No description available.

<p>In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.</p> / Master of Science (MSc)

Within the last decades low-dimensional frustrated quantum spin systems have attracted great interest in the field of modern research. In these systems a competition of various magnetic interactions takes place, leading to an energetically degenerated magnetic ground state, and thus to the occurrence of exotic, unconventional physical properties at low temperatures. This thesis focuses on the quasi one-dimensional frustrated spin chain system linarite, PbCuSO4(OH)2. In this compound the basic building blocks are CuO4 plaquettes which are connected to each other along one crystallographic direction, analogue to a chain. The frustration in linarite is established due to the competition between the magnetic interactions. The nearest-neighbor magnetic spins are coupled ferromagnetically along the chain via a coupling constant J1, while the next-nearest neighbors are coupled antiferromagnetically via a coupling constant J2. For this configuration it is not possible to satisfy all magnetic couplings simultaneously, hence the system is magnetically frustrated. In this work, comprehensive thermodynamic and nuclear magnetic resonance (NMR) studies demonstrate that linarite is one of the richest and most fascinating compounds in the class of low-dimensional frustrated magnets. By means of susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements a rich magnetic phase diagram could be mapped out below a temperature of 2.8 K. The phase diagram contains five different magnetic regions/phases for an external magnetic field pointing along the chain direction. Based on the thermodynamic studies it was possible to calculate the exchange integrals within the frustrated J1-J2 model and extensions of it by using various theoretical approaches. The magnetic microscopic nature of the different long-range magnetic phases present in linarite were investigated by NMR measurements and by collaborative neutron scattering experiments. The ground state (phase I) is identified as an incommensurate elliptical helical structure. Via a theoretical modelling the 1H-NMR spectrum of the ground state could be explained, revealing a rearrangement of the zero-field structure in an external magnetic field of 2.0 T used for the NMR studies. By further increasing the external field the system undergoes a complex spin flop transition in two steps (phase I - phase III - phase IV). In phase III a phase separation takes place where one part of the spins form a circular spiral structure while the remaining fraction form a simple antiferromagnetic structure. In phase IV the remaining circular spiral structure vanishes, so that all spins collectively form the antiferromagnetic collinear phase. The most peculiar physical properties studied in this thesis take place in region V at high fields, showing only tiny features in the thermodynamic properties. The magnetic spins in region V form a sine-wave modulated spin-density structure as identified via NMR and neutron investigations. It is discussed whether region V is related to a multipolar phase or if the spin-density wave structure could possibly coexist with such a phase.

Within the last decades low-dimensional frustrated quantum spin systems have attracted great interest in the field of modern research. In these systems a competition of various magnetic interactions takes place, leading to an energetically degenerated magnetic ground state, and thus to the occurrence of exotic, unconventional physical properties at low temperatures. This thesis focuses on the quasi one-dimensional frustrated spin chain system linarite, PbCuSO4(OH)2. In this compound the basic building blocks are CuO4 plaquettes which are connected to each other along one crystallographic direction, analogue to a chain. The frustration in linarite is established due to the competition between the magnetic interactions. The nearest-neighbor magnetic spins are coupled ferromagnetically along the chain via a coupling constant J1, while the next-nearest neighbors are coupled antiferromagnetically via a coupling constant J2. For this configuration it is not possible to satisfy all magnetic couplings simultaneously, hence the system is magnetically frustrated. In this work, comprehensive thermodynamic and nuclear magnetic resonance (NMR) studies demonstrate that linarite is one of the richest and most fascinating compounds in the class of low-dimensional frustrated magnets. By means of susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements a rich magnetic phase diagram could be mapped out below a temperature of 2.8 K. The phase diagram contains five different magnetic regions/phases for an external magnetic field pointing along the chain direction. Based on the thermodynamic studies it was possible to calculate the exchange integrals within the frustrated J1-J2 model and extensions of it by using various theoretical approaches. The magnetic microscopic nature of the different long-range magnetic phases present in linarite were investigated by NMR measurements and by collaborative neutron scattering experiments. The ground state (phase I) is identified as an incommensurate elliptical helical structure. Via a theoretical modelling the 1H-NMR spectrum of the ground state could be explained, revealing a rearrangement of the zero-field structure in an external magnetic field of 2.0 T used for the NMR studies. By further increasing the external field the system undergoes a complex spin flop transition in two steps (phase I - phase III - phase IV). In phase III a phase separation takes place where one part of the spins form a circular spiral structure while the remaining fraction form a simple antiferromagnetic structure. In phase IV the remaining circular spiral structure vanishes, so that all spins collectively form the antiferromagnetic collinear phase. The most peculiar physical properties studied in this thesis take place in region V at high fields, showing only tiny features in the thermodynamic properties. The magnetic spins in region V form a sine-wave modulated spin-density structure as identified via NMR and neutron investigations. It is discussed whether region V is related to a multipolar phase or if the spin-density wave structure could possibly coexist with such a phase.

The thesis is devoted to the study of in-chain impurities in spin 1/2 antiferromagnetic Heisenberg chains (S=1/2 aHC's)---a model which accompanies the research on magnetism since the early days of quantum theory and which is one of the few integrable spin systems. With respect to impurities it is special insofar as an impurity perturbs the system strongly due to its topology: there is no way around the defect. To what extend the one-dimensional picture stays a good basis for the description of real materials even if the chains are disturbed by in-chain impurities is an interesting question which is addressed in this work. For this purpose, Cu Nuclear Magnetic Resonance (NMR) measurements on the cuprate spin chain compounds SrCuO2 and Sr2CuO3 intentionally doped with nickel (Ni), zinc (Zn) and palladium (Pd) are presented. These materials are well known to be among the best realizations of the S=1/2 aHC model and their large exchange coupling constants allow the investigation of the low-energy dynamics within experimentally easily feasible temperatures. NMR provides the unique ability to study the static and dynamic magnetic properties of the spin chains locally which is important since randomly placed impurities break the translational invariance. Because copper is the magnetically active ion in those materials and the copper nuclear spin is most directly coupled to its electron spin, the NMR measurements have been performed on the copper site. The measurements show in all cases that there are changes in the results of these measurements as compared to the pure compounds which indicate the opening of gaps in the excitation spectra of the spin chains and the emergence of oscillations of the local susceptibility close to the impurities. These experimental observations are compared to theoretical predictions to clarify if and to what extend the already proposed model for these doped systems---the finite spin chain---is suitable to predict the behavior of real materials. Thereby, each impurity shows peculiarities. While Zn and Pd are know to be spin 0 impurities, it is not clear if Ni carries spin 1. To shed some light on this issue is another scope of this work. For Zn impurities, there are indications that they avoid to occupy copper sites, other than in the layered cuprate compounds. Also this matter is considered.

L'étude de l'influence du désordre sur les propriétés critiques des systèmes modèles et des impuretés sur les propriétés magnétiques d'échantillons nanostructurés constitue la ligne directrice de ce travail. L'utilisation des techniques de simulation Monte Carlo en constitue l'outil. Nous nous intéressons à des systèmes de spins en interaction, à 2 ou 3 dimensions, décrits par des modèles présentant des transitions de phase du premier ou du second ordre et nous cherchons à comprendre l'influence de différentes perturbations (apériodiques, désordonnées) sur leurs propriétés critiques. Dans le cas des systèmes tridimensionnels, nous montrons en particulier, grâce à des simulations numériques intensives utilisant les algorithmes d'amas ou multicanoniques, que la détermination des exposants critiques associés à une nouvelle classe d'universalité désordonnée nécessite qu'une attention tout-à-fait particulière soit apportée aux simulations afin de pouvoir distinguer les exposants effectifs des exposants asymptotiques. Nous présentons ensuite la modélisation des propriétés magnétiques d'échantillons nanostructurés (nanoparticules, multicouches amorphes) pour lesquels l'utilisation des techniques de simulation numérique permet de conforter certains modèles théoriques comme les modèles de Néel-Brown et de Stoner-Wohlfarth pour le retournement de l'aimantation ou le modèle d'anisotropie structurale locale pour expliquer l'existence d'une anisotropie magnétique macroscopique dans les multicouches amorphes Fe/Dy. Ainsi, nous avons mis en évidence le fait que le retournement de l'aimantation par rotation uniforme d'une structure ferrimagnétique peut devenir non uniforme pour une structure spérimagnétique avec une augmentation de la coercivité.

Dans cette thèse, j'ai étudié le noyau et le semi-groupe de la chaleur ainsi que les inégalités fonctionnelles associées sur trois espaces modèles de la géométrie sous-elliptique. Cette étude a en fait pour principal objectif de développer et tester de nouvelles techniques et méthodes que l'on espère ensuite pouvoir étendre en géométrie sous-elliptique. Le but avoué est de comprendre en géométrie sous-elliptique une notion de courbure de Ricci minorée par une constante. Ici, les trois espaces modèles sont des groupes de Lie de dimension 3: le groupe de Heisenberg, le groupe SU(2) et le groupe SL(2,R), que l'on munit d'un sous-laplacien: un opérateur différentiel du second ordre invariant à gauche essentiellement auto-adjoint pour la mesure de Haar du groupe qui n'est pas elliptique mais hypoelliptique d'après des résultats de Hörmander. Mes résultats portent tout d'abord sur l'obtention de formules explicites pour les noyaux de la chaleur associés. J'ai ensuite introduit un critère de courbure-dimension de Bakry-Emery généralisé qui, sous certaines conditions d'antisymétrie vérifiées sur nos espaces modèles, permet l'obtention d'estimées du type de Li-Yau. Je me suis enfin intéressé à l'établissement et l'étude d'inégalités de sous-commutation entre le gradient et le semi-groupe de la chaleur. J'ai notamment donné deux nouvelles démonstrations de l'inégalité de H.Q.Li sur le groupe de Heisenberg.

<p>The main result in this thesis is the generalisation of Bergman's diamond lemma for ring theory to power series rings. This generalisation makes it possible to treat problems in which there arise infinite descending chains. Several results in the literature are shown to be special cases of this diamond lemma and examples are given of interesting problems which could not previously be treated. One of these examples provides a general construction of a normed skew field in which a custom commutation relation holds.</p><p>There is also a general result on the structure of totally ordered semigroups, demonstrating that all semigroups with an archimedean element has a (up to a scaling factor) unique order-preserving homomorphism to the real numbers. This helps analyse the concept of filtered structure. It is shown that whereas filtered structures can be used to induce pretty much any zero-dimensional linear topology, a real-valued norm suffices for the definition of those topologies that have a reasonable relation to the multiplication operation.</p><p>The thesis also contains elementary results on degree (as of polynomials) functions, norms on algebras (in particular ultranorms), (Birkhoff) orthogonality in modules, and construction of semigroup partial orders from ditto quasiorders.</p>

<p>This thesis is divided into two parts. In the first part we study thermodynamics of the two-dimensional Heisenberg ferromagnet with dipolar interaction. This interaction breaks the conditions of the Mermin-Wagner theorem, resulting in a finite transition temperature. Our calculations are done within the framework of the self-consistent spin-wave theory (SSWT), which is modified in order to include the dipolar interaction. Both quantum and classical versions of the Heisenberg model are considered.</p><p>The second part of the thesis investigates the chemical bonding in solids from the first principles calculations. A new chemical bonding indicator called balanced crystal orbital overlap population (BCOOP) is developed. BCOOP is less basis set dependent than the earlier indicators and it can be used with full-potential density-functional theory (DFT) codes. We apply BCOOP formalism to the chemical bonding in the high-T_c superconductor MgB2 and the theoretically predicted MAX phase Nb3SiC2. We also study how the chemical bonding results in a repulsive hydrogen–hydrogen interaction in metal hydrides. The role of this interaction in the structural phase transition in Ti3SnHx is investigated.</p>

<p>Theoretical investigations of spectroscopic and magnetic properties of metallic systems in the bulk, as well as in nanostructured materials, have been performed within the density functional theory. The major part of the present work studies the differences between binding energies of electrons tightly bound to the atoms, the so-called core electrons (in contrast with the valence electrons), that is, core-level binding energy shift (CLS). </p><p>By comparison between corresponding elemental core-levels for atoms situated in different chemical environments we obtain fundamental understanding of bonding properties of materials. The method of choice was the complete screening picture, which includes initial and final state effects on the same footing. The usefulness of CLS stems from that it is sensitive to differences in the chemical environment of an atom, which can be affected on one hand by the global composition of e.g. disordered materials, surfaces and interfaces, and on the other hand by the very local environment around an atom. Here CLSs have been obtained for both components in the fcc random alloys AgPd, CuPd, CuNi, CuPt, CuAu, PdAu, NiPd and NiPt. Moreover the model was extended to the Auger kinetic energy shift for the LMM Auger transition in AgPd alloys. Studies were also applied to the near surface and interface regions of PdMn nano structures on Pd(100), thin CuPd and AgPd films on inert Ru(0001), and at interfaces. The disorder broadening on CLS due to local environment effects was calculated in selected alloys.</p><p>A part of the thesis concern investigations related to the magnetic ordering in Invar alloys, including the influence of local environment effects. A study was made for the dependence of effective exchange parameter on the electron concentration, volume and local chemical composition.</p>