This thesis is concerned with how the physical properties of transition metal oxides change due to chemical substitution or intercalation. Experiments using the muon-spin relaxation and rotation (μSR) techniques were carried out at the ISIS Facility (UK) and the Paul Scherrer Institute (CH). In conjunction with the μSR results, the results of heat capacity and magnetic susceptibility experiments are used to provide complementary information on the same samples. Investigations of the properties of the layered triangular lattice magnets NaNiO2 and LiNiO2 are presented. For NaNiO2, all three experimental techniques are used to provide a full survey of the thermodynamic and magnetic properties of this compound. For LiNiO2, μSR studies of notionally stoichiometric and Mg-doped samples were carried out. These showed that Mg doping causes a significant change in the magnetic dynamics of the material, but neither sample exhibits long-range magnetic order. The magnetic ordering of the extensively studied perovskite compounds LaTiO3 and YTiO3 is investigated using μSR. The results were in agreement with previous neutron diffraction studies of the two compounds, but clarified the orientation of the magnetic moments in LaTiO3. It was also possible to make a detailed comparison between the μSR results and those of dipole field calculations of the magnetic field at possible muon stopping sites, allowing these to be deduced and compared with results in other well characterized transition metal oxides. The two titanium chain compounds NaTiSi2O6 and TiOCl exhibit spin gap formation at unusually high temperatures due to unconventional dimerization mechanisms. A model allowing the comparison of X-ray diffraction data, dimerization, and the magnitude of the spin gap is proposed. This is tested against both magnetic susceptibility and μSR data for both compounds. For NaTiSi2O6 both experimental techniques are in reasonable agreement, whereas in TiOCl the results are conclusively different. The origin of this disparity in TiOCl is explored. The intercalation of organic chain molecules into Bi based high-temperature superconductors has previously been demonstrated to extend the interlayer spacing by a factor of up to three without changing the superconducting transition temperature. μSR is used to investigate the London penetration depth, as a function of interlayer spacing, of two series of such samples. The results show a simple trend corresponding to a constant density of superconducting electron pairs in each layer. The consequences of this result are discussed in the context of previously identified scaling relations between superconducting parameters. Results of experiments excluding the possibility of magnetic order and muon-organic radical formation in these samples are presented, as well a preliminary study of the field distributions in a mosaic of intercalated crystallites.

This thesis reports on results in the fields of experimental spin- and general wave dynamics.

Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of ²⁹Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the ²⁹Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of ²⁹Si spins interacting together. I then propose an error correction scheme using the donor and ²⁹Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the ²⁹Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.

<p>Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.</p><p>A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case. </p><p>In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state. </p><p>LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.</p> / Dissertation

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.

The structural and electronic properties of covalently and non-covalently functionalized graphene are investigated by means of first-principles density-functional-theory. The electronic characteristics of non-covalently functionalized graphene by a planar covalent organic framework (COF) are investigated. The aromatic central molecule of the COF acts as an electron donor while the linker of the COF acts as an electron acceptor. The concerted interaction of donor acceptor promotes the formation of planar COF networks on graphene. The distinctive electronic properties of covalently functionalized fluorinated epitaxial graphene are attributed to the polar covalent C–F bond. The partial ionic character of the C–F bond results in the hyperconjugation of C–F σ-bonds with an sp2 network of graphene. The implications of resonant-orbital-induced doping for the electronic and magnetic properties of fluorinated epitaxial graphene are discussed. Isolation of single-walled carbon nanotubes (SWNTs) with specific chirality and diameters is critical. Water-soluble poly [(m- phenyleneethynylene)- alt- (p- phenyleneethynylene)], 3, is found to exhibit high selectivity in dispersing SWNT (6,5). The polymer’s ability to sort out SWNT (6,5) appears to be related to the carbon–carbon triple bond, whose free rotation allows a unique assembly. We have also demonstrated the important role of dispersion forces on the structural and electronic stability of parallel displaced and Y-shaped benzene dimer conformations. Long-range dispersive forces play a significant role in determining the relative stability of benzene dimer. The effective dispersion of SWNT depends on the helical pitch length associated with the conformations of linkages as well as π-π stacking configurations. We have revisited the constructing schemes for a large family of stable hollow boron fullerenes with 80 + 8n (n = 0,2,3,...) atoms. In contrast to the hollow pentagon boron fullerenes the stable structures constitute 12 filled pentagons and 12 additional hollow hexagons. Based on results from density-functional calculations, an empirical rule for filled pentagons is proposed along with a revised electron counting scheme. We have also studied the relative stability of various boron fullerene structures and structural and electronic properties of B80 bucky ball and boron nanotubes. Our results reveal that the energy order of fullerenes strongly depends on the exchange-correlation functional employed in the calculation. A systematic study elucidates the importance of incorporating dispersion forces to account for the intricate interplay of two and three centered bonding in boron nanostructures.

The design, fabrication and performance of an Extraordinary Magnetoresistance (EMR) and a Vertical Mesa Hall Sensor (VMHS) are studied. EMR devices have been fabricated from a 2DEG InAs/GaSb structures which exhibit a low carrier density and high mobility that achieve the best performance. The general electrical magneto-transport properties are given. The experiments investigate mainly different metallic patterns, which are Rectangular, Triangular and Tip pattern between 4-300 K. Probe configurations and the enhancement of relative size of metallic patterns are described. EMR effect is due to current deflection around the metal-semiconductor interface. The results are metallic pattern dependent. Using finite element analysis, good agreement between experimental and theoretical results was found. The best performance sensor is a symmetrical metallic Tip pattern. It is enhanced by the length of the Tip’s point and the large metallic area. This pattern when combines with an asymmetrical probe configuration, exhibits the highest EMR of 900% at –0.275T measured by inner probes and the best sensitivity of 54Ω/T at room temperature. The second study presents in-plane Hall effect sensors made from InSb. A simple device geometry has been used in which current flows in a plane perpendicular to the device surface. Device sensitivity depends on its geometry and a series of different contacts are used to investigate the geometry of the current flow distribution. The structures produced are only sensitive to the presence of one in-plane field component, and they also demonstrate good angular selectivity. Multi-electrodes were used to investigate biasing current from both mesa and substrate condition. We are able to examine the Hall voltage as a function of contact positions and also to create multiple VMHS. Offset reduction of devices has been achieved by moving the ground contacts to re-balance the current distribution under the mesa surface.

Neutron scattering measurements were used to investigate the magnetic and crystal structure and magnetic excitations of three compounds characterized as low-dimensional quantum magnets. The materials are frustrated systems with low spin quantum number. The first was a powder sample of AgNiO₂. The Ni ions form a triangular lattice antiferromagnet in which, according to the published crystal structure, both the orbital order and magnetic couplings are frustrated. However, it is shown here that there was a small distortion of the crystal structure at 365 K, which is proposed to result from charge disproportionation and this relieves the orbital frustration. The magnetic structure was investigated and, below 20 K, the triangular lattice of electron-rich Ni sites was observed to order into antiferromagnetic stripes. Investigations of the magnetic excitations showed that the main dispersions were within the triangular plane, indicating a strong two-dimensionality. The dispersion was larger along the stripes than between the stripes of collinear spins. The second material investigated was CoNb₂O₆, a quasi Ising-like ferromagnet. It was studied with a magnetic field applied transverse to the Ising direction. The magnetic field introduced quantum fluctuations which drove a phase transition at a field comparable to the main exchange interaction. The phase diagram of the magnetic order was mapped outs and a transition from an ordered phase to a paramagnetic phase was identified at high field. This low-temperature high-field phase transition was further investigated by inelastic neutron scattering measurements to observe the change in the energy gap and magnetic excitation spectrum on either side of the transition. The spectrum had two components in the ordered phase and had sharp magnon modes in the paramagnetic phase. The third material was the spin-half layered antiferromagnet CuSb₂O₆. It has a square lattice of Cu²⁺ ions in which the main interaction is across only one diagonal of the square. The magnetic structure was studied by neutron scattering with a field applied along the direction of the zero-field ordered moment. A spin-flop was observed at low field and there was evidence for a high-field transition. The magnetic excitation spectrum was unusual in that it had an intense resonance at 13 meV at the magnetic Brillouin zone boundary.

In this work we investigate themes related to many-body systems in which multiple ground states are accessible, a condition known as frustration. Frustration can arise in a number of contexts, and we consider the consequences of this situation with some examples from condensed-matter physics. In some magnetic materials interactions between spins are such that no single spin configuration provides a unique ground state. In the class of frustrated magnets where the number of ground states is extensive, thermal fluctuations are strong even at temperatures significantly below the interaction strength. At such temperatures spins are highly correlated, and small perturbations may have profound consequences. In this thesis we provide an example of this. By considering classical n-component spins with nearest-neigbour exchange on a frustrated octahedral lattice we show that – in the limit where exchange interactions are large – the system is in a disordered, correlated phase where correlations have the form of a dipole field. This is termed a Coulomb phase. From this phase we induce an ordering transition, lifting the degeneracy with weak, additional short-range interactions. By studying the transition in the solvable limit of n → ∞, we discover that the transition has identical thermodynamics to that of a magnetic system interacting through long-range, dipolar forces. Finally, we provide a more apposite characterisation of the transition, where the high-temperature side of the transition is described through the fluctuations of solenoidal fields, and the ordering corresponds to a condensation of these fields. In a separate part of the thesis, we investigate the influence of disorder on frustrated lattices. We study a two-dimensional tight-binding model with nearest-neighbour hopping and on-site disorder. Restricting the allowed states to being those from the low-lying manifold of ground states, the disorder feeds through to act as effective disorder in the hopping terms, which decay algebraically with distance. The quasi-long range nature of this effective hopping leads to a situation in which the resultant single-particle eigenstates are critical, and we probe their behaviour numerically with a transfer matrix calculation.

The extended kagome lattice, composed of alternating kagome and triangular layers, provides a novel geometry for frustrated magnetism. In this thesis, we study the properties of Heisenberg spins with nearest-neighbour antiferromagnetic interactions on this lattice. In common with many other models of frustrated magnets, this system has highly degenerate classical ground states. It is set apart from other examples, however, by the strong interlayer correlations between triangular layer spins. We study the implications of such correlations in both the statics and dynamics. We characterise classical ground states using a flux picture for a single layer of kagome spins, a theoretical description that sets geometrical bounds on correlations. We quantify the divergent but sub-extensive ground state degeneracy by a Maxwellian counting argument, and verify this calculation by analysing the energy eigenvalues of numerical ground states. We explore the ground state connectedness but do not reach firm conclusions on this issue. We use the self-consistent Gaussian approximation (SCGA) to calculate static spin correlations at finite temperature. The results of these calculations agree well with elastic neutron scattering experiments. We derive an expression for the effective interlayer interaction between kagome spins by integrating out the triangular lattice spins. We use linear spinwave theory to compute the spin excitation spectrum numerically. This shows encouraging similarity with inelastic neutron scattering data on a single-crystal YBaCo$_4$O$_7$ sample, for a wide range of wavevector and frequency. This agreement shows that our spin model is a reasonable description of the physics, and suggests that this numerical technique might be useful for other geometrically frustrated magnets. We study the dynamics analytically using the stochastic SCGA recently developed for the pyrochlore lattice. For technical reasons, we apply this technique on a related model, the stacked kagome lattice, rather than on the extended kagome lattice itself. From this we find slow relaxation at low temperature, with a rate ~ T² compared to the faster ~ T scaling for the pyrochlore. Strikingly, in simulations of the dynamics on the extended kagome lattice by numerical integration of the semiclassical equations of motion, we find two different relaxation rates. Kagome layer spins relax more quickly than the triangular layer spins, having ~ T.