structures of a Y-type hexaferrite Ba_0.5Sr_1.5Zn₂Fe₁₂O₂₂ are observed in a resonant soft X-ray diffraction study. In zero field the system is helimagnetic, and with small applied fields peaks corresponding to a new phase appear. Energy calculations are used to suggest a suitable magnetic structure for the new phase and to show how this relates to the known commensurate phases that are present in low fields. Finally, an experimental setup designed to measure second harmonic generation from non-centrosymmetric crystals is presented, along with static measurements on the multiferroic system MnWO₄. An optical pump / second harmonic probe study is then undertaken, with the result that a pump induced enhancement in the efficiency of the second harmonic generation is observed.

We investigate the properties of the Kitaev honeycomb model with both site dilution and exchange randomness. Embarking on this work, we review disorder in some strongly correlated electron systems, including spin-½ and spin-1 Heisenberg antiferromagnetic chains, two dimensional Heisenberg antiferromagnets, the cuprates and graphene. We outline some aspects of resonating valence bond phases, valence bond solids, spin liquids and quantum computation that are pertinent to an understanding of the Kitaev model. The properties of the Kitaev model without disorder are discussed and it is found to be a critical spin liquid, with algebraic correlations in two spin operators sigma^{alpha}_{i}sigma^{alpha}_{j}, where i and j,/em> are either end of a link of type alpha = x, y or z on the honeycomb lattice. The Kitaev model is exactly solvable and we show that this remains so in the presence of site dilution and exchange randomness. We find that vacancies bind a flux. In the gapped phase, a vacancy forms an effective paramagnetic moment. With two or more vacancies we describe the interaction of their effective moments and show that a finite density of vacancies leads to a divergent macroscopic susceptibility at small fields. In the gapless phase the effective moment has a susceptibility that is, to leading order at small fields, chi(h)~log(1/h). Interaction between the moments from two vacancies on opposite sublattices cuts off this divergence in susceptibility at a large but finite constant. Two vacancies on the same sublattice behave quite differently and we find the combined susceptibility is parametrically larger than that of an isolated vacancy, chi(h)sim [h(log(1/h))^{3/2}]^{-1}. We also investigate the effects of slowly varying, quenched disorder in exchange coupling. We demonstrate that this does not qualitatively affect the susceptibility but show that the heat capacity C ~ T^{2/z}, where z is a measure of the disorder and increases from one with increasing disorder strength.

This thesis presents experimental results on two complex oxide systems: Cu_1-xZn_xO and La_0.7Sr_0.3MnO₃:ZnO. The dynamic magnetoelectric response of these materials is obtained using terahertz time-domain spectroscopy, supported by Fourier-transform infrared spectroscopy, Raman spectroscopy and X-ray diffraction. Evidence for an electromagnon in the multiferroic phase of CuO is presented for the first time. This high temperature (213-230K) electromagnon is linked to intersublattice exchange between two Cu sublattices. The temperature dependence of a magnon in the collinear antiferromagnetic phase is indicative of biquadratic exchange. Broadening of the multiferroic phase on substitution of copper with zinc is reported along with a 25% depression of the Néel temperature due to spin dilution. Phonons and magnons broaden and shift in energy on alloying. However, the electromagnon is relatively insensitive, increasing in energy without widening. This indicates that electromagnons and dynamic magnetoelectric coupling can be mantained even in disordered spin systems. Strong spin-phonon coupling is present in both magnetically ordered phases as shown by the anomalous behavior of the A³<sub style='position: relative; left: -.5em;'>u</sub> phonon at T_N1 and a Raman-active mode associated with a magnetic modulation of a zone-folded acoustic phonon. Dynamic 1THz magnetoresistance is found to be significantly larger than static magnetoresistance in La_0.7Sr_0.3MnO₃:ZnO vertically-aligned nanocolumns on LaAlO₃ substrates. The metal-insulator transition temperature is determined to be 300 K. Temperature dependent static and dynamic resistivity and magnetoresistance are discussed in terms of strain and grain boundary effects. Negative photoconductivity is observed and the dynamic response analysed.

Genetic information is encoded in the long sequence of bases which form DNA, which is replicated during cell division by enzymes known as DNA Polymerases. Polymerases replicate DNA extremely accurately to avoid errors which can cause cell death and diseases such as cancer, although the mechanisms behind these extraordinary fidelities are not well understood. A large conformational change in the protein, in which the “fingers" subdomain closes around an incoming nucleotide, is thought to be implicated in these fidelity mechanisms. Here we present an assay to monitor this conformational change in single polymerase molecules, in real-time. We achieve this using total-internal-reflection-fluorescence (TIRF) microscopy to monitor the fluorescence resonance energy transfer (FRET) of an intra-protein dye labelled DNA Polymerase I (KF) as it binds to surface-immobilised DNA. Initially, we investigated the polymerase fingers-conformations during the pre-chemistry polymerisation reaction, resolving forward and backward rates which would be challenging to observe using ensemble techniques. These observations confirmed that KF closes rapidly around complementary nucleotide, but we discovered that the reverse step, fingers-opening, is particularly slow relative to chemistry. These finger kinetics act to remove the influence of the reaction rate-limiting step on fidelity, surprising given decades of investigations have focused on the rate-limiting step as the key determinant of fidelity. We also use our kinetic measurements to quantify contributions of different reaction steps to the macroscopic error rate of the polymerase. Subsequently, we developed our assay to investigate the fingers-conformations across the entire DNA polymerisation reaction. We observed single-nucleotide incorporations, and processive DNA polymerisation at high and low nucleotide concentrations, which suggested heterogeneous nucleotide incorporation rates. The observations demonstrated that the post-chemistry slow step that limits processive polymerisation occurs before post-chemistry fingers-opening, or is accounted for by post-chemistry fingers-opening. We observe a correlation in turn-over kinetics and binary complex kinetics, suggesting that turn-over rates could be limited by the intrinsic dynamics of the binary complex, as seen in other protein systems, although more work is needed on this.

In this study we looked at several different silicon nanostructures grown for the purpose of optimizing anodes for lithium ion batteries. We primarily focused on two distinct types of structures, nanospirals, and Rugate structures. The samples were designed to have the mechanical robustness to endure the massive expansion caused by lithiation of silicon. All of the samples were grown using an electron beam evaporator. Scanning electron microscope images show that we have achieved the desired structural growth. The spirals were shown to have an average diameter of 343 nm on polished copper, and 366 nm on unpolished copper. The Rugate structures had two distinct sample sets. The first mimicked the design of a thin film. The other formed distinct pillars that grouped into islands. The tops of the islands had an average diameter of 362 nm, while the pillars had an average width varying between 167 nm and 140 nm.

Time-resolved photoluminescence (TRPL) measurements paired with steady-state photoluminescence (SSPL) measurements can help to determine the PL lifetime, shape and position of unresolved bands, capture coefficients, and concentrations of free electrons and defects.PL bands that are obscured in the SSPL spectra can be accurately revealed by TRPL measurements. TRPL measurements are able to show if the PL band originates from an internal transition between different states of the same defect. The main defect-related PL bands in high-purity GaN grown by hydride vapor phase epitaxy (HVPE) which have been investigated are the ultraviolet, blue, green, yellow and red luminescence bands (UVL, BL, GL, YL and RL, respectively). The concentration of free electrons can be calculated from these measurements providing a contactless alternative to the Hall effect method. The lifetime of most defect-related PL bands decreases with increasing temperature. However, the lifetime of the GL band, with a maximum at 2.4 eV observed in the SSPL spectra only at high excitation intensity, increases as a function of temperature. By analyzing the PL intensity decay, the origin of the GL can be attributed to an internal transition from an excited state of the CN defect, which behaves as an optically generated giant trap, to the 0/+ level of the same defect. This first observation of an optically generated giant trap was detected by analyzing the cubic temperature dependence of the electron capture coefficient. Excitation intensity and temperature dependent studies on Mg-doped GaN grown by HVPE were performed. The position of the UVL (3.2 eV) peak blue-shifts with increasing excitation intensity, which can be explained by the presence of potential fluctuations. The BL peak (2.8 eV) also blue-shifts with increasing excitation intensity, and red-shifts as a function of temperature. These shifts can be explained by the transitions originating from a deep-donor to the MgGa acceptor, and the corresponding donor-acceptor pair nature.

This thesis describes the experimental investigation of three different strongly correlated transition-metal oxide systems. The magnetic behaviour of each has been probed using inelastic neutron spectroscopy. A distinctive hour-glass excitation spectrum has been observed in the layered cobaltate La_1.75Sr_0.25CoO₄. This spectrum is similar to that measured in a related cobaltate La_1.67Sr_0.33CoO₄, although it appears broader. The spectrum has been reproduced using a spin wave model derived from a disordered cluster spin glass ground state. Signatures of spin glass behaviour have also been observed in bulk magnetisation measurements of La_1.75Sr_0.25CoO₄. These findings, once more, demonstrate the emergence of an hour-glass spectrum from a ground state that combines quasi-one dimensional magnetic correlations and disorder. Additionally, this study shows that charge and magnetic stripe order persists to lower dopings in La_2-xSr_xCoO₄ than previously thought. The complete magnetic excitation spectrum of the multiferroic compound CuO has been measured for the first time. A high energy, one-dimensional magnetic spectrum is observed and modelled using the Muller ansatz derived for the S=1/2 Heisenberg antiferromagnetic chain. At lower energies, a three-dimension spectrum is observed. The measured spectrum is inconsistent with all previous theoretical estimates of the dominant inter-chain exchange interactions in CuO. The inter-chain dispersion is successfully described by a phenomenological model based on linear spin wave theory. The third material investigated, LuFe₂O₄ demonstrates complex charge and magnetic order, the precise nature of which is still under debate. The full spectrum of in-plane excitations in LuFe₂O₄ has been measured and a complicated dispersion consistent with six magnetic modes is observed. These findings are compatible with structures described by a magnetic unit cell containing six spins. The dispersion can be described by a spin wave model derived from a bilayer structure comprised of charge-rich and charge-poor monolayers. This structure is consistent with the original site-specific model for the 3D magnetic ordering in LuFe₂O₄.

The work in this thesis is divided in three parts. In part one we developed electrodeposition method of Nickel Nanowire in commercial AAO template in constant current (Galvanostatic) mode, further we tried to estimate the growth rate from theory, from saturation magnetization and direct measurement from SEM image. In part two we focused on using the Vector Network Analyzer (VNA) to measure the Ferromagnetic Resonance (FMR))of various magnetic Nanowire arrays. We employed different measurement geometries using microstripline and coplanar waveguide as microwave transmission lines. In part three our aim was to study the magnetic properties of complex ferromagnetic system, especially the effect of interactions on dynamic properties of magnetic nanostructures (nanowire arrays and exchange biased ferromagnetic-antiferromagnetic multilayers). Our effort was centered on using ferromagnetic resonance to understand the dynamic response of these systems.

An experimental Nernst effect measuring system is designed and constructed. The ability to measure the Nernst effect allows completion of a thermoelectric suite of measurements consisting of electrical conductivity, the Seebeck effect, the Hall effect, and the Nernst effect. This suite of measurements gives information about electron transport, carrier concentration, and electron scattering within a thermoelectric sample. Programs were designed in LabView to control the various instruments in the measuring system. Measurements of the Nernst effect were taken on two thermoelectric samples, bismuth nickel telluride and bismuth antimony telluride. These measurements were taken at both constant temperature and constant magnetic field. An error analysis of the Nernst effect measuring system is also presented, with consideration as to future work that can be done to improve the quality of Nernst effect measurements taken from the system.