Various forms of antiferromagnetic exchange interaction among quantized spins in one-dimensional and quasi-one-dimensional lattices are examined. Primary results are reported in two real compounds, the sodium vanadate NaV2O5 and the copper germanate CuGeO3, and in a class of compounds of real materials modeled as dimerized antiferromagnetically coupled spin-1/2 chains susceptible to spin-1 impurity doping and that include such examples as the strontium cuprate Sr14Cu24O41 and vanadium pyrophosphate (VO)2P2O7. Sodium vanadate, NaV2O5, a quarter-filled two-leg ladder compound that was originally thought to be composed of magnetic legs and nonmagnetic legs was subsequently shown to be a charge ordered system below room temperature. Initial models of the material as isolated antiferromagnetically coupled spin-1/2 chains can be mapped to the subsequently resolved magnetic system of the charge ordered state with the spins on molecular orbitals of V-O-V rungs antiferromagentically coupled between neighboring rungs either on the same ladder or on neighboring ladders. Comparing the model's dynamic structure factor to inelastic neutron scattering data could distinguish between the proposed spin coupling schemes and consequently reveal the details of the interaction between the lattice and the "zig-zag" charge density as well as the magnetic stabilization of the low temperature phase. Copper germanate, the first and only known inorganic spin-Peierls compound, exhibits a strong temperature dependent exchange coupling pattern among the spin-1/2 Cu2+ chains. Above the spin-Peierls transition temperature an unmodulated antiferromagnetic nearest neighbor exchange interaction J1 competes with an antiferromagnetic next nearest neighbor interaction J2. The next nearest neighbor exchange represents an effective coupling equivalent to the net effect of all longer range exchange interactions. This frustration to the nearest neighbor spin exchange produces a distinctive magnetic susceptibility χ (T) much different from the Bonner-Fisher susceptibility of the spin-1/2 Heisenberg chain with nearest neighbor antiferromagnetic exchange only. The ratio of the second to first nearest neighbor couplings α = J2/J1 ≈ 0.36 is sufficient to open a spontaneous gap in the spin-wave excitation spectrum at low temperatures. Below TSP = 14K, the dynamical structure factor is used to fit the dimerization δ and the exchange interactions J1 and J2 to the inelastic neutron scattering data of CuGeO3 at T = 10K. It is found that both δ and α increase significantly at lower temperatures, relative to the values obtained in the high temperature phase and at the onset of dimeration at 14 K. Static structure factor calculations how Scattering inconsistent with the δ−J1−J2 model and can be attributed primarily to the phonon degrees of freedom but possibly also to the couplings between chains in the b and a directions of the crystal lattice. Structurally dimerized compounds of antiferromagnetic spin-1/2 chains possess dynamic structure factor and magnetic susceptibility features that are very sensitive to doping with magnetic and nonmagnetic impurities. It is shown that the effects of spin-1 impurities are very similar to those of nonmagnetic (S = 0) impurities if the coupling between impurity and native spin is about the same magnitude as or larger than between native S = 1/2 spins. The microscopic origins of the similarity can be appreciated with the consideration that neighboring spins to the impurity find it more energetically favorable to couple to the impurity than the other spins of the lattice. Thus the spin-1 impurity and its neighboring S = 1/2 spins decouple from the lattice, creating a nonmagnetic break in the chain. The spins that now observe a nonmagnetic cluster on one side can couple to the S = 1/2 spins on the other side with a higher AF correlation than in the pure compound since they do not have to have a fluctuating dimer resonating between two neighbors. Such enhancements to the local correlations can stabilize the global AF order in one dimensional compounds as shown in theoretical and experimental studies of CuGeO3. ED calculations of the dynamic structure factor show that S(q, ω) developes states with ω = 0 in the gap at q = π. Magnetic susceptibilites in the presense of spin-1 impurities were obtained for 80 site chains by QMC simulations and for 16 site chains by ED calculations. An impurity concentration-dependent second peak in the low temperature region reveals an increasing second maximum with T as observed in doped copper germanates and suggests that the results of the study are applicable even to phonon mediated dimerization. This is not immediately apparent because spin-phonon coupling could distort the dimerization patterns. However, experimental and theoretical results show that elastic coupling between chains can stabilize the dimerization pattern due to the impurities and the results will still apply. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2003. / Date of Defense: July 8, 2003. / Antiferromagnetic Exchange Interactions / Includes bibliographical references. / Elbio Dagotto, Professor Directing Thesis; Wolfgang Heil, Outside Committee Member; Adriana Moreo, Committee Member; Jorge Piekarewicz, Committee Member; Mark Riley, Committee Member.

This dissertation investigates equilibrium and dynamical properties of submonolayer chemical adsorption of Br and Cl on single-crystal Ag(100) electrodes. Computational methods, such as Monte Carlo simulations with First-order Reversal Curve analysis, are used along with experimental data. Monte Carlo simulations of a two-dimensional lattice-gas approximation for the adlayer are used to explore equilibrium properties of the system. Lateral interaction energies between adsorbates, as well other system parameters like the electrosorption valency, are determined by fitting simulations to experimental chronocoulometry isotherms. While neither the electrosorption valency nor the lateral interactions show any dependence on the adsorbate coverage for the Br/Ag(100) system, a model in which both are coverage dependent is required to adequately describe the Cl/Ag(100) system. A self-consistent, entirely electrostatic picture of the lateral interactions with coverage dependence is developed, and a relationship between the lateral interactions and the electrosorption valency is investigated for Cl on Ag(100). The adsorbates form a disordered adlayer at low electrochemical potentials. At a more positive electrochemical potential the adlayer undergoes a disorder-order phase transition to an ordered c(2x2) phase. This phase transition produces a peak in the current density observed in cyclic-voltammetry experiments. Kinetic Monte Carlo studies of the lattice-gas model are used to simulate cyclic-voltammetry experiments. The scan-rate dependence of the separation between positive- and negative-going peaks in cyclic-voltammetry simulations are compared to experimental peak separations. This dynamics study identifies the inverse Monte Carlo attempt frequency with a physical timescale. Although kinetic Monte Carlo simulations can provide long-time simulations of the dynamics of physical and chemical systems, this identification is not yet possible in general. To further investigate the dynamics, First-order Reversal Curve (FORC) analysis---a method that was recently developed and used for magnetic systems---is applied to simulations of electrochemical submonolayer adsorption in systems with first- and second-order phase transitions. Not only does this method highlight differences between the two kinds of phase transitions, but it can also be used to recover the equilibrium behavior for systems with a second-order phase transition and slow equilibration from dynamic reversal curves. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Spring Semester, 2006. / Date of Defense: April 3, 2006. / Monte Carlo, Phase Transitions, Halide Electrosorption, Electrochemistry, First-Order Reversal Curve Analysis, Lattice Gas Odel / Includes bibliographical references. / Per Arne Rikvold, Professor Directing Dissertation; Joseph B. Schlenoff, Outside Committee Member; Jorge Piekarewicz, Committee Member; Huan-Xiang Zhou, Committee Member; Linda Hirst, Committee Member.

Emergent phenomena are one of the most profound topics in modern science, addressing the ways that collectivities and complex patterns appear due to multiplicity of components and simple interactions. Ensembles of random Hamiltonians allow one to explore emergent phenomena in a statistical way. In this work we adopt a shell model approach with a two-body interaction Hamiltonian. The sets of the two-body interaction strengths are selected at random, resulting in the two-body random ensemble (TBRE). Symmetries such as angular momentum, isospin, and parity entangled with complex many-body dynamics result in surprising order discovered in the spectrum of low-lying excitations. The statistical patterns exhibited in the TBRE are remarkably similar to those observed in real nuclei. Signs of almost every collective feature seen in nuclei, namely, pairing superconductivity, deformation, and vibration, have been observed in random ensembles. In what follows a systematic investigation of nuclear shape collectivities in random ensembles is conducted. The development of the mean field, its geometry, multipole collectivities and their dependence on the underlying two-body interaction are explored. Apart from the role of static symmetries such as SU(2) angular momentum and isospin groups, the emergence of dynamical symmetries including the seniority SU(2), rotational symmetry, as well as the Elliot SU(3) is shown to be an important precursor for the existence of geometric collectivities. / A Thesis submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctorate of Philosophy in Physics. / Degree Awarded: Summer Semester, 2011. / Date of Defense: May 17, 2011. / Shell Model, Quadrupole Collectivity, Random Interactions / Includes bibliographical references. / Alexander Volya, Professor Directing Thesis; Giray Okten, University Representative; Simon Capstick, Committee Member; Grigory Rogachev, Committee Member; Per Arne Rikvold, Committee Member.

A new angular correlation analysis technique for assigning spins to alpha-unbound states of nuclei that feed alpha-unbound states of other nuclei is described. A kinematically complete experiment was performed to study the reaction ¹²C(¹⁶O, alpha)²⁴Mg*, populating alpha-unbound states of ²⁴Mg that decay to alpha-unbound states of ²⁰Ne, where all final state particles were detected. The new analysis technique was used to unambiguously identify the first Ipi = 12+ state of ²⁴Mg at 26.3 MeV. The new 12+ state is discussed in the context of the collective and shell models. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2007. / Date of Defense: October 31, 2007. / Angular Correlations, Sd-shell, 24Mg / Includes bibliographical references. / Ingo Wiedenhover, Professor Directing Dissertation; Oliver Steinbock, Outside Committee Member; Nicholas E. Bonesteel, Committee Member; Samuel L. Tabor, Committee Member; Alexander S. Volya, Committee Member.

In this dissertation, I present a study of a wide range of organic and inorganic materials using radio frequency (rf) measurement methods. The organic samples under study were λ-(BETS )2 GaCl4 and λ-(BETS )2 FeCl4 . In the λ-(BETS )2 GaCl4 , the H-T superconductivity phase diagram was studied using the tunnel diode oscillator (TDO) method and compared with simultaneous four terminals resistivity measurements. These simultaneous measurements show signs of para-conductivity in this material. The same method was used to study the λ-( BETS )2 FeCl4 sample which is a field induced superconductor (FISC). The inorganic materials that I have studied include Ba 0.55K0.45Fe2 As2 and USb2 . In Ba0.55K0.45Fe 2As2 (which belongs to the recently discovered Pnictide superconductors family), I have studied the H-T phase diagram for magnetic fields applied parallel and perpendicular to the crystallographic c-axis up to 65 tesla and in temperature as low as 4 K . Ba0.55K0.45 Fe2As2 was studied by a new rf technique that I have developed recently (PDO≡Proximity Detector Oscillator). The rf measurements of Ba0.55 K0.45Fe2 As2 from my work support the prediction of an unconventional multigap superconductivity in this material. In the USb 2 sample, a Fermi surfaces measurement was performed by the TDO rf probe and by a torque magnetometer for comparison purposes in high magnetic fields up to 65 tesla and in temperatures above 0.5 K . I found that both the rf and the torque measurements reveal a cylindrical Fermi surface with approximately the same effective mass. However, the rf and the torque measurements reveal some differences in the frequencies obtained from the FFT obtained for each method. In this dissertation, most of the measurements were performed using rf probes like the TDO or the PDO. The PDO method has successfully replaced the TDO method to perform rf measurements in all different kinds of magnets (dc and pulsed). / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2009. / Date of Defense: October 6, 2009. / Includes bibliographical references. / James Brooks, Professor Directing Dissertation; Naresh Dalal, University Representative; Charles H. Mielke, Committee Member; Jorge Piekarewicz, Committee Member; Pedro Schlottmann, Committee Member; David Van Winkle, Committee Member.

We have studied different aspects of magnetic materials in bulk, nanoparticles, and thinfilm form with emphasis on their use in biomedical and technological applications. In this work: 1. We have synthesized several new Gd based compounds and alloys and have optimized their magnetic properties for the self-controlled hyperthermia applications. The self controlled hyperthermia is a new non-invasive technique to employ heat treatment to cure cancerous cells without overheating the normal cells. The need for developing such materials was dictated by the lack of existing magnetic materials with magnetic ordering temperatures in the temperature range of (40-45)0C, which is the critical operating temperature range for the hyperthermia applications. 2. We have produced gold coated Fe-Au nanoparticles which are biocompatible and can easily be functionalized through gold surface for various technological applications, besides hyperthermia applications. Contrary to the previous reports of time dependent degradation of magnetic properties of the Fe-Au nanoparticles, our gold coated nanoparticles are quite robust and their magnetic properties remain unchanged under the ambient conditions. We have made a comprehensive study of the Fe-Au nanoparticles, and have observed that superparamgnetic Fe-Au nanoparticles can be produced with variable Fe content up to 30 at.% and the particle size remains nearly uniform (~ 5 nm). When subjected to annealing at elevated temperatures, the magnetic core in the Fe-Au nanoparticles undergoes various interesting changes and blocking temperature and magnetization increase when nanoparticles are annealed at elevated temperatures. The observation of the Verwey transition at ~ 125K in the magnetization versus temperature data for the samples annealed at 4500C and above indicates the formation of Fe3O4. The absence of any oxide peaks in the as-formed sample and presence of oxide peaks in the samples annealed at 4500C and above in the x-ray diffraction and x-ray photoemission data, as well as in the magnetic data, support the model that Fe-Au alloy core is protected by the Au shell in the as-formed state. Annealing at higher temperatures leads to the segregation of Fe and Au, and oxidation of Fe occurs when Au shell is punctured at the elevated temperatures. Also, we have studied the behavior of the as-formed and annealed Fe-Au nanoparticles in the a.c. field upto a frequency of 1 MHz and have demonstrated their suitability for hyperthermia applications. 3. We have investigated the metal-organic interface for its impact on the magnetic properties by sputtering permalloy (Ni79Fe21) on the self assembled monolayers of polar [16-mercaptohexadecanoic acid (MHA)] and non polar [1-Octadecanethiol (ODT)] organic molecules. It has been observed that permalloy forms films exhibiting ferromagnetic properties for the 4 nm and higher thicknesses on the polar MHA molecules which offer better adhesion to permalloy, on the other hand, it forms scattered superparamgnetic clusters on the ODT molecules which offer poor adhesion. The systematic study of the deposition of permalloy with thickness varying from 2 nm to 70 nm on the self-assembled monolayes of MHA and ODT reveals that the effect of the underlaying organic surfaces decreases as the deposition thickness increases and inplane oriented magnetic thinfilms are produced for 12 nm thickness on both type of surfaces. The squareness of the magnetic hysteresis loop indicates that the best inplane oriented films are produced for the 20 nm thickness, and further increase in the thickness leads to randomization of the orientation of the deposited material on both type of surfaces. We also demonstrated that by sputtering permalloy on the prefabricated templates containing MHA and ODT patterns, small scale (micron size) templates can be made with magnetic and non-magnetic patterns. The dip-pen approach may be used to extend the pattering to submicron and nanoscale level. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Spring Semester, 2009. / Date of Defense: November 26, 2008. / Magnetic Nanoparticles, Curie Temperature, Hyperthermia, Patterning, Superparamagnetism, Polar And Nonpolar Organic Molecules, Self-Assembled Monolayers, Magnetic Thinfilms, Sputtering, Core-Shell Nanoparticles, Blocking Temperature, Coercivity, Annealing, Magnetic Entropy / Includes bibliographical references. / Shahid A. Shaheen, Professor Directing Dissertation; Geoffery F. Strouse, Outside Committee Member; David Van Winkle, Committee Member; David Lind, Committee Member; Nicholas Bonesteel, Committee Member; Jorge Piekarewicz, Committee Member.

The study of nuclear structure at very high angular momentum requires sensitive detector systems in order to detect weak signals. Large gamma-ray arrays were used in this thesis to study the high-spin states in 166;168;170Ta and 160Yb. These arrays were located at facilities such as: Florida State University (FSU), Argonne National Laboratory (ANL), Lawrence Berkeley National Laboratory (LBNL), and Yale University. A study utilizing the Gammasphere spectrometer (the world's most powerful array) resulted in a dramatic expansion of over 400 new gamma-ray transitions organized into 29 rotational bands in the level scheme of 170Ta. Alignment behavior, an additivity of Routhians analysis, and B(M1)/B(E2) transition strength ratios are used to support the configuration assignments made for this nucleus. The observation of linking transitions between almost all of the bands allowed the relative excitation energies to be determined for nearly the entire level scheme. All of the above work on 170Ta, resulted in the most comprehensive high-spin level scheme in odd-odd nuclei to date. A significant expansion has also been made to the level scheme of 168Ta using the FSU gamma-ray array. An additivity of alignment analysis, along with a B(M1)/B(E2) analysis made it possible to assign band configurations. Although an experiment studying the high-spin structure of 166Ta using the Yale University spectrometer (YRAST Ball) was performed, detailed analysis resulted in the observation of no new information. A new extremely low intensity band structure has also been observed in 160Yb from another Gammasphere experiment. This structure is interpreted as the first observation of a stable triaxial shape in Yb nuclei. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Fall Semester, 2008. / Date of Defense: July 21, 2008. / Spectroscopy, High-spin, Tantalum, Odd-Odd, Gamma-Ray / Includes bibliographical references. / Mark A. Riley, Professor Directing Thesis; Sanford Safron, Outside Committee Member; Simon Capstick, Committee Member; Grigory Rogachev, Committee Member; Todd Adams, Committee Member.

We present the results of our numerical studies on the transport properties of strongly correlated nanostructures, particularly quantum dots and single molecules. The main focus is on correlation, interference and phononic effects. Interesting interferences are observed in multilevel quantum dots, and under the appropriate conditions, a novel ferromagnetic phase is observed in coupled double-level quantum dots at quarter filling. Our simulations of experiments involving nonlocal spin control provide more insight of the experimentally observed results. In the case of single molecules, our study of phonon effects reveals that the center-of-mass motion opens a new channel for transport. This channel can interfere destructively with the purely electronic channel leading to a conductance dip. Finally, we propose a new technique to study nanotransport based on the adaptive time-dependent density-matrix renormalization group. The technique is tested for different cases and is very promising particularly in the nonequilibrium case where most other techniques cannot be applied. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2007. / Date of Defense: May 30, 2007. / Quantum Dots, Transport, Correlated Electrons, Kondo Effect / Includes bibliographical references. / Nicholas Bonesteel, Professor Directing Dissertation; Naresh Dalal, Outside Committee Member; Jorge Piekarewicz, Committee Member; David Lind, Committee Member; Jianming Cao, Committee Member.

Reaction physics involving composite objects with internal degrees of freedom is an important subject since it is encountered in the context of nuclear processes like fusion, fission, particle decay, as well as many other branches of science. Quantum tunneling and scattering of a composite object are explored in this work. A few model Hamiltonians are chosen as examples where a two-particle system interacts, in one dimension, with a target that poses a delta-potential or an infinite wall potential. It is assumed that only one of the two components interacts with the target. The study includes the harmonic oscillator and the infinite square well as examples of intrinsic Hamiltonians that do not allow the projectile to break up, and a finite square well and a delta-well as examples of Hamiltonians that do. The Projection Method and the Variable Phase Method are applied with the aim of an exact solution to the relevant scattering problems. These methods are discussed in the context of the pertinent convergence issues related thereto, and of their applicability. Virtual excitations of the projectile into the classically forbidden energy-domain are found to play a dominant and non-perturbative role in shaping reaction observables, giving rise to enhanced or reduced tunneling in various situations. Cusps and discontinuities are found to appear in observables as manifestations of unitarity and redistribution of flux at the thresholds. The intrinsic structure gives rise to resonance-like behavior in tunneling probabilities. It is also shown that there is charge asymmetry in the scattering of a composite object, unlike in the case of a structureless particle. / A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Degree Awarded: Summer Semester, 2011. / Date of Defense: April 6, 2011. / Projection Method, Infinite Square Well, Harmonic Oscillator, Continuum, Charge Asymmetry, Barkas Effect, Enhanced Tunneling, Variable Phase Method, Virtual Channel, Exact Solution / Includes bibliographical references. / Alexander Volya, Professor Directing Thesis; Ettore Aldrovandi, University Representative; Jorge Piekarewicz, Committee Member; Volker Crede, Committee Member; Peng Xiong, Committee Member.

Optical antennas localize energy from incoming electromagnetic waves that oscillate at visible frequencies. Because optical wavelengths are smaller than radio wavelengths, optical antennas are substantially smaller than radio antennas - they are on the order of tens or hundreds of nanometers, where light-matter interactions are described by charge density oscillations. The electromagnetic field response of aluminum optical antennas can be studied using near-field scanning optical microscopy. The spatial and intensity characteristics of the electromagnetic field response from an optical antenna are a function of the antenna geometry and the light-matter interaction. This response will have propagating and nonpropagating field components. Far-field microscopes can measure the propagating components of the field, but these components provide little information about features that are smaller than the diffraction limit, or about half the wavelength of the illuminating light. The nonpropagating components of the field can provide more detailed and localized spatial information, but these components are difficult to measure because their amplitude decays exponentially as they move away from the sample. By introducing a sharp probe into the focus, near-field microscopes can scatter nonpropagating field components into the far-field. Our system illuminates the nanoantenna with laser light, controls a sharp probe in the focus, and collects the scattered light. We have implemented a feedback system to maintain the sub-50 nm probe-sample separation as the probe is scanned with respect to the sample. This feedback system allows us to acquire a high-resolution surface profile image together with an optical image. The spatial resolution of a near-field microscope is limited by the sharpness of the probe and the ability to distinguish photons scattered by the presence of the probe. The optical antenna system has been modeled by approximating the nanoscale aluminum antennas as a dipole orthogonal to the optical axis and the probe as a dipole along the optical axis.