Organic conductors are interesting to study due to their low dimensionality that leads to a number of competing low temperature ground states. Comprised of a number of different molecules that can be varied by the substitution of one atom for another, organic systems also provide a large number of similar compounds that lend themselves to comparison studies. Two such low-dimensional organic conductors, Per2[Pt(mnt)2] and (TMTSF)2ClO4, which are members of large families of compounds, are the topic of this dissertation. Both materials are considered quasi-one-dimensional and have a number of low temperature transitions, some of which can be studied via changes in the magnetic properties of the systems. The Per2[M(mnt)2] family of compounds provides a system for exploring the similarities and differences of the system's properties when the metal M has a localized spin (M = Pt, Ni, and Fe) versus when the metal is diamagnetic (M = Au, Cu, and Co). In the case of Per2[Pt(mnt)2] - one of the compounds of focus in this dissertation - the metallic perylene chains undergo a metal- insulator transition due to the formation of a charge density wave at Tc ~ 8 K, which also occurs in Per2[Au(mnt)2] at 12 K. However, unlike in the M = Au compound, an additional transition occurs in the M = Pt compound due to the localized Pt spins (S = 1/2) on the insulating Pt(mnt)2 chains - the spin chains of Per2[Pt(mnt)2] undergo a spin-Peierls transition at 8 K. One focus of the experimental work of this dissertation focuses on the magnetic properties of the spin chains in Per2[Pt(mnt)2], via inductive susceptibility measurements at temperatures down to 0.5 K and fields up to 60 T. The experimental results show a coupling of the spin-Peierls and charge density wave states below 8 K and 20 T, above which both states are suppressed. Further measurements show a second spin state transition occurs above 20 T that coincides with a field induced insulating state in the perylene chains. These results support a strong coupling between the charge density wave and spin-Peierls state even at high magnetic fields, which are discussed in the context of other experimental results and theories. Additionally, a simple model is developed to explore the possible mechanisms behind the coupling of the two segregated chains. The other experimental part of this dissertation focuses on one member of the (TMTSF)2X family of compounds, where the anion molecule (X) can have an octahedral symmetry (X = PF6, SbF6, AsF6) or a tetrahedral symmetry (X = ClO4, ReO4, BF4). All of these compounds undergo metal-insulator transitions with the formation of a spin density wave, which can be suppressed and replaced by a transition to a superconducting state with the application of pressure in all but the X = ClO4 compound. In (TMTSF)2ClO4, which is the other compound of focus in this dissertation, both the spin density wave state and the superconducting state can be realized at ambient pressure; however, the determination of the state is dependent on the rate at which the material is cooled through an anion ordering temperature. If the sample is cooled too quickly it remains disordered and the sample enters the spin density wave state; on the other hand, if it cools slowly and the anions are allowed to order, superconductivity is realized at 1.2 K. This superconducting state has been experimentally studied with a wide variety of experimental techniques and much is known about its properties. However, nanoparticles of (TMTSF)2ClO4 have recently been realized, which opens up a new avenue of research on this compound, since the bulk properties of a material are often modified when its size approaches the length scale of the ground state order parameter. As such, the experimental work on (TMTSF)2ClO4 in this dissertation focuses on the critical temperature and fields of the superconducting state of the nanoparticles using the same inductive susceptibility technique mentioned above. The experiments on an assembly of (TMTSF)2ClO4 nanoparticles show that the nanoparticles exhibit bulk-like properties similar to those of randomly oriented crystals of the parent compound; possible explanations for this observation and future plans are discussed in this context. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2015. / February 25, 2015. / High Magnetic Fields, One-Dimensional Instabilities, Organic Conductors / Includes bibliographical references. / Stephen Hill, Professor Co-Directing Dissertation; David Graf, Professor Co-Directing Dissertation; Susan Latturner, University Representative; Pedro Schlottmann, Committee Member; Jorge Piekarewicz, Committee Member.

At low temperature (T) and weak magnetic field (B), two dimensional electron systems (2DES) can exhibit strong 1/B-periodic resistance oscillations on application of sufficiently strong microwave radiation. These oscillations are known as microwave induced resistance oscillations (MIROs), MIROs appearing near cyclotron resonance (CR) and its harmonics involve single photon processes and are called integer MIROs while the oscillations near CR subharmonics require multiphoton processes and are called fractional MIROs. Similar strong 1/B periodic resistance oscillations can occur due to strong dc current, and are known as Hall-field resistance oscillations (HIROs). Oscillations also occur for a combination of microwave radiation and strong dc current. In one prominent theory of MIROs, known as the displacement model , electrons make impurity-assisted transitions into higher or lower Landau levels by absorbing or emitting one or more (N) photons. In the presence of combined strong dc current and microwave radiation, electrons make transitions between Landau levels by absorbing or emitting photons followed by a space transition along the applied dc bias. The object of the dissertation is to explore how the different resistance oscillations are affected by strong microwave radiation when multiphoton processes are relevant. We used a coplanar waveguide (CPW) structure deposited on the sample, as opposed to simply placing the sample near the termination of a waveguide as is more the usual practice in this field. The CPW allows us to estimate the AC electric field (E_{AC}) at the sample. In much of the work presented in this thesis we find that higher $N$ processes supersede the competing lower N processes as microwave power is increased. We show this in the presence and in the absence of a strong dc electric field. Finally, we look at the temperature evolution of fractional MIROs to compare the origin of the fractional MIROs with that of integer MIROs. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2014. / November 13, 2014. / Includes bibliographical references. / Lloyd Engel, Professor Co-Directing Dissertation; Irinel Chiorescu, Professor Co-Directing Dissertation; Naresh Dalal, University Representative; Jianming Cao, Committee Member; Nicholas Bonesteel, Committee Member; Alexander Volya, Committee Member.

Transition metal oxides and chalcogenides have been the major focus of studies in condensed matter physics. The complexity of the system, involving spin and orbital effects, as well as lattice degree of freedom, makes them intriguing subjects not only because of these individual effects, but also the effects due to the interaction among them. In AB2X4 materials (A = Mn2+, Co2+, Fe2+; B = V3+, Cr3+; X = O2-, S2-) which crystallize in spinel structure (space group F d -3 m), these effects and their interactions manifest in their transport properties, magnetic ordering, itinerant electron magnetism, structural distortion, and geometrical frustration effect due to the antiferromagnetically coupled B-sites. These effects are dependent on the distance between the interacting cations, which can be varied by chemical substitution or pressure. The main objective of this dissertation is to study the physical properties of Mott-insulator spinels in approaching their critical inter-cationic distances where an insulator-metal transition occurs. Studying the insulator-metal transition in Mott insulators is important in advancing our understanding, especially in the field of fundamental physics and materials engineering, on the intricate relationships between the transport and magnetic properties and the emergence of new behaviors that arise from such properties in these materials. In this dissertation, the behavior of the physical properties of Mn1-xCoxV2O4, AV2O4 (A = Cd, Mg, Zn), and the transport properties of FeCr2S4 in approaching the insulator-metal transition are reported. Mn1-xCoxV2O4, AV2O4, and FeCr2S4 are chosen for this study due to their dominant V-V or Cr-Cr interactions, which are responsible for their transport properties. In Mn1-xCoxV2O4, the vanadium-vanadium distance is varied by means of chemical pressure (chemical substitution) to bring the system closer to the itinerant electron limit given by the critical V-V distance of 2.94 Å. In Mn1-xCoxV2O4, the structural distortion temperature and transport activation energy decreases with decreasing V-V distance, while the magnetic ordering temperature increases. The results of the transport and structural studies are in agreement with the critical V-V distance scenario of electronic delocalization. Next, a comparative structural study on AV2O4 with non-magnetic A-site ions (A = Cd, Mg, Zn) and Mn1-xCoxV2O4 is also reported. The study indicates that while the V-V interactions are dominant, the A-site ions and their magnetism produce a considerable effect on the passage from the localized to delocalized electron limit. This is proven by the two paths that emerge in the V-V distance dependence of the transport and structural properties where one path includes only the AV2O4, whereas the other includes only Mn1-xCoxV2O4. The transport property of FeCr2S4 under high pressure was also studied. Due to the t2g electronic configuration of Cr3+, the Cr-Cr interaction is also dominant. A high pressure measurement using a cubic anvil press up to 8 GPa was performed to induce an insulator-metal transition. The decrease in the Cr-Cr distance with increasing hydrostatic pressure was confirmed by x-ray diffraction measurements. The Bloch parameter of FeCr2S4 was found to be -2.4, which suggests that FeCr2S4 lies in the localized regime. The high pressure transport measurement on FeCr2S4 shows a decrease in the activation energy and an increase in the magnetic transition temperature with increasing hydrostatic pressure. An insulator to metal transition was observed at a pressure of 7.5 GPa with a possible onset at 7 GPa, at which the Cr-Cr distance is 3.44 Å. In the case of Cr-oxides, it was predicted that the critical Cr-Cr distance is 2.84 Å, but it should be higher for a less electronegative anion. Therefore, the difference in the anion species is responsible for the difference of 0.6 Å between the critical Cr-Cr distance in oxides and the actual Cr-Cr distance where the insulator-metal transition occurs. The insulator-metal transition is followed by a structural transformation at P = 8 GPa. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2014. / November 3, 2014. / Includes bibliographical references. / Haidong Zhou, Professor Co-Directing Dissertation; Vladimir Dobrosavljević, Professor Co-Directing Dissertation; Theo M. Siegrist, University Representative; Christianne Beekman, Committee Member; Volker Credé, Committee Member.

Despite over thirty years of research, the origin of high-temperature superconductivity remains unsolved. In these thirty years, the phase diagram for the rst-discovered high-temperature superconductors, the cuprates, has been found to be rather complex and exhibits many different phases such as antiferromagnetism, charge density waves, spin density waves, nematicity, the pseudogap, and of course, superconductivity. Furthermore, several structural instabilities can manifest that affect the stability of these phases. In the La-214 cuprates, for example, it is known the concomitant charge and spin orders (or stripe order) are stabilized by a low-temperature tetragonal structure. The stripe order coincides with a suppression of the superconducting critical temperature, leading the conclusion that these phases either compete or are intertwined. Since the stability of the low-temperature tetragonal structure, and therefore stripes, can be controlled by various dopants, the La-214 cuprates can be used to investigate how these orders intertwine. In this thesis, both striped and unstriped La-214 compounds have been investigated to understand the interplay of these various orders: superconductivity, stripes, and structure. In three distinct studies, using various charge transport techniques, the interplay between these orders is shown to lead to interesting and unexpected behavior. The first study reveals static charge order is in fact a fluctuating order pinned by the structure. The second study shows the two-dimensional nature of the superconductivity in the absence of stripe order, which is speculated to decouple CuO2 planes. Finally, the third study reveals the existence of a hidden order of Cooper pairs in the T=0 field-driven superconducting-normal-state transition when stripes are present. The culmination of these distinct studies lead to a better understanding of the physics of cuprates through the interplay of their various orders, and thus the general phase diagram of high-temperature superconductivity. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / April 19, 2018. / Charge Transport, Cuprates, High-Temperature Superconductivity, Intertwined Orders / Includes bibliographical references. / Dragana Popovic, Professor Co-Directing Dissertation; Vladimir Dobrosavljevic, Professor Co-Directing Dissertation; Vincent Salters, University Representative; Jorge Piekarewicz, Committee Member; Irinel Chiorescu, Committee Member.

Transition metal dichalcogenides (TMDs or TMDCs) have garnered much interest recently due to their weakly layered structures, allowing for mechanical exfoliation down to a single atomic layer. As such, it is pertinent to re-examine the bulk properties of these materials in order to completely understand and predict what is happening in the few-layered limit. A large majority of these systems were first investigated in the 1950s and 1960s. As such, many of the current growth methods rely on these reports, making new growth techniques for lowering defects of importance as well. In this thesis, both topics are taken into consideration and discussed, though the latter remains to be investigated in much more detail and should be the work of future research efforts. Orthorhombic MoTe₂ and its isostructural compound WTe₂ were recently claimed to belong to a new class (type II) of Weyl semimetals characterized by a linear touching between hole and electron Fermi surfaces in addition to nodal lines. These compounds have recently been shown to display very large non-saturating magnetoresistances which have been attributed to nearly perfectly compensated densities of electrons and holes. Here, we present a detailed study on the temperature and angular dependence of the Shubnikov-de-Haas (SdH) effect in the semi-metal WTe₂ and MoTe₂. In WTe₂, we observe four fundamental SdH frequencies and attribute them to spin-orbit split, electron- and hole-like, Fermi surface (FS) cross-sectional areas. Their angular dependence seems consistent with ellipsoidal FSs with volumes suggesting a modest excess in the density of electrons with respect to that of the holes. We show that density functional theory (DFT) calculations fail to correctly describe the FSs of WTe₂. When their cross-sectional areas are adjusted to reflect the experimental data, the resulting volumes of the electron/hole FSs obtained from the DFT calculations would imply a pronounced imbalance between the densities of electrons and holes. We find evidence for field-dependent Fermi surface cross-sectional areas by fitting the oscillatory component superimposed onto the magnetoresistivity signal to several Lifshitz-Kosevich components. We also observe a pronounced field-induced renormalization of the effective masses. Taken together, our observations suggest that the electronic structure of WTe₂ evolves with the magnetic field due to the Zeeman splitting. This evolution is likely to contribute to its pronounced magnetoresistivity. For β-MoTe2, high quality single-crystals were synthesized by flux in excess tellurium. We find that its superconducting transition temperature depends on disorder as quantified by the ratio between the room- and low-temperature resistivities, (residual resistivity ratio, RRR. Similar to WTe₂, its magnetoresistivity does not saturate at high magnetic fields and can easily surpass 10₂⁶%, with the superimposed Shubnikov de Haas oscillations revealing a non-trivial Berry phase of ≃pi. The geometry of the Fermi surface, as extracted from the quantum oscillations, is markedly distinct from the calculated one. A broad anomaly seen in the heat capacity and in the Hall-effect indicates that the crystallographic and the electronic structures evolve upon cooling below 100 K, likely explaining the discrepancy between these recent predictions and our experimental observations. In α-MoTe₂, grown at lower temperatures in vapor transport, we focus on few-layered crystals mechanically exfoliated onto a 270 nm thick SiO₂ layer. Previous reports found that the field-effect mobility of transition metal dichalcogenides TMDs tends to increase, reaching a maximum value when crystals are composed of approximately 10 atomic layers. We show that the overall performance of a MoTe₂ based field-effect transistor is comparable to similar devices based on MoS₂ or MoSe₂. But with an optical gap quite close in value to the one of Si and an enhanced spin-orbit interaction (since Te is a 5p element) suggests that this compound might be particularly suitable for optoelectronic applications in a complimentary range of wavelengths. In the case of MoSe₂, we show that multi-layered (~ 10 atomic layers) field-effect transistors can display ambipolar behavior at room temperature when using a standard combination of metals, Au on Ti, for all the electrical contacts. The 4.33 eV work function of Ti is closely matched by the electron affinity of bulk MoSe₂, 4.45 ± 0.11 eV. This implies that the Fermi level of Ti is very close to the bottom of the conduction band of MoSe₂, and therefore that one should expect a rather small Schottky barrier for electron conduction through the Ti:Au contacts. One extracts through Hall effect measurements, Hall mobilities in excess of 250 cm₂²/(V s) for both holes and electrons at room temperature. These values are remarkable, since they are comparable or higher than most values reported so far for transition metal dichalcogenides at room temperature, but are obtained without the use of high k-dielectrics such as HfO₂, doping, or of a particular combination of metals for the electrical contacts. Our results suggest that improvements in fabrication, and on the quality of the starting material (with a lower amount of defects) could make field-effect transistors based on few atomic layers of synthetic MoSe₂ excellent candidates for complementary logic electronics. Finally, we report on alloys of MoTe₂ and WTe₂, Mo₁₋xWxTe₂, grown by a chemical vapor transport process with the goal of obtaining a phase diagram with respect to doping and temperature. These crystals have been analyzed for composition via EDS and investigated through high resolution transmission electron microscopy, scanning tunneling microscopy (STM) and ARPES. Transmission electron microscopy images clearly show that through W substitution we are able to synthesize both 2H, trigonal prismatic, and Td, orthorhombic structures. As opposed to other reports, we find a phase transition from the 2H- to the Td-phase at 10 % W doping, much lower than expected. This structure is characterized by a linear arrangement of atoms, as opposed to a hexagonal pattern. In addition, through examination of monolayers via TEM, we find that the W disperses randomly amongst the crystal as opposed to forming grain boundaries. Given the crystallinity and quality of the material, mapping the phase diagram should be of relative ease, however this work is still ongoing. As such, the phase diagram has not yet been completed and remains unreported in this manuscript. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2016. / July 13, 2016. / Fermi Surface, Magnetoresistance, MoTe2, Synthesis, TMDs, WTe2 / Includes bibliographical references. / Luis Balicas, Professor Co-Directing Dissertation; Nicholas Bonesteel, Professor Co-Directing Dissertation; Theo Siegriest, University Representative; Mark Riley, Committee Member; Irinel Chiorescu, Committee Member.

This dissertation presents studies on mononuclear single molecule magnets (SMMs) with magnetic properties arising from transition metal ions in trigonal bipyramidal (TBP) coordination environments. We use both experimental and theoretical methods to elucidate the effects of coordination geometry on the magnetic anisotropy of a SMM. The role of an axial magnetic anisotropy is to pin the magnetic moment of the metal ion in one of two preferred orientations, either parallel or anti-parallel to the magnetic easy-axis. For transition metals, maximization of the axial magnetic anisotropy requires stabilization of an unquenched orbital moment that can couple to a ligand field. SMMs with giant magnetic anisotropy play an important role both in terms of fundamental scientific reasons and potential application in information technologies. Thus the studies presented in this dissertation attempt to explore some of the interesting physics in these compounds. The presence of orbitally degenerate states and unquenched orbital momentum pushes the limits of spin-only model. To overcome this limitation, we propose a phenomenological spin-orbit model based on point charge approximation with the goal to investigate orbitally degenerate mononuclear compounds. As an application of our model, we consider two test compounds : Iron(II) and Nickel(II) ions in trigonal bipyramidal (TBP) environments, where we find that the high symmetry configuration supports a large magnetic anisotropy in the absence of Jahn-Teller distortion. The motivation for our phenomenological model stemmed from our detailed EPR measurements performed on a mononuclear Nickel(II) SMM in a TBP environment that revealed an unprecedented magnetic anisotropy, reaching the limits of applicability of the familiar spin-only description. The axial anisotropy estimated for this complex was found to the be the largest so far for a mononuclear Nickel(II) complex; and, importantly, only a very small degree of axial symmetry breaking was detected. This was most likely considered to be due to the unquenched orbital moment in the ground states of the Nickel(II) ion. To further confirm this prediction we performed theoretical studies of the SMM using the phenomenological spin-orbit model. This study showed the suppression of Jahn-Teller effects in trigonal bipyramidal Nickel(II) complex because of rigid, bulky axial ligands. To further understand the effects of using bulky ligands in TBP coordination environments we performed experimental and theoretical studies on a mononuclear Iron(II) SMM. Although the ground states of this complex is also orbitally degenerate, our investigation showed reduced axial magnetic anisotropy compared to Nickel(II) with a very small transverse component. Our phenomenological investigation of the ground states revealed that the magnitude of the first order contribution is strongly dependent on the bond angles, and the spin-orbit coupling constant also plays a significant role in achieving large magnetic anisotropy. Finally, we also explore the effects of different ligand types in Cobalt(II) mononuclear complexes in TBP coordination environments. In these Kramers systems we and that the combination of a 3-fold symmetric ligand and a trigonal space group gives rise to an increase in the easy-plane magnetic anisotropy, while keeping the rhombicity of the system close to zero. This is particularly interesting for quantum information processing, especially in relation to molecules with a large spin ground state characterized by a large easy-plane anisotropy. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester 2018. / June 29, 2018. / Includes bibliographical references. / Stephen Hill, Professor Directing Dissertation; Mykhailo Shatruk, University Representative; Jianming Cao, Committee Member; Nicholas Bonesteel, Committee Member; Jorge Piekarewicz, Committee Member.

Thesis (Ph.D.)--Brown University, 2008. / Advisor: Xinsheng S. Ling. Includes bibliographical references (leaves 111-125).

Two mathematical problems in disordered systems are studied: geodesics in first-passage percolation and conductivity of random resistor networks. In first-passage percolation, we consider a translation-invariant ergodic family {t(b): b bond of Z²} of nonnegative random variables, where t(b) represent bond passage times. Geodesics are paths in Z², infinite in both directions, each of whose finite segments is time-minimizing. We prove part of the conjecture that geodesics do not exist in any fixed half-plane and that they have to intersect all straight lines with rational slopes. In random resistor networks, we consider an independent and identically distributed family {C(b): b bond of a hierarchical lattice H} of nonnegative random variables, where C(b) represent bond conductivities. A hierarchical lattice H is a sequence {H(n): n = 0, 1, 2} of lattices generated in an iterative manner. We prove a central limit theorem for a sequence x(n) of effective conductivities, each of which is defined on lattices H(n), when a system is in a percolating regime. At a critical point, it is expected to have non-Gaussian behavior.

Thesis (Ph.D.) - University of St Andrews, June 2009. / Restricted until 1st December 2009.

<p>The following dissertation shows the results of a series of inelastic neutron scattering experiments on the geometrically frustrated pyrochlore system Tb2Sn2-xTixO7 for x=0, 0.1, 0.2, 0.5, 1, 1.5 and 2. Inelastic neutron scattering measurements were performed on the SEQUOIA direct geometry time-of-flight spectrometer at the Spallation Neutron Source of Oak Ridge National Laboratory. For the two end members, x=0, Tb2Sn2O7 and x=2, Tb2Ti2O7 , they display related, but different exotic ground states, with Tb2Sn2O7 displaying “soft” spin ice order below T_N~0.87K, while Tb2Ti2O7 enters a glassy antiferromagnetic spin ice state below T_g~0.2K.</p> <p>The first two chapters give a brief introduction to the physics of geometrically frustrated magnetism and neutron scattering. Chapter 3 studies the two end members Tb2Ti2O7 and Tb2Sn2O7 experimentally and theoretically. Inelastic neutron scattering measurements and appropriate crystal field calculations together probe the crystal field states associated with the J=6 states of Tb^3+ within the appropriate Fd3m pyrochlore environment. These crystal field states determine the size and anisotropy of the Tb^3+ magnetic moment in each material’s ground state, information that is an essential starting point for any description of the low temperature phase behavior and spin dynamics in Tb2Ti2O7 and Tb2Sn2O7. Chapter 4 treats neutron scattering, as well as accompanying AC magnetic susceptibility and muSR measurements performed by our collaborators on a series of solid solutions Tb2Sn2-xTixO7 showing a novel, dynamic spin liquid state for all x other than the end members x=0 and x=2. This state is the result of disorder in the low lying Tb^3+ crystal field environments which de-stabilizes the mechanism by which quantum fluctuations contribute to ground state selection in Tb2Sn2-xTixO7.</p> / Master of Science (MSc)