The LiHo_xY_{1-x}F_4 magnetic material in a transverse magnetic field B_x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in pure and random disordered systems. We first present analytical and numerical evidences for the validity of an effective spin-1/2 approach to the description of a general dipolar spin glass model with strong uniaxial Ising anisotropy and subject to weak B_x. We relate this toy model to the LiHo_xY_{1-x}F_4 transverse field Ising material. We show that an effective spin-1/2 model is able to capture both the qualitative and quantitative aspects of the physics at small B_x. After confirming the validity of the effective spin-1/2 approach, we show that the field-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline mirror symmetries generates, via the predominant dipolar interactions between Ho^{3+} ions, random fields along the Ising z direction. This identifies LiHo_xY_{1-x}F_4 in B_x as a new random field Ising system. We show that the random fields explain the smearing of the nonlinear susceptibility at the spin glass transition with increasing B_x. In this thesis, we also investigate the phase diagram of non-diluted LiHoF_4 in the presence of B_x, by performing Monte-Carlo simulations. A previous quantum Monte Carlo (QMC) simulation found that even for small B_x where quantum fluctuations are small, close to the classical critical point, there is a discrepancy between experiment and the QMC results. We revisit this problem, focusing on weak B_x close to the classical T_c, using an alternative approach. For small B_x, by applying a so-called cumulant expansion, the quantum fluctuations around the classical T_c are taken into account perturbatively. We derived an effective perturbative classical Hamiltonian, on which MC simulations are performed. With this method we investigate different proposed sources of uncertainty which can affect the numerical results. We fully reproduce the previous QMC results at small B_x. Unfortunately, we find that none of the modifications to the microscopic Hamiltonian that we explore are able to provide a B_x-T phase diagram compatible with the experiments in the small semi-classical B_x regime.

The LiHo_xY_{1-x}F_4 magnetic material in a transverse magnetic field B_x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in pure and random disordered systems. We first present analytical and numerical evidences for the validity of an effective spin-1/2 approach to the description of a general dipolar spin glass model with strong uniaxial Ising anisotropy and subject to weak B_x. We relate this toy model to the LiHo_xY_{1-x}F_4 transverse field Ising material. We show that an effective spin-1/2 model is able to capture both the qualitative and quantitative aspects of the physics at small B_x. After confirming the validity of the effective spin-1/2 approach, we show that the field-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline mirror symmetries generates, via the predominant dipolar interactions between Ho^{3+} ions, random fields along the Ising z direction. This identifies LiHo_xY_{1-x}F_4 in B_x as a new random field Ising system. We show that the random fields explain the smearing of the nonlinear susceptibility at the spin glass transition with increasing B_x. In this thesis, we also investigate the phase diagram of non-diluted LiHoF_4 in the presence of B_x, by performing Monte-Carlo simulations. A previous quantum Monte Carlo (QMC) simulation found that even for small B_x where quantum fluctuations are small, close to the classical critical point, there is a discrepancy between experiment and the QMC results. We revisit this problem, focusing on weak B_x close to the classical T_c, using an alternative approach. For small B_x, by applying a so-called cumulant expansion, the quantum fluctuations around the classical T_c are taken into account perturbatively. We derived an effective perturbative classical Hamiltonian, on which MC simulations are performed. With this method we investigate different proposed sources of uncertainty which can affect the numerical results. We fully reproduce the previous QMC results at small B_x. Unfortunately, we find that none of the modifications to the microscopic Hamiltonian that we explore are able to provide a B_x-T phase diagram compatible with the experiments in the small semi-classical B_x regime.

Die komplizierte Struktur der Energielandschaft wurde am Beispiel des +/- J Spinglas-Modells untersucht. Sie ist in glasartigen Systemen der Schlüssel zum Verständnis einer verlangsamten Dynamik. Es wurde ein enger Zusammenhang zwischen der Dynamik und der Energielandschaft nachgewiesen. Die Energielandschaft wird in +/- J Spinglas Modellsystemen durch Cluster charakterisiert, die infolge ihrer Konnektivität größere Objekte (z.B. Täler) bilden. Einzelne Cluster, aber auch ganze Täler, sind miteinander durch sogenannten Sattelcluster verknüpft. Die physikalischen Eigenschaften werden durch die Strukturen der Verknüpfungen und durch die innere Struktur der Cluster geprägt. Zur Beschreibung der Energielandschaften wurde die genaue Kenntnis der Zustände benutzt. Auf der Grundlage des "branch-and-bound" Verfahrens war es möglich, für kleine Systeme alle Zustände bis zu der dritten Anregung zu bestimmen. Danach wurden die Konfigurationen so sortiert, dass die Beziehungen zwischen ihnen, wie z.B. Nachbarschaften und Clusterzugehörigkeiten, einfach zu finden waren. Es gelang, die exakte Landschaft für Systeme bis L=6 aufzubauen. Für größere Systeme ist es zur Zeit unmöglich, alle niederenergetischen Zustände zu finden. Eine alternative Möglichkeit, die Struktur zu beschreiben, erhält man durch Untersuchung der Verteilung der Overlap. An der Gestalt der Verteilung erkennt man, ob die niederenergetische Struktur kompliziert oder einfach ist. Bei genaueren Untersuchungen ist es sogar möglich, die Anzahl der existierenden Täler abzuschätzen. Die Untersuchungen der Overlap bei 8555 3D Systemen (L=4) weisen darauf hin, dass bei kleineren Grundzustandsenergien die Struktur durch zwei spiegelsymmetrische Täler geprägt ist. Mit wachsender Grundzustandsenergie wird die Struktur der Systeme immer komplizierter. Eine weitere wichtige Komponente der Energielandschaft ist die innere Struktur der Sattelcluster. Ein Sattelcluster besteht aus wenigstens drei Gruppen von Konfigurationen. Zwei Gruppen enthalten Konfigurationen, die mit den Grundzustandsclustern verbunden sind, und die dritte Gruppe verbindet die beiden. Es passiert oft, dass die Konfigurationsgruppen, die verschiedene Grundzustandscluster verbinden, weit voneinander entfernt liegen. Dies wurde als ein wichtiger Aspekt erkannt, der zu einer Verlangsamung dynamischer Prozesse führt. Der andere Aspekt der Energielandschaft ist ihr Zusammenhang mit dem Realraumbild. Das Realraumbild ist als die Lage der Spins auf dem Gitter zu verstehen. Spins kann man zu verschiedenen Spindomänen zusammenfassen, die dann auf natürliche Weise die Struktur der Energielandschaft generieren. Für die Größe der einzelnen Cluster sind die freien Spins verantwortlich. Es wurde bestätigt, dass die Existenz einzelner Täler durch Spindomänen erklärt werden kann. Dabei wird durch das kollektive Umdrehen aller Spins in einer solcher Domäne ein anderer Cluster in einem anderen Tal erzeugt. Neben dem Zusammenhang von Spindomänen und Energielandschaft konnte der Einfluss von bestimmten zusammenhängenden Strukturen freier Spins genauer aufgeklärt werden. Hier ergeben sich Ansatzpunkte für weitergehende Untersuchungen.

No description available.

Le travail expérimental développé pendant cette thèse se situe à l'interface de deux champs en physique de la matière condensée, à savoir les verres de spins et la physique mésoscopique. Les verres de spins ont été largement étudié et font partie des problèmes les plus débattus au cours des années tant d'un point de vue expérimental que théorique. Cet état est caractérisé par des propriétés très particulières qui se font jour lors d'une transition de phase magnétique à très basses températures qui est elle-même inhabituelle. En effet, cette transition est due à un mélange de frustration et de désordre dans la structure magnétique du système. Ce faisant, c'est un système modèle pour les verres et les systèmes frustrés en général. Après bien des efforts, des travaux théoriques ont réussi à décrire l'état fondamental du système au moyen de deux approches différentes et apparemment incompatibles. Cependant, la question de la vraie nature de la phase verre de spin reste grandement débattue.La physique mésoscopique, de son côté, traite du transport électronique dans les échantillons pour lesquels les électrons gardent leur cohérence de phase. Si les électrons restent cohérents, il est possible de voir des effets d'interférences qui sont des signes quantiques de ce qu'il se passe au niveau atomique. Dans cette thèse, il est utilisé pour sonder le désordre aussi bien magnétique que statique dans un verre de spins.Nous montrons que, contrairement à ce qui est cru, de forts changements se déroulent dans le désordre microscopique même à basses températures. Nous prétendons également que ces changements sont purement structuraux et viennent du fait de systèmes dont la distribution en énergie est très large. / The experimental work developed during this PhD is situated at the interface of two fields of condensed matter physics, namely spin glasses and mesoscopic physics. Spin glasses have been widely studied and are one of the problem that has been the most discussed over the years, both on a theoretical and experimental point of view. This state is characterized by very peculiar properties that come to light as it exhibits a magnetic phase transition at low temperatures that is already unusual. Indeed, this transition is due to a mix of frustration and disorder in the magnetic structure of the system, making it an exceptional model system for glasses and frustrated systems in general. After many efforts, theoreticians managed to described the fundamental state of the system by the mean of two different and apparently incompatible approaches. The first one, called RSB theory, is based on a mean-field approximation and predicts a complex phase space with an unconventional hierarchical organization. The second is based on more phenomenological approach and is named Droplet theory. It points towards a unique ground state and explain all the observation by slow relaxation processes. However, the question of the true nature of the spin glass phase is still heavily debated. Mesoscopic physics, for its part, addresses the question of electronic transport for samples in which the electrons keep their phase coherence. If the electrons remains coherent, it is possible to see interference effects that are quantum signs of what happens at the atomic level. In this work, it is used to probe the magnetic and static disorder in spin glasses. Indeed, it is possible to interpret the change in those interferences as changes in the microscopic disorder configuration and to know exactly how the spin glass state evolves. Some work have already tried to use coherent transport in spin glasses but this remains an open field. This work has then be dedicated to the implementation of transport measurement in spin glasses and mesocopic conductors. The first part will be focused on a the experimental setup that was used to perform very precise transport measurements and on the processing of the data taken out of them. In a second part, we will present some general physical characteristics of our samples such as their resistance dependence to the temperature or magnetic field, before extracting the quantum signature in magnetoresistance measurements. Finally, we will discuss the results obtained. We show that strong changes in the microscopic disorder happen even at low temperatures, in opposition to what is believed. We argue that those observed changes are purely structural and come from systems that are widely distributed in energy.

Neste trabalho consideramos o modelo de Potts na árvore de Cayley submetida a um campo magnético. Esse campo pode ser representado pela interação dos spins da árvore com um spin adicional, denominado spin fantasma. Essa nova rede passa a ser chamada de árvore de Cayley fechada e assimétrica. Sendo uma rede hierárquica, ela representa soluções exatas que são obtidas quando as técnicas do grupo de renormalização no espaço real são aplicadas. Subtraindo os efeitos de superfície e considerando somente o interior da árvore (rede de Bethe), esses resultados reproduzem os resultados da aproximação de campo médio de Bethe-Peierls. Com a finalidade de estudar a função de correlação do modelo de Potts na rede de Bethe, consideramos primeiramente uma cadeia de Potts interagindo com um spin fantasma. Através das regras de composição em série e paralelo e do método da quebra e colapso para as trasmissividades térmicas (função de correlação) obtemos uma fórmula de recorrência para a função de correlação entre quaisquer dois spins na cadeia. Mostramos então que pela invariança translacional da rede de Bethe qualquer par de spins pode ser mapeado no sistema anterior. A seguir consideramos o modelo de Potts de um estado na árvore de Cayley fechada e assimétrica. Decimando os spins interiores da unidade geradora da rede, obtemos um mapa polinomial quadrático para a transformação do grupo de renormalização (mapa de Bethe-Peierls). O diagrama de fase desse sistema é então obtido do conjunto de Mandelbrot através de uma transformação de Mobius. O mapa de Bethe-Peierls apresenta dois pontos fixos, que são relacionados com as fases ferro e paramagnética e o regime caótico é identificado com a fase vidro de spin. Esse sistema revela ser o exemplo mais simples de vidro de spin de McKay-Berker-Kirkpatrick. Na rede de Bethe e a campo nulo esse sistema apresenta transições de fase de segunda ordem. Analisando o comportamento crítico da função de correlação e de suas derivadas, vemos que se identificarmos a função de correlação entre o spin fantasma e qualquer spin da rede com a magnetização (por spin) e a função de correlação entre dois spins primeiros vizinhos com a energia interna do sistema, cinco expoentes críticos ((&#948, &#946, &#947 &#8217, &#945, &#945 &#8217) são calculados e satisfazem as relações de escala. Para ilustrar o procedimento recursivo apresentado para calcular a função de correlação entre dois spins separados por ligações m na rede de Bethe, consideramos os spins de Potts de um estado. Obtemos então de forma explícita as correlações para m=1, 2 e 3.0 / In this work we consider the Potts model on the Cayley tree subjected to a magnetic Field. This field can be represented by the interaction of the tree spins with an additional one, denominated ghost spin. This new lattice is then called closed-asymmetric Cayley tree. Being a hierarchical lattice it comes to have exact solutions which are obtained when the real-space renormalization group techniques are applied. Subtracting the surface effects and considering only the tree interior (Bethe lattice), these results reproduce the results of Bethe-Peierls mean-field approximation. With the objective of studying the pair-correlation function of the Potts model on the Bethe lattice, we at first consider a Potts chain interacting with a ghost spin. Throughout the series-parallel composition rules and the break-collapse method for the thermal transmissivities (pair-correlation function) we obtain a recursive relation for the correlation function between any two spins on the chain. We then show, due to the translational invariance of the Bethe lattice, that any pair of spins can be mapped into the latter system. Next we consider the one-state Potts model on the closed asymmetric tree. Decimating the inner spins of the generating unit for the lattice, we obtain a quadratic polynomial map for the renormalization group transformation (Bethe-Peierls map). The phase diagram of this system is obtained from the Mandelbrot set throughout a Mobius transformation. The Bethe-Peierls map has two stable fixed points which are related to the ferro and paramagnetic phases and the chaotic regime is identified with the spin-glass phase. This system turns out to be the simplest example of a McKay-Berker-Kirkpatrick spin glass. On the Bethe lattice with vanishing field this system presents second-order phase transitions. Analyzing the critical behavior of the pair-correlation function and of this derivatives, we see that if we identify the correlation function between the ghost spin and any spin on the lattice with the magnetization (per spin), and the correlation function between two nearest-neighbor spins with the internal energy of the system, five critical exponents (&#948, &#946, &#947 &#8217, &#945, &#945 &#8217) are calculated and they satisfy the scaling relations. In order to illustrate the recursive procedure presented to calculate the pair-correlation function between spins m bonds apart on the Bethe lattice, we consider the one-state Potts spins. We obtain explicitly the correlation for m=1, 2 and 3.

O objeto desta pesquisa consiste em investigar as propriedades estruturais, magnéticas e hiperfinas dos compostos pseudobinários de fases de Laves: Hf(Fe(1-x)Cr(x))2 e (Nb(1-x)Zr(x))Fe2. Para o Hf(Fe(1-x)Cr(x))2, preparamos as amostras como ligas policristalinas e as fundimos por síntese nas concentrações: x = 0,0; 0,1; 0,2; 0,3; 0,4; 0,5; 0,6; 0,7; 0,8; 0,9 e 1,0. O mesmo foi feito para as amostras de (Nb(1-x)Zr(x))Fe2 nas concentrações x = 0,0; 0,1; 0,2; 0,3; 0,4 e 0,5. Todas as amostras fundiram-se num forno de fusão de arco, sob atmosfera de argônio ultrapuro (99.999%). Em seguida investigamos a estrutura cristalina das ligas pelo método do pó, com a técnica de difratometria de Raios X (XRD), obtendo-se os parâmetros de rede e confirmando-se a estrutura de fase hexagonal C14 para as amostras Hf(Fe(1-x)Cr(x))2 nas concentrações 0,0 <= x < 0,9, bem como em todas as outras amostras de (Nb(1-x)Zr(x))Fe2. Depois, determinamos as propriedades magnéticas das ligas Hf(Fe(1-x)Cr(x))2 pela técnica de magnetização a baixas temperaturas em baixos campos magnéticos aplicados de 0 a 7 T e em altos campos magnéticos aplicados de 0 a 16 T. As suscetibilidades AC e DC a baixos campos magnéticos com temperaturas de 4,2 K a 300 K, FC e ZFC, nos indicaram que as ligas de concentrações 0,4 <= x < 0,8 apresentam comportamento \'vidro de spin\', sendo que em x <= 0,3 são aglomerados magnéticos com interação de curto alcance e em x = 0,9 é um superparamagnético. Por tanto, os valores dos momentos magnéticos por átomo de Fe foram calculados para todas as amostras. As medidas de spectroscopia Mössbauer das mesmas amostras de Hf(Fe(1-x)Cr(x))2, na temperatura ambiente, apresentam dois sextetos para a mostras com x = 0,2 e dois dubletos quadrupolares para as demais composições, atribuídos aos sítios cristalográficos 2a e 6h do Fe. Por outra parte, os espectros Mössbauer das amostras de (Nb(1-x)Zr(x))Fe2 à temperatura de 4,2 K, sem campo magnético aplicado e com campo magnético aplicado de 6 e 12 T, sugerem que estes compostos se encontram em um balanço em que coexistem as fases ferromagnéticas e antiferromagnéticas. Finalmente, notamos que no composto (Nb0.6Zr0.4)Fe2 há, uma possível existência de comportamento paramagnético nos Fe do sítio cristalino 2a e, ao mesmo tempo, pouca certeza que o valor do momento magnético seja nulo neste sítio cristalino. / The object of this research consists of investigating the structural, magnetic and hiperfine properties of the pseudobinar Laves phases compounds Hf(Fe(1-x)Cr(x))2 and (Nb(1-x)Zr(x))Fe2. We prepared polycristaline samples alloys and for synthesis melting in the concentrations: x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 e 1.0, for the Hf(Fe(1-x)Cr(x))2 and in the concentrations: x = 0.0, 0.1, 0.2, 0.3, 0.4 e 0.5 for (Nb(1-x)Zr(x))Fe2. We melted them in an arc furnace under pure Argon (99.999%) gas atmosphere. We investigated the cristaline structure of the alloys by the powder XRD technique, obtaining lattice parameters and confirming the structure of hexagonal phase C14 for the samples Hf(Fe(1-x)Cr(x))2 in the concentrations 0.0 <= x <= 0.9 and also in all the other samples produced of (Nb(1-x)Zr(x))Fe2. We investigate the magnetic properties of Hf(Fe(1-x)Cr(x))2 alloys bye the technique of magnetization at low temperatures and low magnetic field applied until 7 T and high magnetic field applied until 16 T. The susceptibility AC and DC at low magnetic fields and temperatures of 4.2 K until 300 indicated that alloys of concentrations 0.4 <= x < 0.8 show spin glass behavior, in x <= 0.3 they are magnetic clusters with short range interactions, and in x = 0.9 is superparamagnetic. The values of the magnetic moments for atom of Fe were calculated for all samples. We measured Mössbauer spectra of the same samples of Hf(Fe(1-x)Cr(x))2 at room temperature, obtaning two sextets for the samples with x < 0.2 and two quadrupolar doublets for the other compositions, that would be attributed to the cristalographic sites 2a and 6h. Also the Mössbauer spectrum of the samples (Nb(1-x)Zr(x))Fe2 at temperature of 4.2 K without magnetic field applied and with magnetic field applied of 6 and 12 T, suggest that those compounds show coexisting ferromagnetic and antiferromagnetic phases. We could note for the compound (Nb0.6Zr0.4)Fe2 a possible existence of the paramagnetic behavior in the Fe of the cristalographic site 2a, but the magnetic moment in this site is not zero.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The present work studies inverse transitions by using two spin glass models: the infinite-range fermionic Ising spin glass (FISG) in the presence of a transverse magnetic field ¡ and Hopfield fermionic Ising spin glass (HFISG) model with a ¡ field. In these models, the spin are written in terms of fermionic operators. In that case, there are four possible eigenvalues of the operator Sz i , two of them non-magnetic. The problem for both models is expressed in the path integral formalism with Grassmann variables. Particularly, the FISG and HFISG models are analysed in the Grand Canonical ensemble, which allows changing the average number occupation of fermions per site by adjusting the chemical potential μ, which is a magnetic dilution mechanism. The Grand Canonical Potential is obtained within the static approximation with replica symmetry and one-step replica symmetry breaking schemes. Firstly, the highly frustrated FISG model is studied. Essentially, for ¡ = 0, a first order inverse transition arises with the increase of μ (dilution). As a consequence, the inverse transitions can be studied under the effect of quantum fluctuations when a transverse magnetic field ¡ is turned on. As main result, it is shown that quantum fluctuations destroy the inverse transitions. Secondly, the role of frustration as ingredient for a model to present naturally inverse transitions is checked by the HFISG model, which allows interpolating from trivial randomness to a highly frustrated regime. In fact, it is shown that for ¡ = 0 and high values of μ, any frustration level presents a inverse transition. Finally, the introduction of the ¡ field in the HFISG model allows to study how the simultaneous adjusting of quantum fluctuations and the level of frustration affects the inverse transition in this model. As a result, it is suggested that the interplay between the dilution and the presence of a frustrated phase has an important role inverse transitions producing. In addition, when the effects of quantum fluctuations are introduced by ¡, the role of dilution seems to be weakened. As a consequence, the inverse transition is destroyed in HFISG model. / O presente trabalho estuda as transições inversas utilizando dois modelos vidro de spin: o modelo de alcance infinito vidro de spin de Ising fermiônico (VSIF) com campo magnético transverso ¡ e o modelo Hopfield vidro de spin Ising fermiônico (HVSIF) com ¡. Nestes modelos, os spins são escritos em termos de operadores fermiônicos. Nesse caso, há quatro autovalores possíveis para o operador Sz i , dois deles não magnéticos. Ambos os modelos são expressos em termos do formalismo das integrais de caminho fermiônicas com variáveis de Grassmann. Particularmente, os modelos VSIF e HVSIF são analisados no ensemble Grão Canônico, que permite variar o número médio de ocupação de férmions por sítio através do ajuste do potencial químico μ. O Potencial Grão Canônico é obtido por meio das soluções com simetria de réplicas e com um passo de quebra de simetria de réplicas utilizando a aproximação estática. Os resultados obtidos a partir dos modelos VSIF e HVSIF podem ser resumidos de acordo com a seguinte ordem: primeiramente, o modelo altamente frustrado VSIF é estudado. Essencialmente, para ¡ = 0, há o surgimento de transição de primeira ordem inversa para valores de μ, que é um mecanismo de diluição magnética. Consequentemente, as transições inversas puderam ser estudadas sob o efeito de flutuações quânticas quando um campo magnético transverso é introduzido nesse modelo. Como resultado principal, é mostrado que flutuações quânticas destroem as transições inversas no modelo VSIF. Em segundo lugar, o papel da frustração como ingrediente para um modelo apresentar naturalmente transições inversas é checado pelo modelo HVSIF, o qual permite analisar diversos regimes de frustração. De fato, é mostrado no modelo HVSIF que independentemente do nível de frustração, sempre há uma transição inversa para valores altos de μ. Finalmente, a introdução do campo ¡ no modelo HVSIF permite estudar de que forma o ajuste simultâneo de flutuações quânticas e intensidade do nível de frustração afetam as transições inversas nesse modelo. Como resultado, sugere-se que a relação entre diluição e a presença de uma fase frustrada tem um importante papel na produção de transições inversas. Em adição, quando efeitos de flutuações quânticas são introduzidas pelo ¡, o papel da diluição parece ser enfraquecido. Nesse caso, as transições inversas são destruídas no modelo HVSIF.

O objeto desta pesquisa consiste em investigar as propriedades estruturais, magnéticas e hiperfinas dos compostos pseudobinários de fases de Laves: Hf(Fe(1-x)Cr(x))2 e (Nb(1-x)Zr(x))Fe2. Para o Hf(Fe(1-x)Cr(x))2, preparamos as amostras como ligas policristalinas e as fundimos por síntese nas concentrações: x = 0,0; 0,1; 0,2; 0,3; 0,4; 0,5; 0,6; 0,7; 0,8; 0,9 e 1,0. O mesmo foi feito para as amostras de (Nb(1-x)Zr(x))Fe2 nas concentrações x = 0,0; 0,1; 0,2; 0,3; 0,4 e 0,5. Todas as amostras fundiram-se num forno de fusão de arco, sob atmosfera de argônio ultrapuro (99.999%). Em seguida investigamos a estrutura cristalina das ligas pelo método do pó, com a técnica de difratometria de Raios X (XRD), obtendo-se os parâmetros de rede e confirmando-se a estrutura de fase hexagonal C14 para as amostras Hf(Fe(1-x)Cr(x))2 nas concentrações 0,0 <= x < 0,9, bem como em todas as outras amostras de (Nb(1-x)Zr(x))Fe2. Depois, determinamos as propriedades magnéticas das ligas Hf(Fe(1-x)Cr(x))2 pela técnica de magnetização a baixas temperaturas em baixos campos magnéticos aplicados de 0 a 7 T e em altos campos magnéticos aplicados de 0 a 16 T. As suscetibilidades AC e DC a baixos campos magnéticos com temperaturas de 4,2 K a 300 K, FC e ZFC, nos indicaram que as ligas de concentrações 0,4 <= x < 0,8 apresentam comportamento \'vidro de spin\', sendo que em x <= 0,3 são aglomerados magnéticos com interação de curto alcance e em x = 0,9 é um superparamagnético. Por tanto, os valores dos momentos magnéticos por átomo de Fe foram calculados para todas as amostras. As medidas de spectroscopia Mössbauer das mesmas amostras de Hf(Fe(1-x)Cr(x))2, na temperatura ambiente, apresentam dois sextetos para a mostras com x = 0,2 e dois dubletos quadrupolares para as demais composições, atribuídos aos sítios cristalográficos 2a e 6h do Fe. Por outra parte, os espectros Mössbauer das amostras de (Nb(1-x)Zr(x))Fe2 à temperatura de 4,2 K, sem campo magnético aplicado e com campo magnético aplicado de 6 e 12 T, sugerem que estes compostos se encontram em um balanço em que coexistem as fases ferromagnéticas e antiferromagnéticas. Finalmente, notamos que no composto (Nb0.6Zr0.4)Fe2 há, uma possível existência de comportamento paramagnético nos Fe do sítio cristalino 2a e, ao mesmo tempo, pouca certeza que o valor do momento magnético seja nulo neste sítio cristalino. / The object of this research consists of investigating the structural, magnetic and hiperfine properties of the pseudobinar Laves phases compounds Hf(Fe(1-x)Cr(x))2 and (Nb(1-x)Zr(x))Fe2. We prepared polycristaline samples alloys and for synthesis melting in the concentrations: x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 e 1.0, for the Hf(Fe(1-x)Cr(x))2 and in the concentrations: x = 0.0, 0.1, 0.2, 0.3, 0.4 e 0.5 for (Nb(1-x)Zr(x))Fe2. We melted them in an arc furnace under pure Argon (99.999%) gas atmosphere. We investigated the cristaline structure of the alloys by the powder XRD technique, obtaining lattice parameters and confirming the structure of hexagonal phase C14 for the samples Hf(Fe(1-x)Cr(x))2 in the concentrations 0.0 <= x <= 0.9 and also in all the other samples produced of (Nb(1-x)Zr(x))Fe2. We investigate the magnetic properties of Hf(Fe(1-x)Cr(x))2 alloys bye the technique of magnetization at low temperatures and low magnetic field applied until 7 T and high magnetic field applied until 16 T. The susceptibility AC and DC at low magnetic fields and temperatures of 4.2 K until 300 indicated that alloys of concentrations 0.4 <= x < 0.8 show spin glass behavior, in x <= 0.3 they are magnetic clusters with short range interactions, and in x = 0.9 is superparamagnetic. The values of the magnetic moments for atom of Fe were calculated for all samples. We measured Mössbauer spectra of the same samples of Hf(Fe(1-x)Cr(x))2 at room temperature, obtaning two sextets for the samples with x < 0.2 and two quadrupolar doublets for the other compositions, that would be attributed to the cristalographic sites 2a and 6h. Also the Mössbauer spectrum of the samples (Nb(1-x)Zr(x))Fe2 at temperature of 4.2 K without magnetic field applied and with magnetic field applied of 6 and 12 T, suggest that those compounds show coexisting ferromagnetic and antiferromagnetic phases. We could note for the compound (Nb0.6Zr0.4)Fe2 a possible existence of the paramagnetic behavior in the Fe of the cristalographic site 2a, but the magnetic moment in this site is not zero.

A very important step in the art of cooking up models for the study of natural phenomena is the identification of the relevant ingredients. Taking into account too many details will lead to an overly complicated model, not at all useful to work with, but neglecting some crucial elements will lead to an equally useless model. So it is often the case that the actual experimental situation presents unavoidable sources of local randomness, whilst the analysed phenomenon does not really rely on presence/absence of such imperfections. For some other set of phenomena, however, disorder can play a crucial role, and must be carefully taken into account. Such is for example the case in certain phases of matter, the spin-glass phase, or the many-body localised phase. In this thesis we explore disorder in both of these situations and also as a theoretical means of testing the regime of liquidity in certain two-dimensional highly frustrated magnetic models. The focus here is placed on classical Heisenberg models defined on lattices consisting of clusters all sites of which interact mutually pairwise. This natural way to introduce frustration has been known in the literature to lead to so-called Coulomb spin-liquids, the single class of classical spin-liquids acknowledged to exist so far in Heisenberg models. Here we show that in fact two different classes of classical spin-liquids can be obtained from similarly defined frustrated models. In one of these, algebraic correlations exist at $T=0$, similar to the Coulomb phase, but the system exhibits a rather different low$-T$ effective action from the Coulomb phase. In the other class, the spin-liquid has spin correlations that decay exponentially with distance, with a correlation length smaller than a lattice spacing even at $T=0$. One special effect of disorder in these models, considered in the form of dilution by non-magnetic impurities, is to nucleate local degrees of freedom, so-called orphans, which express the concomitant spin-liquid phase through their non-trivial fractionalisation. When the associated spin-liquid exhibit algebraic correlations, it is also possible to find new effective spin-glass models as an effective $T=0$ description for interactions between the orphans, leading to so-called `random Coulomb magnets'. One part of this thesis is devoted to the first study of these new models. This investigation consists mainly of Monte Carlo simulations and numerical solution of the relevant large$-n$ equations ($n$ being the number of spin components). A clear spin-glass transition for infinitely large coupling strength is determined for the case of spins with an infinite number of components. The results presented on the situation for a finite number of spin components are more of an exploratory character, and large-scale simulations with further optimization schemes to ensure equilibration are still required to locate the transition. The final investigation treated in this thesis deals with the dynamics in a quantum model with disorder displaying the many-body localized phase, where in addition a periodic drive is applied. For a certain range of driving frequencies and amplitudes, it was found recently that the many-body localized phase is robust. These pioneering studies restricted themselves to an analysis of the stability of such a phase in the long time limit, while very little was known about the dynamics towards the asymptotic fate. Our study focuses on this aspect, and analyses the different dynamical behaviors as one varies the driving parameters, so that the many-body localized phase survives or is destroyed by the driving. We discover that on the border between these two asymptotic fates, a new dynamical behavior emerges, where the system heats up at a very slow, logarithmic in time, rate. / Die Bestimmung der wichtigsten Bestandteile stellt einen sehr wichtigen Schritt in der Kunst des Erstellens von Modellen dar. Die Annahme von zu vielen Details ergibt ein sehr kompliziertes, zu nichts zu gebrauchendes Modell, doch die Vernachlässigung von bedeutenden Zusammenhängen führt ebenfalls zu einem unbrauchbaren Ergebnis. Es ist so z.B. häufig der Fall, dass ein Experiment unter dem Einfluss von unvermeindlichen lokalen Zufälligkeiten steht, die allerdings kaum einen Einfluss auf ein beobachtetes Phänomen haben. Für gewisse Phänomene spielt Unordnung jedoch eine wesentliche Rolle und sie muss sehr genau in Betracht gezogen werden. Das ist für bestimmte Phasen, wie beispielsweise Spinglas oder die Vielteilchen-Lokalisation, der Fall. In dieser Dissertation untersuchen wir ungeordnete Systeme, die solche Phasen aufweisen. Außerdem verwenden wir Unordnung als ein theoretisches Werkzeug für die Analyse von bestimmten `Spinflüssigkeiten' in zweidimensionalen Spinmodellen. Der Fokus liegt hierbei auf klassischen Heisenberg Modellen definiert auf Gittern, die aus einer Anordnung von Clustern bestehen, sodass jede einzelne paarweise Heisenberg-Wechselwirkung innerhalb eines Clusters stattfindet. Dadurch weist das System geometrische Frustration auf und in mehreren Fällen tritt eine sogennante Coulomb Spinflüssigkeit ---die bislang einzig bekannte Klasse von klassischen Spinflüssigkeit in Heisenberg Modellen--- auf. Wir zeigen, dass mindestens zwei weitere Arten von klassischen Spinflüssigkeiten in solchen Modellen zu finden sind. Für die eine Klasse sind Spinkorrelationen zu erwarten, die algebraisch mit der Entfernung bei $T=0$ abnehmen, ähnlich wie für eine Coulomb Phase. Diese neu entdeckte Spinflüssigkeit lässt sich jedoch von der Coulomb Phase durch eine neue effektive Tieftemperatur-Theorie unterscheiden. Für die andere Klasse von Spinflüssigkeiten sind die Spinkorrelationen kurzreichweitig, und selbst bei $T=0$ nehmen sie exponentiell ab, mit einer Korrelationslänge, die kleiner als ein Gitterabstand ist. Unordnung, in der Form von nicht-magnetischen Störstellen, kann lokale Freiheitsgrade entstehen lassen (diese werden in der Literatur auch als `Orphans', Waisen, bezeichnet). Die Orphans verweisen durch ihre `Fraktionierung' eindeutig auf die nicht trivialen Korrelationen der spinflüssigen Phase. Falls die Spinflüssigkeit algebraische Korrelationen aufweist, findet man auch langreichweitige Wechselwirkungen zwischen den Orphans bei $T=0$. Dies führt zu neuen Spinglasmodellen, sogenannten `Random Coulomb Magnets'. Ein Teil dieser Dissertation ist der Untersuchung solcher Modelle gewidmet. Diese Untersuchung besteht hauptsächlich aus Monte Carlo Simulationen und numerischer Lösung der relevanten Large-$n$ Gleichungen (wobei $n$ hier auf die Anzahl an Spinkomponenten hinweist). In dem Fall von Spins mit unendlich vielen Spinkomponenten können wir einen eindeutigen Spinglas Phasenübergang für eine unendlich große Kopplungsstärke bestimmen. Die entsprechenden Ergebnisse für den Fall von Spins mit einer endlichen Anzahl an Spinkomponenten sind von einem exploratorischen Charakter. Zusätzliche Simulationen, die möglicherweise weitere Optimierungsschema verwenden um Äquilibrium zu gewährleisten, sind noch von nöten um eine eindeutige Aussage über den Übergang in solchen Fällen zu treffen. Der letzte Teil dieser Dissertation widmet sich der Untersuchung der Dynamik eines ungeordneten Quantenmodells. Das ausgewählte Modell weist die sogennante Vielteilchen-lokalisierte Phase auf, und wir untersuchen insbesondere den Effekt eines periodischen Antriebs auf die Dynamik des Systems. Für eine bestimmte Auswahl der Antriebs-frequenz und -amplitude, wurde es bereits vor kurzem bewiesen, dass die Vielteilchen-lokalisierte Phase diese Störung übersteht. Unsere Studie ist darauf ausgelegt, wie sich die Dynamik des Systems durch Variation der Antriebsparameter ändert, so dass die Vielteilchen-lokalisierte Phase für lange Zeit entweder den Antrieb übersteht oder von ihm zerstört wird. Wir konnten dadurch entdecken, dass an der Grenze zwischen diesen beiden Fällen ein neues dynamisches Verhalten entsteht, bei der das System eine sehr langsame, logarithmisch mit der Zeit, Erwärmung aufweist.