A condutância de fios quânticos definidos em uma geometria de \"split gate\" varia em platôs quantizados de 2e2/h em relação à ocupação dos seus modos transversais [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. Em gráficos da condutância esta ocupação é dada pelo potencial aplicado aos eletrodos que formam o fio. Em 1996 observou-se experimentalmente nestes gráficos [Thomas et al. Phys. Rev. Lett. 77, 135 (1996)] que quando apenas um modo transversal é ocupado a condutância exibe um platô anômalo adicional em 0.7X2e2/h. Desde então, a origem desta anomalia 0.7 é associada a fenômenos dependentes de spin, porém sua descrição teórica permanece como importante objeto de pesquisa. Recentemente, observou-se que na presença de altos campos magnéticos, cruzamentos de modos transversais de spins opostos também geram estruturas anômalas no gráfico da condutância [Graham etal. Phys. Rev. Lett. 91, 136404 (2003)]. Os análogos 0.7, assim chamados devido à semelhança com a anomalia 0.7, são usualmente relacionados ou como anti-crossings ou como transições de fase magnética. Motivado pela concordância quantitativa com experimentos de um trabalho anterior em magnetotransporte em 2DEGs e transições de fase de ferromagnetismo de efeito Hall quântico via teoria do funcional da densidade dependente de spin (SDFT) [Freire e Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], propomos aqui um modelo similar para estudar na magnetocondutância de fios quânticos. Utilizamos (i) a SDFT resolvendo as equações de Kohn-Sham autoconsistentemente dentro da aproximação de densidade local de spin para obter a estrutura eletrônica do fio quântico e (ii) o formalismo de Landauer-Büttiker para calcular a condutância do fio no regime de resposta linear. Em nosso modelo, a anomalia e os análogos 0.7 aparecem devido a transições ferromagnéticas que rearranjam de forma abrupta os modos transversais do fio quântico próximos ao nível de Fermi. Nossos resultados teóricos apresentam boa concordância com os dados de Graham et al. / At low temperatures the conductance of a quantum wires exhibits plateaus at integer multiples of 2e2/h due to the quantization of the transverse modes [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. This conductance behavior is understood within an independent particles model. In 1996 Thomas et al.[Phys. Rev. Lett. 77, 135 (1996)] showed experimentally that when only one transverse mode is occupied, the conductance displays an additional plateau at 0.7 X 2e2/h the so-called 0.7 anomaly. Further experiments have shown that in the presence of high in-plane magnetic fields, similar structures also appear in the conductance near the crossings of spin-split transverse modes [Graham et al. Phys. Rev. Lett. 91, 136404 (2003)]. These so-called 0.7 analogs, due to their similarity to the 0.7 anomaly, are usually related to either anti-crossings or magnetic phase transitions. Motivated by the quantitative agreement with experiments of a previous theoretical work on magnetotransport in 2DEGs and quantum Hall ferromagnetic phase transitions via the Spin Density Functional Theory (SDFT) [Freire and Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], here we propose a similar model to investigate the magnetoconductance of interacting quantum wires. We use (i) the SDFT via the Kohn-Sham self-consistent scheme within the local spin density approximation to obtain the quantum wire electronic structure and (ii) the Landauer-Büttiker formalism to calculate the conductance of a quantum wire in the linear response regime. Our results show good agreement with the data of Graham et al.

<p>The subjects of the thesis are theoretical first principles calculations of X-ray absorption (XA) spectra and current induced spin transfer torque. XA spectra calculated from atomic multiplet theory and from band structure calculations, based on density functional theory for La_0.7Sr_0.3MnO₃ have been compared to experiment. The comparison shows that the effect of the core hole created in the XA process must be considered in the calculation. The theory by Mahan, Nozières and De Dominicis (MND) of dynamical core hole screening is generalised to multiband systems and implemented in first principle calculations. Calculations of the XA spectrum of graphite, including dynamical core hole screening, are shown to better reproduce the relative intensity of the peaks in the experimental spectrum compared to static calculations based on the local density of state of a core excited atom. In combination with experiments the developed method to calculate XA spectra is used to investigate the electronic structure of mixed valent Yb, hydrogen storage in carbon nanotubes and the structure of liquid water. Moreover, a method to calculate the current induced spin transfer torque in materials with a helical spin density wave from first principles has been developed. The method is applied to rare earth metals and it is shown that a current along the axis of spin rotation induces a torque which gives rise to a rotation of the magnetisation direction.</p>

The subjects of the thesis are theoretical first principles calculations of X-ray absorption (XA) spectra and current induced spin transfer torque. XA spectra calculated from atomic multiplet theory and from band structure calculations, based on density functional theory for La0.7Sr0.3MnO3 have been compared to experiment. The comparison shows that the effect of the core hole created in the XA process must be considered in the calculation. The theory by Mahan, Nozières and De Dominicis (MND) of dynamical core hole screening is generalised to multiband systems and implemented in first principle calculations. Calculations of the XA spectrum of graphite, including dynamical core hole screening, are shown to better reproduce the relative intensity of the peaks in the experimental spectrum compared to static calculations based on the local density of state of a core excited atom. In combination with experiments the developed method to calculate XA spectra is used to investigate the electronic structure of mixed valent Yb, hydrogen storage in carbon nanotubes and the structure of liquid water. Moreover, a method to calculate the current induced spin transfer torque in materials with a helical spin density wave from first principles has been developed. The method is applied to rare earth metals and it is shown that a current along the axis of spin rotation induces a torque which gives rise to a rotation of the magnetisation direction.

A condutância de fios quânticos definidos em uma geometria de \"split gate\" varia em platôs quantizados de 2e2/h em relação à ocupação dos seus modos transversais [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. Em gráficos da condutância esta ocupação é dada pelo potencial aplicado aos eletrodos que formam o fio. Em 1996 observou-se experimentalmente nestes gráficos [Thomas et al. Phys. Rev. Lett. 77, 135 (1996)] que quando apenas um modo transversal é ocupado a condutância exibe um platô anômalo adicional em 0.7X2e2/h. Desde então, a origem desta anomalia 0.7 é associada a fenômenos dependentes de spin, porém sua descrição teórica permanece como importante objeto de pesquisa. Recentemente, observou-se que na presença de altos campos magnéticos, cruzamentos de modos transversais de spins opostos também geram estruturas anômalas no gráfico da condutância [Graham etal. Phys. Rev. Lett. 91, 136404 (2003)]. Os análogos 0.7, assim chamados devido à semelhança com a anomalia 0.7, são usualmente relacionados ou como anti-crossings ou como transições de fase magnética. Motivado pela concordância quantitativa com experimentos de um trabalho anterior em magnetotransporte em 2DEGs e transições de fase de ferromagnetismo de efeito Hall quântico via teoria do funcional da densidade dependente de spin (SDFT) [Freire e Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], propomos aqui um modelo similar para estudar na magnetocondutância de fios quânticos. Utilizamos (i) a SDFT resolvendo as equações de Kohn-Sham autoconsistentemente dentro da aproximação de densidade local de spin para obter a estrutura eletrônica do fio quântico e (ii) o formalismo de Landauer-Büttiker para calcular a condutância do fio no regime de resposta linear. Em nosso modelo, a anomalia e os análogos 0.7 aparecem devido a transições ferromagnéticas que rearranjam de forma abrupta os modos transversais do fio quântico próximos ao nível de Fermi. Nossos resultados teóricos apresentam boa concordância com os dados de Graham et al. / At low temperatures the conductance of a quantum wires exhibits plateaus at integer multiples of 2e2/h due to the quantization of the transverse modes [van Wees et al. Phys. Rev. Lett. 60, 848 (1988) & Wharam et al. J. Phys. C: solid state phys. 21, L209 (1988)]. This conductance behavior is understood within an independent particles model. In 1996 Thomas et al.[Phys. Rev. Lett. 77, 135 (1996)] showed experimentally that when only one transverse mode is occupied, the conductance displays an additional plateau at 0.7 X 2e2/h the so-called 0.7 anomaly. Further experiments have shown that in the presence of high in-plane magnetic fields, similar structures also appear in the conductance near the crossings of spin-split transverse modes [Graham et al. Phys. Rev. Lett. 91, 136404 (2003)]. These so-called 0.7 analogs, due to their similarity to the 0.7 anomaly, are usually related to either anti-crossings or magnetic phase transitions. Motivated by the quantitative agreement with experiments of a previous theoretical work on magnetotransport in 2DEGs and quantum Hall ferromagnetic phase transitions via the Spin Density Functional Theory (SDFT) [Freire and Egues, Phys. Rev. Lett. 99, 026801 (2007) & Ferreira et al. Phys. Stat. Sol. (c) 3, 4364 (2006)], here we propose a similar model to investigate the magnetoconductance of interacting quantum wires. We use (i) the SDFT via the Kohn-Sham self-consistent scheme within the local spin density approximation to obtain the quantum wire electronic structure and (ii) the Landauer-Büttiker formalism to calculate the conductance of a quantum wire in the linear response regime. Our results show good agreement with the data of Graham et al.

Apresentamos uma teoria para obtenção de seções de choque de espalhamento inelástico de luz via mecanismos de flutuações de densidade de carga e spin em um gás de elétrons não-uniforme formado por um sistema multi-camadas de GaAs periodicamente &#948-dopadas com concentração eletrônica relativamente alta. Os cálculos, onde estão inclusos efeitos da interação coulombiana entre os portadores, efeitos de correlação e troca dinâmicos e o acoplamento com fônons LO, foram efetuados em condições de extrema ressonância com o gap de split-off do GaAs. Em tais condições, a estrutura detalhada dos níveis de energia dos buracos de spin-split torna-se extremamente importante e é fundamental para o surgimento do espectro de partícula independente apresentado nos espectros polarizados. Este comportamento é revelado através da seção de choque de espalhamento que consiste da parte imaginária de uma função resposta constituída de um termo de caráter de partícula independente e outro de caráter coletivo. De forma a levar em conta o amortecimento das flutuações de densidade, propõe-se uma função espectral baseada na conservação da corrente local. Comparação com formas de linha experimentais disponíveis para o caso de espectros despolarizados mostram excelente concordância. No caso dos espectros polarizados a concordância se deu em nível semi-quantitativo, já que excitações de caráter coletivo obtidas experimentalmente apresentaram intensidade menor do que aquelas fornecidas pela teoria. Tal discrepância é atribuída a efeitos de desordem introduzidas no processo de dopagem e que implicam na quebra das regras de conservação de momentum. / We present a theory for the inelastic light scattering cross-section for the mechanisms of charge and spin-density fluctuations in the relatively high concentration of the non-uniform electron gas of a multi-layered &#948-doped GaAs system. The calculations are done in conditions of extreme resonance with the spin-split edge of GaAs and include the effects of Coulomb interactions between the carriers, dynamical exchange-correlations and coupling with LO phonons. In such conditions, the detailed energy level structure of the spin-split holes becomes extremely important and is responsible by the single-particle behavior presented in the polarized spectrum. This behavior revealed by the scattering cross-section derived from the imaginary part of a response function, consists of a term showing single particle character and another displaying collective character. To include the damping of the density fluctuations, a spectral function is proposed based on the foreknowledge that the local current must be conserved. Comparison with the available experimental line-shapes for the depolarized spectra show excellent agreement. In the case of polarized spectra the agreement was given in semi-quantitative terms as experimental collective excitations present less intensity than those calculated by the theory. Such difference is attributed to disorder effects produced during the doping process which results in break down of momentum conservation rules.

Le travail présenté dans cette thèse porte sur l'application de la spectroscopie RMN pour l'étude de matériaux magnétiques moléculaires. Une attention particulière est consacrée aux systèmes magnétiques possédant des cyanures : des briques de construction, des complexes de cyanure polymétalliques et des réseaux étendus (analogues bleu de Prusse) à faible dimension. Par le biais d’exemples spécifiques, nous essayons de montrer que la spectroscopie RMN peut être utilisée comme une puissante sonde magnétique et structurale des systèmes paramagnétiques (chapitre 2, 4, 5). De plus, la RMN est également utilisée pour étudier l’équilibre de spin, en solution, d’une famille de complexes à transition de spin Fe(II) (chapitre 3). En dehors de la spectroscopie RMN, différentes techniques comprenant la spectroscopie FT-IR et UV-Vis (à l'état solide et solution), l’analyse thermogravimétrique (ATG), la diffraction aux rayons X, la résonance paramagnétique électronique (RPE), la diffraction de neutrons polarisés (uniquement pour le composé [Fe(Tp)(CN)3]-) et la magnétométrie SQUID sont utilisées afin d’obtenir une caractérisation structurale et électronique fiable des matériaux magnétiques sondés. Ces techniques permettent également de rationaliser et de soutenir les résultats obtenus à partir de spectroscopie RMN. Par ailleurs, des calculs théoriques de certains composés ont été effectués à l’aide de la méthode DFT (en collaboration avec les théoriciens) afin de soutenir les observations expérimentales. Le premier chapitre de la thèse revient sur quelques concepts de base de la spectroscopie RMN, à l'état solide et en solution, et expose brièvement quelques exemples d'études de systèmes paramagnétiques en RMN. La partie expérimentale de ce même chapitre met l'accent sur l'utilisation de la spectroscopie RMN 13C et 15N à l'état solide pour sonder les propriétés magnétiques locales, estimer la densité de spin et sa répartition sur les ligands cyanures. Une question fondamentale pour les magnéto-chimistes est ainsi soulevée : comment l'électron non apparié, délocalisé de la source paramagnétique sur le ligand pontant, donne t-il naissance à l'interaction magnétique d'échange? Dans le troisième chapitre de la thèse, la spectroscopie RMN 1H paramagnétique en solution a été utilisée pour étudier des complexes mononucléaires Fe(II) commutables, c’est-à-dire pouvant subir un changement de leurs propriétés magnétiques (et optiques) sous l’influence de stimuli externes. L’équilibre de transition de spin thermo-induit des complexes [FeII(R-bik)3]2+ a été étudié par RMN 1H, à température variable, et les résultats ont été comparés à ceux obtenus avec des techniques différentes. Le quatrième chapitre traite de la caractérisation magnéto-structurale de certains complexes polynucléaires fondé sur la nouvelle brique de construction cyanurée [CoIII(Me2Tp)(CN)3]-. La spectroscopie RMN du noyau quadripolaire 59Co est employée comme sonde pour suivre à différente température, le comportement magnétique des systèmes moléculaires contenant du Co(III). La RMN 59Co permet par ailleurs, l’étude du mécanisme d'extension de spin sur le pont cyanure... / The work presented in this Ph.D. dissertation focuses on the application of NMR spectroscopy for studying molecular magnetic materials. A particular attention is devoted to cyanide-contaning magnetic systems: cyanide building blocks, low-dimensional polymetallic complexes and extended networks (Prussian blue analogues). Basically, we try to show through selected examples that NMR can be used as a powerful structural and magnetic probe to address a variety of questions related to paramagnetic materials (chapter 2, 4, 5). Besides, we also use here NMR to study spin equilibrium in solution in a family of Fe(II) spin-crossover complexes (chapter 3). Apart from the use of various NMR techniques, different physical techniques including FT-IR and UV-Vis spectroscopy (in solid-state and solution), TGA, X-ray diffraction, EPR spectroscopy, Polarized neutron diffraction (only for [Fe(Tp)(CN)3]- compound), and SQUID magnetometry are used to obtain reliable structural and electronic characterization of the probed magnetic materials and to rationalize and support the results obtained from NMR spectroscopy. Theoretical DFT calculations (in collaboration with theoreticians) are also performed on some selected compounds to support the experimental observations. The first chapter of the dissertation provides a short overview of some basic concepts of NMR spectroscopy in solid state and in solution and gives very briefly some few examples of NMR studies on a variety of paramagnetic systems. The first experimental chapter of the thesis focuses on the use of 13C and 15N solid-state NMR spectroscopy to probe local magnetic properties and to estimate the spin density and its distribution onto the cyanide ligands. It thus addresses a fundamental question for magnetochemists: how the unpaired electron delocalized from the paramagnetic source onto the bridging ligand to give rise to the magnetic exchange interaction? In the third chapter of the thesis, the solution state paramagnetic 1H NMR spectroscopy has been used to study Fe(II) mononuclear switchable complexes, which undergo a change of their magnetic (and optical) properties upon external stimuli. More specifically, the thermally-induced spin-crossover equilibria of the [FeII(R-bik)3]2+ complexes has been studied by variable temperature 1H NMR and the results are compared to those obtained by other techniques. The fourth chapter deals with the magneto-structural characterization of some polynuclear complexes based on the new cyanide-based [CoIII(Me2Tp)(CN)3]- building block. NMR spectroscopy of the quadrupolar 59Co nucleus is used as a probe for following the magnetic behaviour of these Co(III) containing molecular systems at different temperature. It also allows to investigate the spin extension mechanism over the cyanide bridge. Finally the chapter 5 intends to explore the use of 113Cd NMR spectroscopy as both a local structural and magnetic probe for studying Fe-Cd based molecular materials...

Techniques based on principle of nuclear magnetic resonance (NMR) belong to the most modern methods for studying physical, chemical and biological properties of materials [1]. Their universality predestinates them for application in a wide range of scientific disciplines, e.g. in medicine to study properties of tissues. Advantages of techniques utilizing principle of NMR consist in their noninvasiveness and thoughtfulness to human health or studied material. In addition, no undesirable effects of magnetic force field have been so far proved by research. Objectives of this Diploma Thesis are evaluation of MR images of tissue cultures and determination of protons amount included in them. Theoretic part of the Thesis is devoted to the bases of NMR and provides basic overview of MR methods. The spin echo method (SE) is described in more details, including the process of assessment of technique’s parameters, e.g. general magnetization. Practical part of Diploma Thesis is focused on determination of integral of image intensity of clusters of early somatic embryos. Intensity integrals characterizing number of protons in growing cluster were calculated from MR images of spruce embryos contaminated by lead. The intensity of an image weighted by spin density is proportionate to the number of proton nuclei in the chosen slice. The Thesis describes further evaluation of relaxation time T2 from MR images weighted by spin density. Following part is dealing with determination of diffusion from MR images with application of compensation methods, three-measurement arrangement and presentation of obtained results. Images were processed by use of MATLAB and MAREVISI programs.

Nous avons développé un modèle et un programme d'affinement joint des densités de charge et spin. Lors des premiers tests plusieurs difficultés sont apparues et ont été étudiées puis résolues notamment par la mise en place de contraintes. Après la mise en place d'un programme stable d'affinement joint nous avons testé celui-ci sur le complexe MnCu(pba)...(H2O)3...2H2O, ou pba représente le 1,3-propylenbis(oxamato) en réutilisant les données provenant d'une expérience de diffraction de neutrons polarisés et en effectuant une nouvelle expérience de diffraction des rayons X à 10K, température à laquelle l'expérience de diffraction des neutrons polarisés a été conduite. Cette étude a permis de tester trois schémas de pondération, ainsi que les contraintes. Ces tests ont montré que l'affinement joint permet de retrouver les résultats des différents affinements séparés mais aussi d'aller plus loin en autorisant un affinement de la densité de spin avec plus de paramètres pertinents. Suite à ces premiers tests nous nous sommes intéressés à un complexe azido cuivre (Cu2L2(N3)2 avec L=1,1,1-trifluoro-7-(dimethylamino)-4-méthyle-5-aza-3-heptène-2-onato). L'affinement joint a permis d'avoir accès, pour la première fois, à la densité de valence expérimentale résolue en spin et d'affiner également des paramètres de contraction/dilatation différents pour la valence avec un spin up ou un spin down. Dans le dernier chapitre nous avons étudié un complexe de cobalt qui présentait des propriétés magnétiques intéressantes. Cependant la particularité magnétique du composé venant d'une forte anisotropie magnétique a rendu l'étude par affinement joint délicate dans un premier temps, c'est pourquoi nous avons étudié ce composé uniquement d'un point de vue de la densité de charge. Cette étude a tout de même permis de mettre en évidence expérimentalement à 100K un angle de torsion de 39° entre les axes principaux des atomes de cobalt, prédit par la théorie / We developed a model and a refinement program for charge and spin densities. During the first tests several difficulties have arisen and have been investigated and solved by implementation of constraints. After the establishment of stable joint refinement program, we tested it on the MnCu(pba)...(H2O)3...2H2O, with pba = 1,3-propylenbis(oxamato) complex reusing data from an experiment of polarized neutron diffraction and making a new experience of X-ray diffraction at 10K. This study tested three weighting schemes and constraints. These tests showed that the joint refinement give access to the same results as the separated refinements but also allow us to go further by refining the spin density with more pertinent parameters. Following these initial tests, we were interested in a copper azido complex (Cu2L2(N3)2 with L=1,1,1-trifluoro-7-(dimethylamino)-4-methyl-5-aza-3-hepten-2-onato). The joint refinement give us access for the first time to the experimental spin-resolved valence density and also to refine the parameters of contraction / expansion for spin up or spin down separately. In the last chapter we studied a cobalt complex which shows interesting magnetic properties. However, the magnetic properties of the compound come from a high magnetic anisotropy which complicates a study by joint refinement. That is why we studied only the charge density of this compound. This study still allowed to show experimentally a torsion angle of 39° between the principal axes of the cobalt atoms, which was predicted by a previous theoretical study

Une étude théorique basée sur la théorie de la fonctionnelle de la densité (DFT) a été réalisée sur un ensemble de complexes organométalliques mono, di et trinucléaires à base de fer, de ruthénium ou de platine. Les résultats obtenus sur les complexes mononucléaires à base de fer révèlent que la longueur du chaînon π de carbone n'a qu'une influence mineure sur les propriétés électroniques mais affectent les propriétés spectroscopiques. Une étude entreprise sur des systèmes contenant un ligand aromatique polycyclique a montré que la présence de molécules de solvant coordonnant abaisse les barrières énergétiques et par conséquence, facilite le réarrangement haptotropique du greffon organoruthénium sur le ligand organique. L'étude théorique réalisée sur des nouveaux systèmes de type [2]rotaxane a révélé que la longueur du chaînon π du fil moléculaire enfilé au travers d'un macrocycle influence les énergies d'interaction non covalente dans ces systèmes. Il a été montré que ces interactions non covalentes sont principalement dues à des liaisons hydrogène formées entre le macrocycle et le fil moléculaire. / A theoretical study based on density functional theory (DFT) was performed on several series of organometallic mono, bi and trinuclear iron, ruthenium and platinum based complexes. The results on mononuclear iron based complexes indicate that the length of the π carbon bridge in these systems has only a minor influence on the electronic properties but affect somewhat the spectroscopic properties. A study was conducted on systems containing polycyclic aromatic ligand showing that the presence of a coordinating solvent molecule in the viscinity of the metal atom bound on top of the polycycle strongly lowers the energy barriers and consequently facilitates the haptotropic rearrangement of the grafted organoruthenium entity. The theoretical study of new systems of [2]rotaxane type has revealed that the length of the π bridge of the molecular wire threaded in a macrocycle influences the weak noncovalent interaction energies in these systems. It has been shown that these noncovalent interactions are mainly due to hydrogen bonds formed between the macrocycle and the threaded molecular wire.

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.