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This thesis presents the results of muon-spin relaxation (µ⁺<abbr>SR</abbr>) studies into magnetic materials, and demonstrates how these results can be exploited to quantify the materials’ low moments and reduced dimensionality. Dipole-field simulations, traditionally used to estimate likely muon sites within a crystal structure, are described. A novel Bayesian approach is introduced which allows bounds to be extracted on magnetic moment sizes and magnetic structures—previously very difficult using µ⁺<abbr>SR</abbr>—based on reasonable assumptions about positions in which muons are likely to stop. The simulations are introduced along with relevant theory, and MµCalc, a platform-independent program which I have developed for performing the calculations is described. The magnetic ground states of the isostructural double perovskites Ba₂NaOsO₆ and Ba₂LiOsO₆ are investigated with µ⁺<abbr>SR</abbr>. In Ba₂NaOsO₆ long-range magnetic order is detected via the onset of a spontaneous muon-spin precession signal below <var>T</var>_c = 7.2(2) K, while in Ba₂LiOsO₆ a static but spatially-disordered internal field is found below 8 K. Bayesian analysis is used to show that the magnetic ground state in Ba₂NaOsO₆ is most likely to be low-moment (˜ 0.2<var>µ</var>_B) ferromagnetism and not canted antiferromagnetism. Ba₂LiOsO₆ is antiferromagnetic and a spin-flop transition is found at 5.5 T. A reduced osmium moment is common to both compounds, probably arising from a combination of spin–orbit coupling and frustration. Results are also presented from µ⁺<abbr>SR</abbr> investigations concerning magnetic ordering in several families of layered, quasi–two-dimensional molecular antiferromagnets based on transition metal ions such as <var>S</var> = ½ Cu²⁺ bridged with organic ligands such as pyrazine. µ⁺<abbr>SR</abbr> allows us to identify ordering temperatures and study the critical behaviour close to <var>T</var>_N , which is difficult using conventional probes. Combining this with measurements of in-plane magnetic exchange <var>J</var> and predictions from quantum Monte Carlo simulations allows assessment of the degree of isolation of the 2D layers through estimates of the effective inter-layer exchange coupling and in-layer correlation lengths at <var>T</var>_N. Likely metal-ion moment sizes and muon stopping sites in these materials are identified, based on probabilistic analysis of dipole-fields and of muon–fluorine dipole–dipole coupling in fluorinated materials.

The twin questions of how and why protein molecules fold into the specific topologies which enable them to fulfill their biological function have been the subject of continuous scientific investigation since the early twentieth century. Interactions between biological macromolecules and water are obviously crucial to both folding and function but attempts to gain understanding are impeded by the size and complexity of these systems. A useful approach is to consider much simpler model systems which capture some essential element of real biological systems but are experimentally and theoretically tractable. N-methylacetamide (NMA) is a minimal model of the peptide linkage which forms the backbone of protein molecules. Its behaviour in aqueous solution therefore captures the important competition between peptide - peptide and peptide - water hydrogen bonds which arises in protein hydration. In this thesis aqueous NMA solutions are studied across the full concentration range using classical molecular dynamics simulation. This gives access to the complete spectrum of behaviour between the two important limiting cases of dilute NMA in water and, conversely, dilute water in NMA. Water is now known to be an active player in biological interactions and the simple system studied here displays significant disruption of the structure and dynamics of pure water with the addition of only a small proportion of peptide groups. At dilute NMA concentrations water molecules continue to form system-size hydrogen bonded networks. Water molecules appear to optimise their local tetrahedral order by forming hydrogen bonds with a combination of NMA and water neighbours, rather than solely with members of their own species. NMA molecules hydrogen bond through the amide and carbonyl groups to form linear and branched chains in both the pure liquid and in the aqueous solutions. In the NMA rich region water molecules preferentially donate both hydrogens to chain-end or midchain carbonyl oxygens, forming bridges between NMA chains which resemble buried water configurations found in protein cavities. These bridge structures are thought to contribute to the observed slowing of the system dynamics at these concentrations. The investigation of dynamics by classical simulation is complemented by a quasielastic neutron scattering study of NMA in its liquid and aqueous phases.

<p> Micro- and nano-mechanical resonators with low mass and high vibrational frequency are often studied for applications in mass and force detection where they can offer unparalleled precision. They are also excellent systems with which to study nonlinear phenomena and fundamental physics due to the numerous routes through which they can couple to each other or to external systems. </p><p> In this work we study the structural, thermal, and nonlinear properties of various micro-mechanical systems. First, we present a study of graphene-coated silicon nitride membranes; the resulting devices demonstrate the high quality factors of silicon nitride as well as the useful electrical and optical properties of graphene. We then study nonlinear mechanics in pure graphene membranes, where all vibrational eigenmodes are coupled to one another through the membrane tension. This effect enables coherent energy transfer from one mechanical mode to another, in effect creating a graphene mechanics-based frequency mixer. In another experiment, we measure the resonant frequency of a graphene membrane over a wide temperature range, 80K - 550K, to determine whether or not it demonstrates the negative thermal expansion coefficient predicted by prevailing theories; our results indicate that this coefficient is positive at low temperatures &ndash; possibly due to polymer contaminants on the graphene surface &ndash; and negative above room temperature. Lastly, we study optically-induced self-oscillation in metal-coated silicon nitride nanowires. These structures exhibit self-oscillation at extremely low laser powers (~1&mu;W incident on the nanowire), and we use this photo-thermal effect to counteract the viscous air-damping that normally inhibits micro-mechanical motion.</p>

This doctoral thesis presents density functionalcalculations applied in several domains of interest in solidstate physics and materials science. Non-collinear magnetismhas been studied both in an artificial multi-layer structure,which could have technological relevance as a magnetic sensordevice, and as excitations in 3d ferromagnets. The intricatebulk crystal structure of γ-alumina has been investigated.An improved embedded cluster method is developed and applied tostudy the geometric and electronic structures and opticalabsorption energies of neutral and positively charged oxygenvacancies in α-quartz. Ab initio total energycalculations, based on the EMTO theory, have been used todetermine the elastic properties of Al1-xLixrandom alloys in the face-centered cubiccrystallographic phase. The obtained overall good agreementwith experiment demonstrates the applicability of the quantummechanics formulated within the framework of the DensityFunctional Theory for mapping the structural and mechanicalproperties of random alloys against chemical composition.

<p> The Moore-Read Pfaffian and anti-Pfaffian states have been under scrupulous review as candidates which describe the fractional quantum Hall effect at filling factor 5/2. Quantum states in the universality class of the Moore-Read Pfaffian/anti-Pfaffian have non-trivial intrinsic topological order and support low-energy non-Abelian excitations that have applications in fault-tolerant topological quantum computing schemes. Both states are exact ground states of three-body Hamiltonians that explicitly break particle-hole symmetry. We study the topological order of a competing ansatz state &PSgr;₂ that is the exact ground state of a two-body Hamiltonian that preserves particle-hole symmetry. In particular, we calculate the bipartite entanglement entropy and spectra in the lowest Landau level in the spherical geometry for &PSgr;₂. We perform such calculations for a finite number of electrons up to 14. We then extrapolate to the thermodynamic limit the topological entanglement entropy &gamma; as a measure of the topological order of the ansatz and compare to the known value of the Moore-Read Pfaffian/anti-Pfaffian state. We also study the orbital entanglement spectra for &PSgr;₂ and compare with the Moore-Read Pfaffian and two-body Coulomb ground states. We show that our extrapolation of &gamma; lies within the uncertainty of the known value of &gamma; for the Moore-Read Pfaffian state, and that the orbital entanglement spectra of &PSgr;₂ assumes a similar structure to that of the two-body Coulomb interaction.</p><p>

<p> Superconducting pairs are able to leak into non-superconducting materials when placed in close proximity. In the presence of ferromagnetism pair correlations are modified by the magnetization; singlet Cooper pairs transform into a mixture of singlet and triplet correlations. In this work we analyze how pair correlations are modified in a magnetic Josephson junction in the clean limit, and consider the effect of different magnetic configurations. We use a tight-binding Hamiltonian and the Bogoliubov-de Gennes(BdG) formalism, to describe the proximity system. Applying the Bogoliubov-Valatin transformation we generate the BdG equations in matrix form. We use an iterative process to diagonalize the matrix together with solving the self-consistency relation for the pair potential &Delta; numerically. From the solution we construct Gor'kov functions which are used to describe the pair amplitudes and Josephson current through the junction. Taking the simplest case first we apply our method to a normal metal Josephson junction and match our model to known results. We then apply it to a homogeneous magnetic Josephson junction and investigate how certain parameters such as magnetization and temperature affect the properties of the junction. Finally our methodology is applied to an inhomogeneous magnetic Josephson junction, to study the differing effects between gradual and abrupt changes in the magnetization on the pair correlations.</p>

<p>This thesis aims to build upon the previous work done on the magnetic relaxation of iron(II) phthalocyanine (FePc) thin films by exploring the dynamic aspects of coercive fields in order to determine whether FePc can be classified as a low-dimensional material known as a single chain magnet. In thin films, the chain length is controlled by deposition temperature and therefore systematic studies of the chain-length dependent properties can be made. Hysteresis loops of FePc thin-films with five different chain lengths ranging from approx. 30 nm to 300 nm were measured at a range of sweep speeds from 10.4 mT/s to 1.07 mT/s. Each measurement was repeated at 5 different temperatures in the interval from 2.5 K to 3.8 K, where hysteresis was observed. Significant reductions in coercivity with slower sweep speeds reveal the non-equilibrium behavior of the magnetic states. Mean-field theory based on one-dimensional chains within a Glauber-Ising model suggests a power law behavior of coercivity with sweep rate. Indeed all experimental data is consistent with that behavior. The critical exponent varies from 0.521 to 0.153 for short to long chains. Given the limited observational window, coercivity due to inter-chain coupling cannot fully be ruled out, yet a large dynamic response in the coercivity supports the notion of a single chain magnet.