The physics of iron pnictides has been the subject of intense research for half a decade since the discovery of superconductivity in doped LaFeAsO in 2008. By now there exists a large number of different materials that are summarized under the term "pnictides'' with significant differences in their crystal structure, electronic properties, and their phase diagrams. This thesis is concerned with the investigation of the various phase transitions that are observed in the underdoped compounds of the pnictide subgroups RFeAsO, where R is a rare-earth element, and AFe_2As_2, where A is an alkaline-earth element. These compounds display two closely bound transitions from a tetragonal to an orthorhombic phase and from a paramagnetic to an antiferromagnetic metal. Both symmetry-broken phases are suppressed by doping or pressure and close to their disappearance superconductivity sets in. The superconducting state is stabilized until some optimal doping or pressure is reached and gets suppressed thereafter. The central goal of this thesis is to improve our understanding of the interplay between these three phases and to describe the various phase transitions. We start from an itinerant picture that explains the magnetism as a result of an excitonic instability and show how the other phases can be included into this picture. This approach is based on the the observation that the compounds we are interested in have a Fermi surface with multiple nested electron and hole pockets and that they have small to intermediate interaction strengths. The thesis starts with a study of the doping dependence of the antiferromagnetic phase transition in four different five-orbital models. We use the random-phase approximation to determine the transition temperature, the dominant ordering vector, and the contribution of the different orbitals to the ordering. This allows us to identify the more realistic models, which give results that are in good agreement with experimental observations. In addition to the frequently made assumption of orbital-independent interaction potentials we study the effect of a reduction of the interaction strengths that involve the d_{xy} orbital. We find that this tunes the system between two different nesting instabilities. A reduction of the interactions that involve the d_{xy} orbital also enhances the tendency towards incommensurate (IC) order. For a weak reduction this tendency is compensated by the presence of the orthorhombic phase. However, for a reduction of 30%, as it is suggested by constrained random-phase-approximation calculations, we always find large doping ranges, where a state with IC order has the highest transition temperature. We continue the investigation of the magnetic phase transition by studying the competition of different possible types of antiferromagnetic order that arises from the presence of two degenerate nesting instabilities with the ordering vectors (pi,0) and (0,pi). We derive a Ginzburg-Landau free energy from a microscopic two-band model and find that the presence of the experimentally observed stripe phase strongly depends on the number and size of the hole pockets in the system and on the doping. We show that within the picture of a purely magnetically driven nematic phase transition, which breaks the C_4 symmetry and induces the orthorhombic distortion, the nematic phase displays exactly the same dependence on the model parameters as the magnetic stripe phase. We propose that in addition to the purely magnetically driven nematic instability there is a ferro-orbital instability in the system that stabilizes the nematic transition and, thus, explains the experimentally observed robustness of the orthorhombic transition. We argue that including a ferro-orbital instability into the picture may also be necessary to reproduce the transition from simultaneous first-order transitions into an orthorhombic antiferromagnetic state to two separate second-order transitions, which is observed as a function of doping. Finally, a study of the superconducting phase transition inside the antiferromagnetic phase that is observed in some pnictide compounds is presented. We present an approach to calculate the fluctuation-mediated pairing interaction in the spin-density-wave phase of a multiband system, which is based on the random-phase approximation. This approach is applied to a minimal two-band model for the pnictides to study the effect of the various symmetry-allowed bare on-site interactions on the gap symmetry and structure. We find a competition between various even- and odd-parity states and over a limited parameter range a p_x-wave state is the dominant instability. The largest part of the parameter space is dominated by even parity states but the gap structure sensitively depends on the bare interactions. We propose that the experimentally observed transition from a nodeless to a nodal gap can be due to changes in the on-site interaction potentials.

Im Rahmen dieser Arbeit wurden die Kondo-Gitter YbT2Si2 (T = Rh, Ir, Co) und CeTPO (T = Ru, Os, Fe, Co) untersucht. In diesen Systemen treten starke ferromagnetische Korrelationen der 4f-Momente zusammen mit ausgeprägter Kondo-Wechselwirkung auf, deren theoretische Beschreibung bislang sehr kontrovers diskutiert wird. Diese Arbeit liefert damit einen essentiellen experimentellen Beitrag zur Physik von ferromagnetischen Kondo-Gittern. So konnten qualitativ hochwertige Einkristalle von YbRh2Si2 hergestellt und erstmalig an einem Schwere-Fermion-System deren kritische Fluktuationen um den magnetischen Phasenübergang analysiert werden. Weiterhin konnte das bis dahin unverstandene Auftreten einer Elektron-Spin-Resonanz (ESR)-Linie in YbT2Si2 auf ferromagnetische Korrelationen zurückgeführt werden. Außerdem wurde mit CeFePO ein neues Schwere-Fermion-System mit starken ferromagnetischen Korrelationen entdeckt sowie mit dem isoelektronischen CeRuPO der seltene Fall eines ferromagnetisch geordneten Kondo-Gitters realisiert. / Within the context of this thesis the Kondo lattices YbT2Si2 (T = Rh, Ir, Co) and CeTPO (T = Ru, Os, Fe, Co) were investigated. In these systems strong ferromagnetic correlations of the 4f-moments together with pronounced Kondo interactions are present, whose theoretical description are pres-ently controversial discussed. Therefore, this work gives an essential experimental contribution to the physics of ferromagnetic Kondo lattices. The main results include the growth of high-quality single crystals of YbRh2Si2 and the first analysis of the critical fluctuations around the magnetic phase transition in a heavy fermion system. Furthermore, the unexpected observation of an electron spin resonance in YbT2Si2 could be ascribed to ferromagnetic correlations. Moreover, a new heavy fermion system CeFePO with strong ferromagnetic correlations was found and with the isoelec-tronic CeRuPO the rare case of a ferromagnetic Kondo-lattice discovered.

This thesis presents a comprehensive study of the magnetic properties and of quantum phase transitions (QPTs) of two different systems which have been investigated by means of low-temperature magnetization measurements. The systems are the heavy-fermion Yb(Rh1-xCox)2Si2 (metallic) and the quantum magnet NiCl2-4SC(NH2)2 (insulator). Although they are very different materials, they share two common properties: magnetism and QPTs. Magnetism originates in Yb(Rh1-xCox)2Si2 from the trivalent state of the Yb3+ ions with effective spin S = 1=2. In NiCl2-4SC(NH2)2, the magnetic Ni2+ ions have spin S = 1. These magnetic ions are located on a body-centered tetragonal lattice in both systems and, in this study, the QPTs are induced by an external magnetic field. In Yb(Rh1-xCox)2Si2 the evolution of magnetism from itinerant in slightly Co-doped YbRh2Si2 to local in YbCo2Si2 is examined analyzing the magnetic moment versus chemical pressure x phase diagram in high-quality single crystals, which indicates a continuous change of dominating energy scale from the Kondo to the RKKY one. The physics of the antiferromagnet YbCo2Si2 can be completely understood. On the other hand, the physics of pure and slightly Co-containing YbRh2Si2 is much more complex, due to the itinerant character of magnetism and the vicinity of the system to an unconventional quantum critical point (QCP). The field-induced AFM QCP in Yb(Rh0.93Co0.07)2Si2 and in pure YbRh2Si2 under a pressure of 1.5GPa is characterized by means of the magnetic Grüneisen ratio. The final part of this thesis describes quantum criticality near the field-induced QCP in NiCl2-4SC(NH2)2 . These results will be compared to the theory of QPTs in Ising and XY antiferromagnets. Since the XY -AFM ordering can be described as BEC of magnons by mapping the spin-1 system into a gas of hardcore bosons, the temperature dependence of the magnetization for a BEC is analytically derived and compared to the results just below the critical field. The remarkable agreement between the BEC theory and experiments in this quantum magnet is one of the most prominent examples of the concept of universality.:1 Introduction 1 2 Theoretical concepts 5 2.1 Ce- and Yb-based 4f-electron systems . . . . . . . . . . . . . . . . 5 2.1.1 Crystalline electric field . . . . . . . . . . . . . . . . . . . . 6 2.2 Heavy-fermion systems . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Fermi liquid theory . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Kondo eff ect . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 RKKY interaction . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.4 Doniach phase diagram . . . . . . . . . . . . . . . . . . . . . 12 2.3 Quantum phase transitions . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Spin density wave scenario . . . . . . . . . . . . . . . . . . . 16 2.3.2 Local quantum critical point scenario . . . . . . . . . . . . . 17 2.3.3 Global phase diagram . . . . . . . . . . . . . . . . . . . . . 18 2.3.4 The Grüneisen ratio . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Spins are almost bosons . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Experimental methods 31 3.1 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1 Magnetization measurements . . . . . . . . . . . . . . . . . 32 3.2 Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 Faraday magnetometer . . . . . . . . . . . . . . . . . . . . . 35 3.2.1.1 Measurement of the force . . . . . . . . . . . . . . 35 3.2.1.2 Capacitive cell . . . . . . . . . . . . . . . . . . . . 35 3.2.1.3 Design and performance of the cell . . . . . . . . . 37 3.2.1.4 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1.5 Background contributions . . . . . . . . . . . . . . 42 3.2.1.6 Calibration . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1.7 Magnets characteristics . . . . . . . . . . . . . . . 44 3.2.1.8 Installation in a dilution refrigerator . . . . . . . . 45 3.2.2 SQUID magnetometer . . . . . . . . . . . . . . . . . . . . . 47 3.3 Magnetization measurements at high pressure . . . . . . . . . . . . 48 3.3.1 Experimental setup for M(H - T) under pressure . . . . . . . 50 4 Yb(Rh1-xCox)2Si2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 4.1 Introduction and motivation . . . . . . . . . . . . . . . . . . . . . . 51 4.1.1 The heavy-fermion compound YbRh2Si2 . . . . . . . . . . . 53 4.1.2 The antiferromagnet YbCo2Si2 . . . . . . . . . . . . . . . . 58 4.1.3 Isoelectronic substitution of Co for Rh: Yb(Rh1-xCox)2Si2 . . . .62 4.2 Itinerant vs. local magnetism in Yb(Rh1-xCox)2Si2 . . . . . . . . . 67 4.2.1 Magnetization of Yb(Rh1-xCox)2Si2 with 0 x 0.27 . . . 67 4.2.1.1 YbRh2Si2 and Yb(Rh0.93Co0.07)2Si2 . . . . . . . . . 67 4.2.1.2 Yb(Rh0.88Co0.12)2Si2 . . . . . . . . . . . . . . . . . 71 4.2.1.3 Yb(Rh0.82Co0.18)2Si2 . . . . . . . . . . . . . . . . . 73 4.2.1.4 Yb(Rh0.73Co0.27)2Si2 . . . . . . . . . . . . . . . . . 74 4.2.1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.2 Magnetization of Yb(Rh1-xCox)2Si2 with x = 0.58 and x = 1 . . . . . 79 4.2.3 Evolution from itinerant to local magnetism . . . . . . . . . 83 4.3 Field-induced QCP in Yb(Rh0.93Co0.07)2Si2 . . . . . . . . . . . . . . 88 4.4 YbRh2Si2 under hydrostatic pressure . . . . . . . . . . . . . . . . . 96 4.4.1 Magnetization vs. field . . . . . . . . . . . . . . . . . . . . . 97 4.4.2 Comparison with 1.28 GPa . . . . . . . . . . . . . . . . . . . 99 4.4.3 Magnetization vs. temperature . . . . . . . . . . . . . . . . 101 4.4.4 Field-induced QCP at 1.5 GPa . . . . . . . . . . . . . . . . 103 4.4.5 The magnetic Grüneisen ratio . . . . . . . . . . . . . . . . . 105 4.5 The magnetic phase diagrams of YbCo2Si2 . . . . . . . . . . . . . . 107 4.5.1 Magnetization vs. temperature . . . . . . . . . . . . . . . . 107 4.5.2 Magnetization vs. fi eld . . . . . . . . . . . . . . . . . . . . . 109 4.5.3 H - T phase diagrams . . . . . . . . . . . . . . . . . . . . 114 4.5.4 Ac-susceptibility . . . . . . . . . . . . . . . . . . . . . . . . 117 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5 NiCl2-4SC(NH2)2 . . . . . . . . . . . . . . . . . . . . . . . .121 5.1 Introduction and motivation . . . . . . . . . . . . . . . . . . . . . . 121 5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.1 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.2.2 Comparison between theory and experiment . . . . . . . . . 126 5.2.3 Magnetic phase diagram . . . . . . . . . . . . . . . . . . . . 129 5.2.4 Speci c heat . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.2.5 The magnetic Grüneisen ratio . . . . . . . . . . . . . . . . . 131 5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6 General conclusions . . . . . . . . . . . . . . . . . . . . . . . .135 Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . .139

La technique des répliques est une technique formidable prenant ses origines de la physique statistique, comme un moyen de calculer l'espérance du logarithme de la constante de normalisation d'une distribution de probabilité à haute dimension. Dans le jargon de physique, cette quantité est connue sous le nom de l’énergie libre, et toutes sortes de quantités utiles, telle que l’entropie, peuvent être obtenue de là par des dérivées. Cependant, ceci est un problème NP-difficile, qu’une bonne partie de statistique computationelle essaye de résoudre, et qui apparaît partout; de la théorie des codes, à la statistique en hautes dimensions, en passant par les problèmes de satisfaction de contraintes. Dans chaque cas, la méthode des répliques, et son extension par (Parisi et al., 1987), se sont prouvées fortes utiles pour illuminer quelques aspects concernant la corrélation des variables de la distribution de Gibbs et la nature fortement nonconvexe de son logarithme negatif. Algorithmiquement, il existe deux principales méthodologies adressant la difficulté de calcul que pose la constante de normalisation: a). Le point de vue statique: dans cette approche, on reformule le problème en tant que graphe dont les nœuds correspondent aux variables individuelles de la distribution de Gibbs, et dont les arêtes reflètent les dépendances entre celles-ci. Quand le graphe en question est localement un arbre, les procédures de message-passing sont garanties d’approximer arbitrairement bien les probabilités marginales de la distribution de Gibbs et de manière équivalente d'approximer la constante de normalisation. Les prédictions de la physique concernant la disparition des corrélations à longues portées se traduise donc, par le fait que le graphe soit localement un arbre, ainsi permettant l’utilisation des algorithmes locaux de passage de messages. Ceci va être le sujet du chapitre 4. b). Le point de vue dynamique: dans une direction orthogonale, on peut contourner le problème que pose le calcul de la constante de normalisation, en définissant une chaîne de Markov le long de laquelle, l’échantillonnage converge à celui selon la distribution de Gibbs, tel qu’après un certain nombre d’itérations (sous le nom de temps de relaxation), les échantillons sont garanties d’être approximativement générés selon elle. Afin de discuter des conditions dans lesquelles chacune de ces approches échoue, il est très utile d’être familier avec la méthode de replica symmetry breaking de Parisi. Cependant, les calculs nécessaires sont assez compliqués, et requièrent des notions qui sont typiquemment étrangères à ceux sans un entrainement en physique statistique. Ce mémoire a principalement deux objectifs : i) de fournir une introduction a la théorie des répliques, ses prédictions, et ses conséquences algorithmiques pour les problèmes de satisfaction de constraintes, et ii) de donner un survol des méthodes les plus récentes adressant la transition de phase, prédite par la méthode des répliques, dans le cas du problème k−SAT, à partir du point de vu statique et dynamique, et finir en proposant un nouvel algorithme qui prend en considération la transition de phase en question. / The replica trick is a powerful analytic technique originating from statistical physics as an attempt to compute the expectation of the logarithm of the normalization constant of a high dimensional probability distribution known as the Gibbs measure. In physics jargon this quantity is known as the free energy, and all kinds of useful quantities, such as the entropy, can be obtained from it using simple derivatives. The computation of this normalization constant is however an NP-hard problem that a large part of computational statistics attempts to deal with, and which shows up everywhere from coding theory, to high dimensional statistics, compressed sensing, protein folding analysis and constraint satisfaction problems. In each of these cases, the replica trick, and its extension by (Parisi et al., 1987), have proven incredibly successful at shedding light on keys aspects relating to the correlation structure of the Gibbs measure and the highly non-convex nature of − log(the Gibbs measure()). Algorithmic speaking, there exists two main methodologies addressing the intractability of the normalization constant: a) Statics: in this approach, one casts the system as a graphical model whose vertices represent individual variables, and whose edges reflect the dependencies between them. When the underlying graph is locally tree-like, local messagepassing procedures are guaranteed to yield near-exact marginal probabilities or equivalently compute Z. The physics predictions of vanishing long range correlation in the Gibbs measure, then translate into the associated graph being locally tree-like, hence permitting the use message passing procedures. This will be the focus of chapter 4. b) Dynamics: in an orthogonal direction, we can altogether bypass the issue of computing the normalization constant, by defining a Markov chain along which sampling converges to the Gibbs measure, such that after a number of iterations known as the relaxation-time, samples are guaranteed to be approximately sampled according to the Gibbs measure. To get into the conditions in which each of the two approaches is likely to fail (strong long range correlation, high energy barriers, etc..), it is very helpful to be familiar with the so-called replica symmetry breaking picture of Parisi. The computations involved are however quite involved, and come with a number of prescriptions and prerequisite notions (s.a. large deviation principles, saddle-point approximations) that are typically foreign to those without a statistical physics background. The purpose of this thesis is then twofold: i) to provide a self-contained introduction to replica theory, its predictions, and its algorithmic implications for constraint satisfaction problems, and ii) to give an account of state of the art methods in addressing the predicted phase transitions in the case of k−SAT, from both the statics and dynamics points of view, and propose a new algorithm takes takes these into consideration.

Les signatures de l’existence des phonons sont omniprésentes dans les propriétés des matériaux. En première approximation, on peut scinder l'effet des phonons sur la structure électronique en deux contributions. D’une part, l'interaction électron-phonon capture la réponse électronique aux vibrations des noyaux du cristal, et d’autre, l'énergie libre de la population de phonons modifie le volume cristallin à l’équilibre. En plus d'être responsables de la dépendance en température de la structure électronique, ces deux mécanismes affectent les niveaux d'énergie à température nulle, à travers le mouvement du point zéro et l'énergie du point zéro. Cette thèse analyse l’apport de ces deux mécanismes à la renormalisation du point zéro (ZPR) de l'énergie de la bande interdite des semi-conducteurs. Une généralisation du modèle de Fröhlich prenant en compte l'anisotropie et les dégénérescences présentes dans les matériaux réels révèle que l'interaction non adiabatique entre les électrons et les noyaux domine le ZPR dans les matériaux polaires. La prise en compte de ce mécanisme dans l'évaluation de l'interaction électron-phonon est déterminante pour reproduire adéquatement les données expérimentales. L'approche développée par Grüneisen, qui néglige communément les effets du point zéro, reproduit la dilatation du point zéro du réseau (ZPLE) et sa contribution au ZPR obtenues avec la méthode standard basée sur la minimisation de l'énergie libre à moindre coût numérique, y compris pour les matériaux anisotropes. La contribution du ZPLE au ZPR total, qui a reçu peu d'attention dans la littérature, peut atteindre de 20% à plus de 80% de la contribution de l'interaction électron-phonon, y compris dans des matériaux constitués de noyaux légers. Elle domine même le ZPR du GaAs dans le contexte de la DFT semi-locale. Il est donc essentiel de traiter les deux contributions sur le même pied d'égalité pour modéliser le ZPR avec précision. L'inclusion du couplage spin-orbite (SOC) diminue le ZPR d'un ensemble substantiel de matériaux cubiques de structure zinc-blende, diamant et rock-salt. L'essentiel de cette variation tire son origine de l'effet du SOC sur les énergies électroniques statiques, qui provient en grande partie de la variation des masses effectives des bandes de valence au point \(\Gamma\). La réduction du ZPR peut être estimée à partir d'un modèle de Fröhlich généralisé auquel on a introduit le SOC. Les subtilités numériques liées au traitement de la séparation de Dresselhaus dans les matériaux non centrosymétriques sont discutées. On démontre enfin comment l'effet combiné de l'interaction électron-phonon et de la dilatation thermique affecte le diagramme de phase topologique du BiTeI. L'augmentation de la température repousse l'apparition de la phase d'isolant topologique \(\mathbb{Z}_2\) vers des pressions plus élevées et élargit la plage de pressions correspondant à la phase intermédiaire de type semi-métal de Weyl. Le caractère orbital dominant des extrema de bande influence significativement leur sensibilité à la pression et au changement de topologie. Pour guider la recherche expérimentale de phases topologiquement non triviales dans les matériaux de façon adéquate, les études numériques doivent donc considérer l'effet de la température. / Phonon signatures are ubiquitous in material properties. At first order, the effect of phonons on the electronic structure can be split into two contributions. On the one hand, the electron-phonon interaction captures the electronic response to the vibrations of the nuclei. On the other hand, the free energy of the phonon population modifies the crystalline volume at equilibrium. In addition to driving the temperature dependence of the electronic structure, these two mechanisms affect the energy levels at zero temperature through zero-point motion and zero-point energy. This thesis investigates the contribution of these two mechanisms to the zero point renormalization (ZPR) of the band gap energy of semiconductors. A generalized Fröhlich model taking into account the anisotropy and degeneracies occurring in real materials reveals that the non-adiabatic interaction between electrons and nuclei dominates the ZPR in polar materials. Taking this mechanism into account when evaluating the electron-phonon interaction is crucial to reproduce experimental data adequately. The Grüneisen formalism, which commonly neglects zero-point effects, reproduces the zero-point lattice expansion (ZPLE) and its contribution to the ZPR obtained from the standard method based on free energy minimization at lower numerical cost, including for anisotropic materials. The ZPLE contribution to the total ZPR, which has received little attention in the literature, can reach from 20% to more than 80% of the contribution of the electron-phonon interaction, including in materials containing light atoms. It even dominates the ZPR of GaAs within semilocal DFT. Therefore, both contributions should be treated on an equal footing to model the ZPR accurately. The inclusion of spin-orbit coupling (SOC) decreases the ZPR of a substantial set of cubic materials of zincblende, diamond and rocksalt structure. This variation originates mostly from the effect of SOC on the static electronic eigenvalues, which comes largely from the variation of the effective masses of the valence bands at the \(\Gamma\) point. The reduction of the ZPR can be estimated from a generalized Fröhlich model in which SOC has been introduced. Numerical subtleties related to the treatment of Dresselhaus separation in non-centrosymmetric materials are discussed. We finally show how the combination of electron-phonon interaction and thermal expansion affects the topological phase diagram of BiTeI. An increase in temperature pushes the \(\mathbb{Z}_2\) topological insulator phase towards higher pressures and widens the pressure range corresponding to the Weyl semi-metal intermediate phase. The leading orbital character of the band extrema significantly influences their sensitivity to variations in pressure and topology. To adequately guide the experimental search for topologically non-trivial phases in materials, numerical studies must therefore consider the effect of temperature.

[pt] Este trabalho tem como objetivo estudar a expansão térmica extrínseca e intrínseca do Al2-xInxW3O12, suas transições de fase e higroscopicidade para as fases: x = 0,2; 0,4; 0,7 e 1. Os pós foram obtidos pelo método de co-precipitação. Esta técnica permite a produção de materiais cerâmicos avançados por meio de reações químicas suaves em temperaturas relativamente baixas usando em solução aquosa. A família Al2-xInxW3O12 faz parte do que se pode classificar como cerâmicas termomióticas (do grego thermo para calor e mio para contração) e pertence à família A2M3O12 (A = cátion trivalente, M = cátion hexavalente), com expansão térmica negativa ou quase zero. Este fato torna esta cerâmica uma candidata potencial em aplicações que requerem materiais com alta resistência ao choque térmico. Na literatura, encontramos poucos estudos sistemáticos que relatam parâmetros de interesse no sistema Al2-xInxW3O12, como os coeficientes de expansão térmica (CET) e suas transições de fase. Portanto, o presente trabalho tem como objetivo determinar os coeficientes de expansão intrínsecos (determinados por difração de raios X que é relativa às variações nos parâmetros de rede do material) e o coeficiente de expansão extrínseco (obtido por dilatometria que leva em consideração a variação intrínseca e também extrínseca, dimensões do material, estas últimas relacionadas a defeitos microestruturais) do sistema Al2-xInxW3O12, temperaturas de transição de fase (monoclínica e ortorrômbica) na faixa de x = 0,2 a x = 1. Além disso, este estudo pretende relatar a higroscopicidade deste sistema (usando termogravimetria). Os resultados mostraram que o Al2-xInxW3O12 adotou uma estrutura ortorrômbica em temperatura ambiente para as composições x = 0,2; 0,4; 0,7 e uma estrutura monoclínica para a composição x = 1. Na fase x = 1, uma transição de fase monoclínica para ortorrômbica ocorreu perto de 200 oC. Finalmente, o sistema Al2-xInxW3O12 apresentou baixa higroscopicidade nas quatro fases estudadas. / [en] The Al2-xInxW3O12 family is part of thermomiotic ceramics (from the Greek thermo for heat and mio for contraction) and belongs to the A2M3O12 family (A = trivalent cation, M = hexavalent cation), wich can show negative or near zero thermal expansion. This fact makes this ceramic a potential candidate in applications that require materials with high resistance to thermal shock. In the literature, we found few systematic studies that report parameters of interest in Al2-xInxW3O12 system such as the coefficients of thermal expansion (CTE) and its phase transitions. Therefore, the present work aims to determine the intrinsic coefficients of expansion (determined by X-ray diffraction that is relative to variations in the material s lattice parameters) and the extrinsic coefficient of expansion (obtained by dilatometry which takes into account intrinsic and also extrinsic variations in dimension, these later related to microstructural defects) of Al2-xInxW3O12, phase transition temperatures (monoclinic to orthorhombic) in the range between x = 0.2 to x = 1. In addition, this study intends to report hygroscopicity of this system (using thermogravimetry). The results showed that Al2-xInxW3O12 adopted an orthorhombic structure at room temperature (RT) for x = 0.2; 0.4; 0.7 compositions and monoclinic structure for x = 1 composition. In x = 1 phase, a monoclinic to orthorhombic phase transition occurred close to 200 oC. Finally, the Al2-xInxW3O12 system presented low hygroscopicity in all four studied phases.

Dans cette thèse, nous avons répondu à certaines questions ouverts dans le domaine de la dynamique hors équilibre des systèmes quantiques unidimensionnels fermés. Durant ces dernières années, les avancées dans les techniques expérimentales ont revitalisé la recherche théorique en physique de la matière condensée et dans l'optique quantique. Nous avons traité trois sujets différents et en utilisant des techniques à la fois numériques et analytiques. Dans le cadre des techniques numériques, nous avons utilisé des méthodes de diagonalisation exacte, l'algorithme du groupe de renormalisation de la matrice densité en fonction du temps (t-DMRG) et l'algorithme de Lanczos. Au début, nous avons étudié la dynamique quantique adiabatique d'un système quantique près d'un point critique. Nous avons démontré que la présence d'un potentiel de confinement modifie fortement les propriétés d'échelle de la dynamique des observables en proximité du point critique quantique. La densité d'excitations moyenne et l'excès d'énergie, après le croisement du point critique, suivent une loi algébrique en fonction de la vitesse de la trempe avec un exposant qui dépend des propriétés spatio-temporelles du potentiel. Ensuite, nous avons étudié le comportement de bosons ultra-froids dans un réseau optique incliné. En commençant par l'hamiltonien de Bose-Hubbard, dans la limite de Hard-Core bosons, nous avons développé une théorie hydrodynamique qui reproduit exactement l'évolution temporelle d'une partie des observables du système. En particulier, nous avons observé qu'une partie de bosons reste piégée, et oscille avec une fréquence qui dépend de la pente du potentiel, au contraire, une autre partie est expulsée hors de la rampe. Nous avons également analysé la dynamique du modèle de Bose-Hubbard en utilisant l'algorithme t-DMRG et l'algorithme de Lanczos. De cette façon, nous avons mis en évidence le rôle de la non-intégrabilité du modèle dans son comportement dynamique. Enfin, nous avons abordé le problème de la thermalisation dans un système quantique étendu. À partir de considérations générales, nous avons introduit la notion de profil de température hors équilibre dans une chaîne des bosons à coeur dure. Nous avons analysé la dynamique du profil de temperature et, notamment, ses propriétés d'échelle / In this thesis we have addressed some open questions on the out-of-equilibrium dynamics of closed one-dimensional quantum systems. In recent years, advances in experimental techniques have revitalized the theoretical research in condensed matter physics and quantum optics. We have treated three different subjects using both numerical and analytical techniques. As far as the numerical techniques are concerned, we have used essentially exact diagonalization methods, the adaptive time-dependent density-matrix renormalization-group algorithm (t-DMRG) and the Lanczos algorithm. At first, we studied the adiabatic quantum dynamics of a quantum system close to a critical point. We have demonstrated that the presence of a confining potential strongly affects the scaling properties of the dynamical observables near the quantum critical point. The mean excitation density and the energy excess, after the crossing of the critical point, follow an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. After that, we have studied the behavior of ultra-cold bosons in a tilted optical lattice. Starting with the Bose-Hubbard Hamiltonian, in the limit of Hard-Core bosons, we have developed a hydrodynamic theory that exactly reproduces the temporal evolution of some of the observables of the system. In particular, it was observed that part of the boson density remains trapped, and oscillates with a frequency that depends on the slope of the potential, whereas the remaining packet part is expelled out of the ramp. We have also analyzed the dynamics of the Bose-Hubbard model using the tDMRG algorithm and the Lanczos algorithm. In this way we have highlighted the role of the non-integrability of the model on its dynamical behavior. Finally, we have addressed the issue of thermalization in an extended quantum system. Starting from quite general considerations, we have introduced the notion of out-of-equilibrium temperature profile in a chain of Hard-Core bosons. We have analyzed the dynamics of the temperature profile and especially its scaling properties

Rare-earth nickel borocarbids RNi2B2C are particularly suitable for investigations on one of the most interesting problems in modern solid-state physics: these compounds display competition and coexistence of superconductivity and magnetism. Depending on the R3+ ion, the transition temperatures are in an experimentally easy accessible range of 1 K to 25 K. This thesis presents experimental studies on the interplay of both ordering phenomena. Neutron diffraction is used to determine the magnetic order and the resulting changes of the crystal structure. Experiments are performed on polycrystalline and single crystal samples in dependence on temperature and external magnetic fields. The Ni-B stoichiometry of the tetragonal RNi2B2C compounds is systematically varied and the magnetic R3+ ions are partially substituted by other magnetic or nonmagnetic R?3+ ions. The experimental results are compared with macroscopic magnetic and electrical properties. For HoNi2B2C three different magnetic structures are found in a narrow temperature range. While for two magnetic structures the Ho3+ moments are modulated along the c axis, a third magnetic structure with a modulation in a direction is observed. Both, partial substitution of Ho3+ ions and variation of the Ni-B stoichiometry, strongly modify the formation of these different types of magnetic order. The comparison with the concomitant changes of the superconducting properties yields the following scenario for HoNi2B2C-based compounds: superconductivity coexists with both magnetic structures with modulations in c direction. However, the onset of magnetic order weakens the superconductivity. For the magnetic structure with modulation along the a axis, components of the magnetic moments arise in c direction. The resulting local magnetic fields on Ni sites yield a strong suppression of the superconductivity. The observed competition between superconductivity and the magnetic structure with modulation along the a axis strongly suggests that the modification of the electronic structure due to the superconducting state influences the magnetic ordering. As a further impact of the magnetism in RNi2B2C compounds with R = Ho, Dy, Tb and Er changes of the crystal structure are investigated. Using high-resolution neutron diffraction, tetragonal-to-orthorhombic lattice distortions are found. They are induced by those magnetic structures with either parallel or anti-parallel alignement of R3+ magnetic moments. The direction of the lattice distortions, the dependence of their size on the square of the effective ordered magnetic moment and on the type of the R3+ ions indicate that the magneto-elastic interactions are determined by crystal-field effects. This fact also facilitates the elucidation of the magnetic phase diagrams by neutron diffraction experiments in external magnetic fields. For a given phase, absence or presence of magneto-elastic lattice distortions restrict the set of possible magnetic structures. For HoNi2B2C the magnetic phases reported in literature are confirmed. The experimental results for DyNi2B2C are interpreted using a simple model to determine the magnetic structures. Based on mean field calculations, the differences in the magnetic structures for increasing and decreasing magnetic fields can be understood as very strong hysteresis effects in connection with first-order phase transitions. / Seltenerd-Nickel-Borkarbid-Verbindungen RNi2B2C sind bestens zur Untersuchung eines der interessantesten Probleme der modernen Festkörperphysik geeignet: Diese Substanzen weisen Konkurrenz und Koexistenz von Supraleitung und Magnetismus auf, wobei die vom R3+-Ion abhängigen Übergangstemperaturen in einem experimentell gut zugänglichen Bereich von 1 K bis 25 K liegen. Die vorliegende Dissertation stellt experimentelle Arbeiten zum Wechselspiel der beiden Ordnungsphänomene vor. Für poly- und einkristalline Proben werden die magnetischen Ordnungen und resultierende Veränderungen der Kristallstruktur mittels Neutronendiffraktion in Abhängigkeit von der Temperatur und vom äußeren Magnetfeld bestimmt und mit den makroskopischen magnetischen und elektrischen Eigenschaften verglichen. Hierbei werden die tetragonalen RNi2B2C-Verbindungen gezielt in ihrer Ni-B-Stöchiometrie variiert sowie die magnetischen R3+-Ionen partiell durch andere magnetische als auch unmagnetische R?3+-Ionen substituiert. Für HoNi2B2C werden in einem engen Temperaturbereich drei verschiedene magnetische Strukturen nachgewiesen. Während in zwei magnetischen Ordnungen die Ho3+-Momente entlang der c-Achse moduliert sind, wird für die dritte magnetische Ordnung eine Modulation in a-Richtung beobachtet. Sowohl durch die partielle Substitution der Ho3+-Ionen als auch durch die Ni-B-Stöchiometrievariation wird die Ausprägung der magnetischen Strukturen stark modifiziert. Der Vergleich mit den ebenfalls veränderten supraleitenden Eigenschaften ergibt das folgende Bild für die HoNi2B2C-Verbindungen: Die Supraleitung koexistiert mit den beiden c-Achsen-modulierten magnetischen Strukturen, das Einsetzen der magnetischen Ordnung führt jedoch zu einer Schwächung der Supraleitung. Die a-Achsen-modulierte magnetische Struktur weist Momentkomponenten in c-Richtung auf, die auf Grund der resultierenden lokalen Magnetfelder an den Ni-Plätzen eine starke Unterdrückung der Supraleitung bewirken. Die beobachtete Konkurrenz zwischen der Supraleitung und der a-Achsen-modulierten magnetischen Struktur gibt andererseits einen starken Hinweis darauf, daß die Modifizierung der elektronischen Struktur im supraleitenden Zustand auf das magnetische System rückwirkt. Als weitere Auswirkung des Magnetismus kommt es in RNi2B2C-Verbindungen mit R = Ho, Dy, Tb und Er zu Veränderungen der Kristallstruktur. Mittels hochauflösender Neutronendiffraktion werden magnetisch induzierte, tetragonal-zu-orthorhombische Gitterverzerrungen für diejenigen magnetischen Ordnungen nachgewiesen, bei denen die magnetischen Momente der R3+-Ionen parallel bzw. antiparallel ausgerichtet sind. Die Richtung der Gitterverzerrung, die Abhängigkeit ihrer Größe vom Quadrat des geordneten magnetischen Momentes als auch von der Art der R3+-Ionen deuten darauf hin, daß die magneto-elastischen Wechselwirkungen durch Kristallfeldeffekte bestimmt werden. Diese Einsicht unterstützt auch die Aufklärung der magnetischen Phasendiagramme mittels magnetfeldabhängiger Neutronenbeugungsexperimente. Für eine magnetische Phase schränkt das Auftreten bzw. Fehlen der magneto-elastischen Effekte die Vielfalt der möglichen magnetischen Strukturen ein. Die aus der Literatur bekannten magnetischen Phasen von HoNi2B2C werden bestätigt. Für DyNi2B2C werden die experimentellen Ergebnisse unter Nutzung eines einfachen Modelles interpretiert und die magnetischen Strukturen bestimmt. Anhand von Molekularfeldrechnungen können die Unterschiede in den magnetischen Strukturen für ansteigendes und für abnehmendes Magnetfeld als sehr starke Hystereseeffekte in Zusammenhang mit Phasenübergängen erster Ordnung gedeutet werden.

Die intermetallischen Verbindungen der RCu2-Serie (R = Seltenerd-Elemente) zeigen eine ungewöhnliche Vielfalt von magnetischen Strukturen in Abhängigkeit von Temperatur und äußerem Magnetfeld. Diese Vielfalt ist verursacht durch das Wechselspiel von indirekter Austauschwechselwirkung und anisotropem kristallelektrischen Feld. Die RCu2-Verbindungen kristallisieren in der CeCu2-Struktur, welche als orthorhombische Verzerrung der hexagonalen AlB2-Struktur verstanden werden kann. Ziel der vorliegenden Arbeit ist es, RCu2-Verbindungen mit magnetischer Röntgenbeugung bzw. resonanter magnetischer Röntgenstreuung zu untersuchen, teilweise ergänzt durch Neutronenbeugungsexperimente. Dem zur Neutronenbeugung komplementären Charakter der Röntgenmethoden entspricht es, dass dabei spezielle Details der magnetischen Strukturen untersucht werden. Zusätzlich zur Untersuchung der magnetischen Eigenschaften und Strukturen und zur Suche nach den Ursachen für die auftretenden Phasenübergänge werden magnetoelastische Kopplungen in der pseudohexagonalen Substanzgruppe betrachtet (R = Nd, Gd, Tb, Dy). Der Zusammenhang von kristalliner und magnetischer Struktur wird auch unter Variation und Mischung der Elemente auf dem Seltenerd-Platz erforscht (Tb(1-x)DyxCu2, Tb(1-x)PrxCu2, Dy(1-x)YxCu2). Für die Untersuchung des elementspezifischen Magnetismus bei Vorhandensein mehrerer magnetischer Atomsorten in einem Kristall ist dabei die resonante magnetische Röntgenstreuung die einzig verfügbare Methode. Im Tb0.5Dy0.5Cu2 wird dabei ein unerwartetes Verhalten im Temperaturverlauf der magnetischen Strukturen beobachtet. Ergebnisse aus ergänzenden Neutronenbeugungsexperimenten werden ebenfalls vorgestellt und mittels Rietveld-Verfeinerung der kristallinen und magnetischen Strukturen ausgewertet. Im Ergebnis der Arbeit sind die untersuchten magnetischen Strukturen näher bekannt. Magnetoelastische Wechselwirkungen werden unter Verwendung von Beugungsmethoden neuartig gemessen. / The intermetallic compounds of the RCu2 series (R = rare earths) show a large variety of magnetic structures depending on temperature and external field, mainly caused by the interplay of an indirect exchange interaction and the anisotropy of the crystalline electric field. The RCu2 compounds crystallize in the CeCu2 structure, which can be described as an orthorhombic distortion of the hexagonal AlB2 structure. The aim of the present work is the investigation of RCu2 compounds by using resonant and nonresonant magnetic x-ray scattering, supplemented by neutron scattering. Because of the complementarity of magnetic x-ray and neutron scattering this investigation reveals new details of the magnetic structures of the studied compounds. Magnetic properties and magnetic structures are investigated as well as magnetic phase transitions and magneto-elastic coupling in the pseudohexagonal compounds. The correlation between the crystallographic structure and the magnetic structures is studied for different rare earths (R = Nd, Gd, Tb, Dy) but also for partial substitution of magnetic rare earths by magnetic or nonmagnetic ions on the rare earth site (Tb(1-x)DyxCu2, Tb(1-x)PrxCu2, Dy(1-x)YxCu2). Resonant magnetic x-ray scattering is the only method available to investigate the element specific magnetism in crystals with different magnetic ions. By the study of the Tb resonance and the Dy resonance on Tb0.5Dy0.5Cu2 an unexpected developement of the magnetic structures with temperature is observed. The results of supplementary neutron scattering experiments are presented and analyzed by Rietveld refinement of the crystallographic and magnetic structures, mainly focussed on TbCu2. In summary, new insights into the different magnetic structures of RCu2 compounds are gained. The strong magneto-elastic coupling is studied by different scattering methods applied to this problem for the first time.

Zur Messung pyrelektrischer Koeffzienten wurde ein Messplatz nach einem erweiterten SHARP-GARN-Verfahren entwickelt und zur Untersuchung von Phasenumwandlungen in Pyroelektrika eingesetzt. Einerseits konnten pyroelektrische Messungen im elektrischen Feld die Pyroelektrizität einer neuen durch elektrisch angetriebene Defektmigration erzeugten Phase in Strontiumtitanat nachweisen. Andererseits gelang es, Ferroelektrizität in der Hochtemperaturphase von Poly(Vinylidenfluorid-Trifluorethylen), mittels phasenreiner Präparation der Hochtemperaturphase unterhalb der CURIEtemperatur und anschließender Polarisierung, nachzuweisen. Ferner ließen sich mittels thermisch angeregter Pyroelektrika Redoxprozesse antreiben, was durch Desinfektion von Escherichia coli Bakterien in wässriger Lösung mittels Lithiumniobat und -tantalat gezeigt wurde. Die Hypothese der Desinfektion durch reaktive Sauerstoffspezies konnte durch spektroskopisch nachgewiesene OH-Radikale - erzeugt mittels thermisch angeregter Bariumtitanatnanopartikel - belegt werden.