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This work is focused on the parent compounds of the Fe-chalcogenide superconductors. For this purpose poly- and single-crystalline forms of tetragonal β-FexSe, Fe1+yTe, Fe1+yTe1-xSex and Fe(1+y)-xMxTe (M = Ni, Co) have been prepared. Second focal points of this study are the low-temperature structural phase transitions and physical property changes in tetragonal Fe1+yTe which are induced by composition, external pressure, and cationic substitution.

The response of materials under extreme temperature and pressure conditions is a topic of great significance because of its relevance in astrophysics, geophysics, and inertial confinement fusion. In recent years, environments exceeding several hundred gigapascals in pressure have been produced in the laboratory via laser-based dynamic loading techniques. Shock-loading is of particular interest as the shock provides a fiducial for measuring time-dependent processes in the lattice such as phase transitions. Time-resolved x-ray diffraction is the only technique that offers an insight into these shock-induced processes at the relevant spatial (atomic) and temporal scales. In this study, nanosecond resolution x-ray diffraction techniques were developed and implemented towards the study of shock-induced phase transitions in polycrystalline materials. More specifically, the capability of a focusing x-ray diffraction geometry in high-resolution in situ lattice measurements was demonstrated by probing shock-compressed Cu and amorphous metallic glass samples. In addition, simultaneous lattice and free surface velocity measurements of shock-compressed Mg in the ambient hexagonal close packed (hcp) and shock-induced body centered cubic (bcc) phases between 12 and 45 GPa were performed. These measurements revealed x-ray diffraction signals consistent with a compressed bcc lattice above a shock pressure of 26.2±1.3 GPa, thus capturing for the first time direct lattice evidence of a shock-induced hcp to bcc phase transition in Mg. Our measurement of the hcp-bcc phase boundary in Mg was found to be consistent with the calculated boundary from generalized pseudopotential theory in the pressure and temperature region intersected by the principal shock Hugoniot. Furthermore, the subnanosecond timescale of the phase transition implied by the shock-loading conditions was in agreement with the kinetics of a martensitic transformation. In conclusion, we report on the progress and future work towards time-resolved x-ray diffraction measurements probing solid-liquid phase transitions in high Z polycrystalline materials, specifically Bi. / text

The series of compounds [M(H2O)2(15-crown-5)](NO3)2, M = Mg, Mn, Co, Cu and Zn, has been extended to include two new phases for M = Fe and two new phases for M = Ni. The system [M(H2O)2(15-crown-5)](NO3)2 is remarkable for having many high-Z’ phases (Z’ > 1) with similar packing and for having solid-solid phase transitions through which there is no significant loss of crystallinity. The synthesis of the analogous Ni complex was carried out. Single-crystal X-ray diffraction showed that the coordination of the Ni2+ ion is different from that of the other six M2+ ions in the system [M(H2O)2(15-crown- 5)](NO3)2. High temperature phases with high Z’ (8) were isolated for M = Mg, Fe and Zn. The refinements of such phases are challenging because of the lack of information in the diffraction patterns. Full details of the refinements for these three phases are discussed. Six other Ni(II) complexes consisting of Ni2+, NO3-, 15-crown-5 and different solvents were found when efforts were made to synthesize the compound [Ni(H2O)2(15-crown- 5)](NO3)2. In these chemically different environments, the Ni2+ ions are not coordinated by the 15-crown-5 molecules; rather, one-dimensional H-bonded chains are formed from uncomplexed 15-crown-5 molecules and the Ni(II) complexes. Among these six Ni(II) complexes, the compounds [Ni(H2O)6](NO3)2·(15-crown-5)·H2O, [Ni(H2O)6](NO3)2·(15-crown-5)·2H2O and [Ni(H2O)2(MeCN)(NO3)2]·(15-crown- 5)·MeCN were found to have reversible solid-solid phase transitions between structurally related phases. In all of these transitions, no significant crystal damage was detectable. The two latter systems are unusual because their phase sequences include three transitions and four phases between 90 and 295 K and because of the existence of high-Z’ phases. These high-Z’ phases are best depicted as being intermediate to low- and hightemperature phases. A method based on thermal analyses and X-ray diffraction has been developed for studying such sets of phase transitions.

<p>In this thesis, material properties have been examined under extreme conditions in computer-based calculations.</p><p>The research on iron (Fe), nickel (Ni), and ferropericlase (Mg_1-xFe_xO) are not only important for our understanding of the Earth, but also for an improved knowledge of these materials <i>per se</i>.</p><p>An embedded-atom model for Fe demonstrated to reproduce properties such as structure factors, densities and diffusion constants, and was employed to evaluate temperature gradients at Earth core conditions. A similar interaction together with a two-temperature method was applied for the analysis of shock-induced melting of Ni. For Mg_1-xFe_xO, the magnetic transition pressure was shown to increase with iron content. Furthermore, the C₄₄ softening with pressure and iron composition supports the experimentally observed phase transition for Mg_0.8Fe_0.2O at 35 GPa.</p><p>The properties of high density helium (He) is of great interest as the gas is one of the most abundant elements in the solar system. Furthermore, He and neon (Ne) are often used as pressure media in diamond anvil cells. The melting of He showed a possible fcc-bcc-liquid transition starting at T=340 K, P=22 GPa with a Buckingham potential, whereas the bcc phase was not seen with the Aziz form. For Ne, Monte Carlo calculations at ambient pressure showed very accurate results when extrapolating the melting temperatures to an infinite cluster limit. At high pressure, a one-phase <i>ab initio</i> melting curve showed a match with one-phase L-J potential results, which could imply a correspondence between <i>ab initio</i>/classical one-phase/two-phase calculations.</p><p>In the search for hard materials, <i>ab initio</i> calculations for four TiO₂ phases were compared. Just as imposed by experiment, the cotunnite phase was found to be very hard. The anomalous elastic behavior of the superconducting group-<i>V</i> metals V, Nb, Ta was found to be related to shrinking nesting vectors and the electronic topological transition (ETT).</p>

In this work we investigate themes related to many-body systems in which multiple ground states are accessible, a condition known as frustration. Frustration can arise in a number of contexts, and we consider the consequences of this situation with some examples from condensed-matter physics. In some magnetic materials interactions between spins are such that no single spin configuration provides a unique ground state. In the class of frustrated magnets where the number of ground states is extensive, thermal fluctuations are strong even at temperatures significantly below the interaction strength. At such temperatures spins are highly correlated, and small perturbations may have profound consequences. In this thesis we provide an example of this. By considering classical n-component spins with nearest-neigbour exchange on a frustrated octahedral lattice we show that – in the limit where exchange interactions are large – the system is in a disordered, correlated phase where correlations have the form of a dipole field. This is termed a Coulomb phase. From this phase we induce an ordering transition, lifting the degeneracy with weak, additional short-range interactions. By studying the transition in the solvable limit of n → ∞, we discover that the transition has identical thermodynamics to that of a magnetic system interacting through long-range, dipolar forces. Finally, we provide a more apposite characterisation of the transition, where the high-temperature side of the transition is described through the fluctuations of solenoidal fields, and the ordering corresponds to a condensation of these fields. In a separate part of the thesis, we investigate the influence of disorder on frustrated lattices. We study a two-dimensional tight-binding model with nearest-neighbour hopping and on-site disorder. Restricting the allowed states to being those from the low-lying manifold of ground states, the disorder feeds through to act as effective disorder in the hopping terms, which decay algebraically with distance. The quasi-long range nature of this effective hopping leads to a situation in which the resultant single-particle eigenstates are critical, and we probe their behaviour numerically with a transfer matrix calculation.

Dans cette thèse, nous discutons l'influence d'un réseau qui possède une topologie non triviale sur les propriétés collectives d'un modèle hamiltonien pour spins,le modèle $XY$, défini sur ces réseaux.Nous nous concentrons d'abord sur la topologie des chaînes régulières et du réseau Petit Monde (Small World), créé avec le modèle Watt- Strogatz.Nous contrôlons ces réseaux par deux paramètres $\gamma$, pour le nombre d' interactions et $p$, la probabilité de ré-attacher un lien aléatoirement.On définit deux mesures, le chemin moyen $\ell$ et la connectivité $C$ et nous analysons leur dépendance de $(\gamma,p)$.Ensuite,nous considérons le comportement du modèle $XY$ sur la chaîne régulière et nous trouvons deux régimes: un pour $\gamma<1,5$,qui ne présente pas d'ordre longue portée et un pour $\gamma>1,5$ où une transition de phase du second ordre apparaît.Nous observons l'existence d'un état ​​métastable pour $\gamma_ {c} = 1,5$. Sur les réseaux Petit Monde,nous illustrons les conditions pour avoir une transition et comment son énergie critique $\varepsilon_{c}(\gamma,p)$ dépend des paramètres $(\gammap$).Enfin,nous proposons un modèle de réseau où les liens d'une chaîne régulière sont ré-attachés aléatoirement avec une probabilité $p$ dans un rayon spécifique $r$. Nous identifions la dimension du réseau $d(p,r)$ comme un paramètre crucial:en le variant,il nous est possible de passer de réseaux avec $d<2$ qui ne présentent pas de transition de phase à des configurations avec $d>2$ présentant une transition de phase du second ordre, en passant par des régimes de dimension $d=2$ qui présentent des états caractérisés par une susceptibilité infinie et une dynamique chaotique. / In this thesis we discuss the influence of a non trivial network topology on the collective properties of an Hamiltonian model defined on it, the $XY$ -rotors model. We first focus on networks topology analysis, considering the regular chain and a Small World network, created with the Watt-Strogatz model. We parametrize these topologies via $\gamma$, giving the vertex degree and $p$, the probability of rewiring. We then define two topological parameters, the average path length $\ell$and the connectivity $C$ and we analize their dependence on $\gamma$ and $p$. Secondly, we consider the behavior of the $XY$- model on the regular chain and we find two regimes: one for $\gamma<1.5$, which does not display any long-range order and one for $\gamma>1.5$ in which a second order phase transition of the magnetization arises. Moreover we observe the existence of a metastable state appearing for $\gamma_{c}=1.5$. Finally we illustrate in what conditions we retrieve the phase transition on Small World networks and how its critical energy $\varepsilon_{c}(\gamma,p)$ depends on the topological parameters $\gamma$ and $p$. In the last part, we propose a network model in which links of a regular chain are rewired according to a probability $p$ within a specific range $r$. We identify a quantity, the network dimension $d(p,r)$ as a crucial parameter. Varying this dimension we are able to cross over from topologies with $d<2$ exhibiting no phase transitions to ones with $d>2$ displaying a second order phase transition, passing by topologies with dimension $d=2$ which exhibit states characterized by infinite susceptibility and macroscopic chaotic dynamical behavior.

A emergência de fenômenos coletivos e correlações de longo alcance impossibilitam a inferência de propriedades de sistemas como um todo a partir de suas partes componentes. A modelagem destes sistemas frequentemente ocorre mediante emprego de operadores de spin localizados em grafos com topologias não-triviais. Aqui, mostramos que o operador de momento angular de muitos corpos une o estudo de diversos sistemas complexos, desde a sistemas epidêmicos até cadeias magnéticas de spin. Para o modelo epidêmico SIS, determinamos a matriz de transição do processo estocástico correspondente e mostramos suas soluções para grafos regulares e aleatórios, por meio de técnicas geralmente empregadas em sistemas fortemente correlacionados. Já no modelo de Dicke, identificamos o vínculo que explica a relevância e o efeito finito de operadores anti-girantes para duas espécies atômicas confinadas numa cavidade óptica que interagem com radiação eletromagnética. Por fim, o papel do momento angular também é identificado para duas cadeias quânticas de spin 1/2 acopladas, as quais modelam nanoestruturas magnéticas heterogêneas. A estrutura de bandas é calculada, enquanto efeitos espúrios de superfície são removidos pela introdução de quasipartículas dotadas de grau de liberdade de spin adicional / The emergence of collective phenomena and long range correlations makes it impossible to infer the properties of whole systems from their components. Their modeling often occurs through the use of localized spin operators, taking place within graphs with non-trivial topologies. Here, we show that the many-body angular momentum operator connects the study of several complex systems, ranging from epidemic systems to magnetic spinchains. For the SIS epidemic model, we calculate the transition matrix of the corresponding stochastic process and show the corresponding solutions for regular and random graphs, using techniques generally employed in strongly correlated systems. For the Dicke model we identify the constraint that explains the relevance and finite size effect of anti-rotating operators, for two atomic species, confined within an optical cavity, and interacting with electromagnetic radiation. Finally, the role of angular momentum is also identified for two coupled quantum spinchains 1/2 which model heterogeneous magnetic nanostructures. The band structure is calculated, while spurious surface effects are removed due to the introduction of quasiparticles with an additional spin degree of freedom.

Neste trabalho analisamos o comportamento dinâmico de um modelo clássico e de um modelo quântico de spins na presença de um campo magnético externo. Para estudar a dinâmica de um sistema de spins clássico utilizamos um modelo de Ising bidimensional com interações entre spins primeiros vizinhos na direção vertical diferente daquelas entre spins primeiros vizinhos na horizontal. Através do formalismo da equação mestra, e considerando o processo estocático de Glauber dentro da aproximação de pares dinâmica, determinamos os diagramas de fases estacionários para o modelo na presença de campos magnéticos estáticos e oscilantes no tempo. Dependendo dos valores da razão entre os acoplamentos na horizontal e na vertical, da frequência e da amplitude do campo oscilante, obtemos diagramas de fases onde estão presentes os ordenamentos ferromagnético, paramagnético e antiferromagnético. Além disso, a transição entre as fases pode ser contínua ou descontínua dependendo dos valores dos parâmetros. O modelo também pode apresentar um comportamento tricrítico. O modelo de Ising em um campo transverso unidimensional à temperatura nula foi o modelo escolhido para estudarmos a resposta de sistemas quânticos de spins sujeitos a campos magnéticos que oscilam periodicamente no tempo. Usamos a aproximação de campo médio e simulações de Monte Carlo para determinar a linha de transição contínua entre as fases ferromagnética e paramagnética presentes no diagrama de fases dinâmico do modelo. / In this work we have analized the dynamical behavior of a classical and of a quantum spin model subject external magnetic fields. For a better understanding of the dynamics of a classical spin system we have chosen a two-dimensional Ising model with interactions between first neighbors in the horizontal direction different from that of the vertical direction. By using the master-equation formalism and taking the stochastic Glauber process, within the dynamical pair approximation, we have determined the stationary phase diagrams of the model for static and oscillating magnetic fields. Depending on the values of the ratio between the horizontal and vertical couplings, the frequency and the amplitude of the time dependent field, we have obtained phase diagrams where the ferromagnetic, paramagnetic and antiferromagnetic phases are present. Besides, the transition between these phases can be continuous or discontinuous depending on the values of the parameters. The model may display also a tricritical behavior. We have also chosen the transverse Ising model in one dimension at zero temperature to study the response of the quantum spin systems subject to time dependent external fields. We have used the mean-field approximation and the Monte Carlo simulations to determine the continuous transition line between the ferromagnetic and paramagnetic phases.