Magnetic properties and Spin dynamics in magnetic Molecular Rings

Molecular nanomagnets are spin clusters whose topology and magnetic interactions can be modulated at the level of the chemical synthesis. They are formed by a small number of transition metal ions coupled by the Heisenberg's exchange interactions. Each cluster is magnetically isolated from its neighbors by organic ligands, making each unit not interacting with the others. Therefore, we can investigate the magnetic properties of an isolated molecular nanomagnet by bulk measurements. The present thesis has been mostly devoted to the experimental investigation of the magnetic properties and spin dynamics of different classes of antiferromagnetic (AF) molecular rings. This study has been exploiting various techniques of investigations, such as Nuclear Magnetic Resonance (NMR), muon spin relaxation (muSR) and SQUiD magnetometry. We investigate the magnetic properties and the phonon-induced relaxation dynamics of the first regular Cr9 antiferromagnetic (AF) ring, which represents a prototype frustrated AF ring. The magnetically-open AF rings like Cr8Cd are model systems for the study of the microscopic magnetic behaviour of finite AF Heisenberg chains. In this type of system the different magnetic behaviour depends length and on the parity of the chain (odd or even). In order to study the local spin densities on the Cr sites, the Cr-NMR spectra was collected at low temperature. The experimental result confirm the theoretical predictions for the spin configuration. Finally, the study of Dy6, the first rare-earth based ring that has been ever synthesized, has been performed by AC-SQuID and muSR measurements. We found that the dynamics is characterized by more than one characteristic correlation time, whose values depend strongly on the applied field.

Equilibrium properties of disordered spin models with two-scale interactions

Methods for understanding classical disordered spin systems with interactions conforming to some idealized graphical structure are well developed. The equilibrium properties of the Sherrington-Kirkpatrick model, which has a densely connected structure, have become well understood. Many features generalize to sparse Erdös- Rényi graph structures above the percolation threshold and to Bethe lattices when appropriate boundary conditions apply. In this paper, we consider spin states subject to a combination of sparse strong interactions with weak dense interactions, which we term a composite model. The equilibrium properties are examined through the replica method, with exact analysis of the high-temperature paramagnetic, spin-glass, and ferromagnetic phases by perturbative schemes. We present results of replica symmetric variational approximations, where perturbative approaches fail at lower temperature. Results demonstrate re-entrant behaviors from spin glass to ferromagnetic phases as temperature is lowered, including transitions from replica symmetry broken to replica symmetric phases. The nature of high-temperature transitions is found to be sensitive to the connectivity profile in the sparse subgraph, with regular connectivity a discontinuous transition from the paramagnetic to ferromagnetic phases is apparent.

A study of mechanochemical reactions of spin traps in hydrocarbon polymers

The identification and quantification of spin adducts and their reduction products (>NOH, >NOR) formed from nitroso compounds and nitrones in EPR and PP during spin trapping techniques have been examined. The nitroxyl yield and polymer bound nitroxyl percentage formed from these spin traps were found to be strongly dependent on the nature of spin trap and radical generator, processing temperature, and irradiation time. The nitroxyl yield and % bound nitroxyl of the spin traps improved significantly in the presence of Trigonox 101 and 2-0H benzophenone. The effect of these spin traps used as normal additive and their spin adducts in the form of EPR-masterbatch on the photo and thermal-oxidation of PP have been studied. Aliphatic nitroso compounds were found to have much better photo-antioxidant activity than nitrones and aromatic nitroso compounds, and their antioxidant activity improved appreciably in the presence of, a free radical generator, Trigonox 101, before and after extraction. The effect of heat, light and oxidising agent (meta-dichloro per benzoic acid) on the nitroxyl yield of nitroso tertiary butane in solution as a model study has been investigated and a cyclic regenerative process involving both chain breaking acceptor and chain breaking donor process has been proposed.

Studies of the effects of molecular encounters on N.M.R. spin-lattice relaxation times

This thesis is concerned with investigations of the effects of molecular encounters on nuclear magnetic resonance spin-lattice relaxation times, with particular reference to mesitylene in mixtures with cyclohexane and TMS. The purpose of the work was to establish the best theoretical description of T1 and assess whether a recently identified mechanism (buffeting), that influences n.m.r. chemical shifts, governs Tl also. A set of experimental conditions are presented that allow reliable measurements of Tl and the N. O. E. for 1H and 13C using both C. W. and F.T. n.m.r. spectroscopy. Literature data for benzene, cyclohexane and chlorobenzene diluted by CC14 and CS2 are used to show that the Hill theory affords the best estimation of their correlation times but appears to be mass dependent. Evaluation of the T1 of the mesitylene protons indicates that a combined Hill-Bloembergen-Purcell-Pound model gives an accurate estimation of T1; subsequently this was shown to be due to cancellation of errors in the calculated intra and intemolecular components. Three experimental methods for the separation of the intra and intermolecular relaxation times are described. The relaxation times of the 13C proton satellite of neat bezene, 1,4 dioxane and mesitylene were measured. Theoretical analyses of the data allow the calculation of Tl intra. Studies of intermolecular NOE's were found to afford a general method of separating observed T1's into their intra and intermolecular components. The aryl 1H and corresponding 13C T1 values and the NOE for the ring carbon of mesitylene in CC14 and C6H12-TMS have been used in combination to determine T1intra and T1inter. The Hill and B.P.P. models are shown to predict similarly inaccurate values for T1linter. A buffeting contribution to T1inter is proposed which when applied to the BPP model and to the Gutowsky-Woessner expression for T1inter gives an inaccuracy of 12% and 6% respectively with respect to theexperimentally based T1inter.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Generalized mean field approximation for parallel dynamics of the Ising model

The dynamics of the non-equilibrium Ising model with parallel updates is investigated using a generalized mean field approximation that incorporates multiple two-site correlations at any two time steps, which can be obtained recursively. The proposed method shows significant improvement in predicting local system properties compared to other mean field approximation techniques, particularly in systems with symmetric interactions. Results are also evaluated against those obtained from Monte Carlo simulations. The method is also employed to obtain parameter values for the kinetic inverse Ising modeling problem, where couplings and local field values of a fully connected spin system are inferred from data. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

A new 3-D polymeric spin transition compound: [tris(1,4-bis-(tetrazol-1-yl) butane-N1,N1′)iron(II)] bis(perchlorate)

A series of novel polymeric compounds of formula [M(btzb)3][ClO4]2 (Mll = Fe, Ni or Cu) with btzb = 1,4-bis-(tetrazol-1-yl)butane have been prepared and their physical properties investigated. The btzb ligand has been prepared and its crystal structure determined, together with a tentative crystal structure of the 3-D compound [Fe(btzb)3][ClO4]2. The model of the latter shows two symmetry-related, interpenetrating Fe-btzb networks in which the iron(II) ions approach each other as close as 8.3 and 9.1 Å. This supramolecular catenane undergoes a sharp thermal spin transition around 160 K with hysteresis (20 K) along with a pronounced thermochromic effect. The spin crossover behaviour has been followed by magnetic, DSC, optical spectroscopy and 57Fe Mössbauer spectroscopy measurements. Irradiation with green light at low temperature leads to population of the metastable high-spin state for the thermally active iron(ll) ions. The nature of the spin crossover behaviour has been discussed in detail.

Seminar 1 impurity in the tomonaga-luttinger model:a functional integral approach

This chapter explains a functional integral approach about impurity in the Tomonaga–Luttinger model. The Tomonaga–Luttinger model of one-dimensional (1D) strongly correlates electrons gives a striking example of non-Fermi-liquid behavior. For simplicity, the chapter considers only a single-mode Tomonaga–Luttinger model, with one species of right- and left-moving electrons, thus, omitting spin indices and considering eventually the simplest linearized model of a single-valley parabolic electron band. The standard operator bosonization is one of the most elegant methods developed in theoretical physics. The main advantage of the bosonization, either in standard or functional form, is that including the quadric electron–electron interaction does not substantially change the free action. The chapter demonstrates the way to develop the formalism of bosonization based on the functional integral representation of observable quantities within the Keldysh formalism.

One- and two-step spin-crossover behavior of [Fe(II)(isoxazole)6]2+ and the structure and magnetic properties of triangular [Fe(III)3O(OAc)6(isoxazole)3][ClO4)]

The structure and spin-crossover magnetic behavior of [FeII16][BF4]2 (1 = isoxazole) and [FeII16][ClO4]2 have been studied. [FeII16][BF4]2 undergoes two reversible spin-crossover transitions at 91 and 192 K, and is the first two-step spin transition to undergo a simultaneous crystallographic phase transition, but does not exhibit thermal hysteresis. The single-crystal structure determinations at 260 [space group P3̄, a = 17.4387(4) Å, c = 7.6847(2) Å] and at 130 K [space group P1̄, a = 17.0901(2) Å, b = 16.7481(2) Å, c = 7.5413(1) Å, α = 90.5309(6)°, β = 91.5231(6)°, γ = 117.8195(8)°] reveal two different iron sites, Fe1 and Fe2, in a 1:2 ratio. The room-temperature magnetic moment of 5.0 μB is consistent with high-spin Fe(II). A plateau in μ(T) having a moment of 3.3 μB centered at 130 K suggests a mixed spin system of some high-spin and some low-spin Fe(II) molecules. On the basis of the Fe−N bond distances at the two temperatures, and the molar fraction of high-spin molecules at the transition plateau, Fe1 and Fe2 can be assigned to the 91 and 192 K transitions, respectively. [FeII16][ClO4]2 [space group P3̄, a = 17.5829(3) Å, c = 7.8043(2) Å, β = 109.820 (3)°, T = 295 K] also possesses Fe1:Fe2 in a 1:2 ratio, and magnetic measurements show a single spin transition at 213 K, indicating that both Fe1 and Fe2 undergo a simultaneous spin transition. [FeII16][ClO4]2 slowly decomposes in solutions containing acetic anhydride to form [FeIII3O(OAc)613][ClO4] [space group I2, a = 10.1547(7) Å, b = 16.5497(11) Å, c = 10.3205(9) Å, β = 109.820 (3)°, T = 200 K]. The isosceles Fe3 unit contains two Fe···Fe distances of 3.2844(1) Å and a third Fe···Fe distance of 3.2857(1) Å. The magnetic data can be fit to a trinuclear model with ℋ = −2J(S1·S2 + S2·S3) − 2J13(S1·S3), where J = −27.1 and J13 = −32.5 cm-1.

Insights into the influence of solvent polarity on the crystallization of poly(ethylene oxide) spin-coated thin films via in situ grazing incidence wide-angle X-ray scattering

Controlling polymer thin-film morphology and crystallinity is crucial for a wide range of applications, particularly in thin-film organic electronic devices. In this work, the crystallization behavior of a model polymer, poly(ethylene oxide) (PEO), during spin-coating is studied. PEO films were spun-cast from solvents possessing different polarities (chloroform, THF, and methanol) and probed via in situ grazing incidence wide-angle X-ray scattering. The crystallization behavior was found to follow the solvent polarity order (where chloroform < THF < methanol) rather than the solubility order (where THF > chloroform > methanol). When spun-cast from nonpolar chloroform, crystallization largely followed Avrami kinetics, resulting in the formation of morphologies comprising large spherulites. PEO solutions cast from more polar solvents (THF and methanol) do not form well-defined highly crystalline morphologies and are largely amorphous with the presence of small crystalline regions. The difference in morphological development of PEO spun-cast from polar solvents is attributed to clustering phenomena that inhibit polymer crystallization. This work highlights the importance of considering individual components of polymer solubility, rather than simple total solubility, when designing processing routes for the generation of morphologies with optimum crystallinities or morphologies.

Refinement methods for software architecture design using the software architecture model

Modern software systems are often large and complicated. To better understand, develop, and manage large software systems, researchers have studied software architectures that provide the top level overall structural design of software systems for the last decade. One major research focus on software architectures is formal architecture description languages, but most existing research focuses primarily on the descriptive capability and puts less emphasis on software architecture design methods and formal analysis techniques, which are necessary to develop correct software architecture design. ^ Refinement is a general approach of adding details to a software design. A formal refinement method can further ensure certain design properties. This dissertation proposes refinement methods, including a set of formal refinement patterns and complementary verification techniques, for software architecture design using Software Architecture Model (SAM), which was developed at Florida International University. First, a general guideline for software architecture design in SAM is proposed. Second, specification construction through property-preserving refinement patterns is discussed. The refinement patterns are categorized into connector refinement, component refinement and high-level Petri nets refinement. These three levels of refinement patterns are applicable to overall system interaction, architectural components, and underlying formal language, respectively. Third, verification after modeling as a complementary technique to specification refinement is discussed. Two formal verification tools, the Stanford Temporal Prover (STeP) and the Simple Promela Interpreter (SPIN), are adopted into SAM to develop the initial models. Fourth, formalization and refinement of security issues are studied. A method for security enforcement in SAM is proposed. The Role-Based Access Control model is formalized using predicate transition nets and Z notation. The patterns of enforcing access control and auditing are proposed. Finally, modeling and refining a life insurance system is used to demonstrate how to apply the refinement patterns for software architecture design using SAM and how to integrate the access control model. ^ The results of this dissertation demonstrate that a refinement method is an effective way to develop a high assurance system. The method developed in this dissertation extends existing work on modeling software architectures using SAM and makes SAM a more usable and valuable formal tool for software architecture design. ^

Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator

We study the helical edge states of a two-dimensional topological insulator without axial spin symmetry due to the Rashba spin-orbit interaction. Lack of axial spin symmetry can lead to so-called generic helical edge states, which have energy-dependent spin orientation. This opens the possibility of inelastic backscattering and thereby nonquantized transport. Here we find analytically the new dispersion relations and the energy dependent spin orientation of the generic helical edge states in the presence of Rashba spin-orbit coupling within the Bernevig-Hughes-Zhang model, for both a single isolated edge and for a finite width ribbon. In the single-edge case, we analytically quantify the energy dependence of the spin orientation, which turns out to be weak for a realistic HgTe quantum well. Nevertheless, finite size effects combined with Rashba spin-orbit coupling result in two avoided crossings in the energy dispersions, where the spin orientation variation of the edge states is very significantly increased for realistic parameters. Finally, our analytical results are found to compare well to a numerical tight-binding regularization of the model.

Global relativistic folding optical potential and the relativistic Green's function model

Optical potentials provide critical input for calculations on a wide variety of nuclear reactions, in particular, for neutrino-nucleus reactions, which are of great interest in the light of the new neutrino oscillation experiments. We present the global relativistic folding optical potential (GRFOP) fits to elastic proton scattering data from C-12 nucleus at energies between 20 and 1040 MeV. We estimate observables, such as the differential cross section, the analyzing power, and the spin rotation parameter, in elastic proton scattering within the relativistic impulse approximation. The new GRFOP potential is employed within the relativistic Green's function model for inclusive quasielastic electron scattering and for (anti) neutrino-nucleus scattering at MiniBooNE kinematics.

Spin and spatial dynamics in electron-impact scattering off S-wave He using R-matrix with Time-Dependence theory

R-matrix with time-dependence theory is applied to electron-impact ionisation processes for He in the S-wave model. Cross sections for electron-impact excitation, ionisation and ionisation with excitation for impact energies between 25 and 225 eV are in excellent agreement with benchmark cross sections. Ultra-fast dynamics induced by a scattering event is observed through time-dependent signatures associated with autoionisation from doubly excited states. Further insight into dynamics can be obtained through examination of the spin components of the time-dependent wavefunction.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.