La loi de Moore est basée sur l’observation empirique qu’environ chaque deux années, le nombre de transistors dans des circuits denses intégrées double. Cette tendance s'est bien maintenue au cours des dernières décennies (années 1970 et suivantes). Cependant, la miniaturisation continue des transistors entraîne une augmentation significative des pertes d’énergie par le courant de fuite, ce qui augmente la consommation d'énergie de veille. Cette perte d’énergie est devenue un problème majeur dans la microélectronique pendant les dernières années, ce qui rend plus difficile le développement des nouvelles technologies. L’une des solutions est de placer des éléments mémoire non-volatile dans le puce, qui retiennent la configuration du transistor pendant la mise hors tension et permettent de le restaurer à la mise sous tension. Les Magnetic Random Access Memories (MRAM) sont considérées par l'ITRS comme un candidat crédible pour le remplacement potentiel de SRAM et de DRAM au-delà du nœud technologique de 20 nm. Bien que les exigences de base pour la lecture et l'écriture d'un élément de mémoire unique sont remplies, l'approche actuelle basée sur Spin Torque Transfer (STT) souffre d'un manque inné de la flexibilité. Le courant électrique entraine le retournement de l’aimantation de la couche ferromagnétique libre par le transfert du moment angulaire d’une couche ferromagnétique adjacent. Ainsi les éléments de mémoire basées sur STT ont deux terminaux dont les voies de courant pour « écriture » et « lecture » sont définies par la forme de «pillar». L’optimisation indépendant des paramètres d’écriture et de lecture reste, donc, très difficile. Au même temps, la densité de courant trop haute, nécessaire pour écrire, conduit à la vieillissement prémature du jonction tunnel. En conséquence, l’intégration MRAM dans la technologie du semi-conducteur reste, donc, difficile.Démonstrations récentes de reversement d’aimantation entrainées par l’injection d’un courant planaire dans des heterostructures métal lourd/ferromagnet ont attiré l’attention croissante sur les couples de spin basé sur le transfert du moment angulaire par l’effet Hall de spin et les effets d’interface. Contrairement à STT-MRAM, la SOT-MRAM a trois terminaux, dont les voies de courant pour « écriture » et « lecture » sont indépendantes. Cela permet d’améliorer les paramètres « écriture » et « lecture » de manière indépendante. Pour contrôler et optimiser les SOT il est nécessaire de comprendre très bien leur origine. Cela reste l’une des plus importantes questions dont on n’a pas une réponse définitive. Dans ce contexte, plusieurs études ont conclu sur un modèle basé seulement sur l’effet Hall de spin, en même temps que d’autres ont suggéré un modèle basé sur une contribution combiné de l’effet Hall de spin et l’effet d’interface.L’objectif de cette thèse est de réaliser une étude systématique sur les effets d’interface sur les SOT dans des heterostructures métal lourde/ferromagnet a base de Pt, avec aimantation planaire.Dans ce but, cette thèse explore trois voies différentes. Premièrement nous avons modifié le rapport entre les effets d’interface et les effets bulk en changeant l’épaisseur de la couche de Pt et en suivant l’évolution des SOT. En deuxième nous avons exploré des différents empilements métal lourde/ferromagnet afin d’étudier différentes interfaces. Finalement, nous avons changé les propriétés des interfaces soit par changer la structure cristalline soit par oxydation. La technique de mesure, la méthode d’analyse de données associé et les aspects théoriques nécessaires pour l’interprétation des données sont aussi détaillés dans ce manuscrit. / Moore’s law is based on empirical observation and states that every two years approximately, the number of transistors in dense integrated circuits doubles. This trend has held up well in the past several decades (1970s and onwards). However, the continuous miniaturisation of transistors brings about a significant increase in leakage current, which increases the stand-by power consumption. This energy loss has become a major problem in microelectronics during the last several years, making the development of new technologies more difficult. One of the solutions that can address this issue is to place non-volatile memory elements inside the chip, that retain the configuration of the transistor during power-off and allow to restore it at power-on. Magnetic Random Access Memories (MRAM) are considered by the ITRS as a credible candidate for the potential replacement for SRAM and DRAM beyond the 20 nm technological node. Though the basic requirements for reading and writing a single memory element are fulfilled, the present approach based on Spin Transfer Torque (STT) suffers from an innate lack of flexibility. The electric current drives the magnetization switching of a free ferromagnetic layer by transferring angular momentum from an adjacent ferromagnet. Therefore, STT-based memory elements are two terminal devices in which the “pillar” shape defines both the “read” and the “write” current paths. Independent optimisation of the reading and writing parameters is therefore difficult, while the large writing current density injected through the tunnel barrier causes its accelerated ageing, particularly for fast switching. Consequently, the integration of MRAM into semiconductor technology poses significant difficulties.Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal (HM)/ferromagnet (FM) heterostructures have drawn increasing attention to spin-torques based on orbital-to-spin momentum transfer induced by Spin Hall and interfacial effects (SOTs). Unlike STT-MRAM, the in-plane current injection geometry of SOT-MRAM allows for a three-terminal device which decouples the “read” and “write” mechanisms, allowing the independent tuning of reading and writing parameters. However, an essential first step in order to control and optimise the SOTs for any kind of application, is to better understand their origin. The origin of the SOTs remains one of the most important unanswered questions to date. While some experimental studies suggest a SHE (Spin Hall Effect)-only model for the SOTs, others point towards a combined contribution of the bulk (SHE) and interface (Rashba Effect and Interfacial SHE). At the same time, many studies start with a SHE only hypothesis and do not consider interfacial effects. Furthermore, there are not so many systematic studies on the effects of interfaces. This thesis tries to fill in this gap, by providing a systematic study on the effects of interfaces on the SOTs, in Pt-based NM/FM/HM multilayers with in-plane magnetic anisotropy. For this purpose, this thesis explores three different, but related avenues. First, we changed the interface/bulk effect ratio by modifying the Pt thickness and following the evolution of the SOTs. Second, we explored different HM/FM/NM combinations, in order to study different interfaces. And third, we changed the properties of the interfaces by changing the crystallographic structure of the interface and by oxidation. The measurement technique and associated data analysis method, as well as the theoretical considerations needed for the interpretation of the results are also detailed in this manuscript.

Cette thèse étudie les régions d'irrégularité marquée dans les spectres électroniques des dimères alcalins. Ces perturbations, qui rendent difficile voire impossible l’attribution habituelle et sans ambiguïté des nombres quantiques moléculaires, sont produites par de forts couplages spin-orbite. Des méthodes numériques nous permettent de résoudre l'équation de Schrödinger radiale pour de tels systèmes. Nous avons élaboré des stratégies permettant d’utiliser des formes analytiques pour les courbes d’énergie potentielle moléculaire et pour les fonctions de couplage spin-orbite. Nous prenons en compte les perturbations d’origine spin-orbite, et les effets de couplage spin-rotation dans des calculs d’états couplés, en utilisant des techniques numériques de différences finies et les méthodes de collocation, avec hamiltoniens moléculaires appropriés. La méthode a été testée avec succès sur des données publiées sur NaK, et également sur des données expérimentales obtenues pour des paires d’états électroniques excités fortement couplés (A 1Σ+(u) et b 3Π(u) pour Rb2 et pour NaCs), suite à des expériences de fluorescence induite par laser analysée par spectrométrie de Fourier. En optimisant les paramètres des potentiels moléculaires et des fonctions spin-orbite par le biais d’ajustements itératifs par moindres carrés non-linéaires, les modèles permettent d'atteindre la précision expérimentale (limite Doppler) actuelle. Les résultats sont controlés par étude des effets de substitution isotopique et des intensités observées. Un schéma pour refroidissement optique de NaCs a été proposé à partir des probabilités de transition calculées. / This thesis investigates regions of marked irregularity in the electronic spectra of alkali dimers. These perturbations, which make it difficult (if not impossible) to give the usual unambiguous assignment of molecular quantum numbers, are caused by strong spin-orbit coupling between close-lying electronic states. Numerical methods allow us to solve the radial Schrödinger equation for such systems. We have developed strategies to use analytical forms for molecular energy potentials and spin-orbit coupling functions in order to represent such situations, using Hund’s case (a) basis sets. Calculations are then performed using finite difference and collocation methods, with appropriate coupled-channel molecular Hamiltonians that take into account spin-orbit and spin-rotation interactions. Our analytical mapping procedure, based on a reduced variable representation of the radial coordinate, improves the computational efficiency for uniform finite-difference grid solutions of the coupled channel equations. The method has been successfully tested on published data for NaK (D 1Πd 3Πstates), and also on experimental data obtained by laser induced fluorescence and Fourier transform spectrometry for pairs of strongly coupled excited electronic states of heavier alkali species, Rb2 and NaCs (A 1Σ+(u) and b 3Π(u) states). Optimising the parameters of molecular potentials and spin-orbit functions through iterative non-linear least squares fits, the models achieve the current (Doppler limited) experimental level of precision. The validity of the results is confirmed by investigating the effects of isotopic substitution and intensity patterns. Results have been used to predict transition probabilities for a two-step optical cooling cycle for the NaCs molecule. / Данная диссертационная работа посвящена изучению возмущений в электронно-колебательно-вращательных спектрах димеров щелочных металлов. Нерегулярности вколебательно-вращательной структуре, вызванные сильным спин-орбитальнымвзаимодействием близко лежащих электронных состояний осложняют, а иногда и делаютневозможным, однозначное отнесение линий в молекулярных спектрах. В данной работе, врамках метода связанных колебательных каналов, разработана модель неадиабатическогоописания энергетических и радиационных свойств синглет-триплетных комплексоввозмущенных состояний, подчиняющихся промежуточным a-b-c случаям связи по Гунду взависимости от величины вращательного квантового числа и межъядерного расстояния.Ключевыми параметрами этой модели являются потенциальные кривые рассматриваемыхсостояний и функции спин-орбитального взаимодействия. Аналитическая замена радиальнойкоординаты в сочетании с аналитическим представлением варьируемых функций позволилиповысить эффективность решения системы уравнений Шредингера для рассматриваемыхсистем, а также улучшить экстраполяционные свойства неэмпирических функцийпотенциальной энергии. Предложенный подход использован для анализа (представленных влитературе) ровибронных энергий молекулы NaK (D1Π , d3Π состояния), а такжеоригинальных экспериментальных данных, полученных в данной работе методом лазерно-индуцированной флуоресценции для сильно возмущенных электронных состояний Rb2 иNaCs ( A1Σ(u)+ и b3Π(u) состояния). Проверка адекватности полученных структурныхпараметров выполнена путем предсказания и сопоставления с экспериментом (1)энергетических свойств для различных изотопомеров; (2) распределения относительныхинтенсивностей в спектрах лазерно-индуцированной флуоресценции с локальновозмущенных уровней комплексов в основное электронное состояние. Результаты,полученные для молекул NaCs, были использованы для расчета оптимальных путейдвухступенчатой оптической конверсии неустойчивых электронно-возбужденных молекул,образующихся в результате столкновений холодных атомов, на низший по энергиировибронный уровень основного электронного состояния.

Notre étude porte sur des matériaux à effets relativistes importants. L'hamiltonien semi-relativiste, couplé aux équations de Maxwell (EM), permet de déduire les sources de courant et de densité, incluant des termes de second ordre (polarisations de spin et de Darwin). Différents modèles sont développés par expansion des EM. L'étude ab initio montre que (1) le désordre atomique peut produire le ferrimagnétisme (FM) dans GaFeO3 (GFO) multiferroïque, (2) les états 3d Fe des octaèdres déformés ont une levée de dégénérescence tétraédrique (théorie du champ cristallin), (3) la polarisation électrique concorde avec l'expérience, (4) le mécanisme magnétoélectrique (ME) direct est insuffisant pour expliquer le ME observé. Pour Cr2O3, le calcul de l'état massif sous contraintes biaxiales n'explique pas son FM, la taille de l'échantillon ou l'excès d'oxygène pourrait de fait être important. Enfin, nous avons développé le XAS et le XMCD dans le code VASP et calculé ces spectres pour GFO. / We studied the physics of materials where relativistic effects are important. We first coupled the semi-relativistic Hamiltonian with the Maxwell's equations, and derived the current and density sources, which included second-order terms like the spin and Darwin polarizations. Different models were developed, by expanding the Maxwell's equations. We then performed ab initio studies to explain (1) site disorders as the origin of ferrimagnetism in multiferroic GaFeO3 (GFO), (2) crystal-field theory where the Fe 3d states at the deformed octahedra have tetrahedral splittings, (3) the electric polarization as a function of temperature, and (4) the insufficiency of the direct magnetoelectric (ME) mechanism to explain observed ME behavior. For Cr2O3, bulk calculations for different biaxial strains failed to explain its ferromagnetism, indicating that size or excess-O effects might be important. Finally, we implemented XAS and XMCD in VASP and computed these spectra for GFO.

Computational chemistry has gained interest as a characterization tool to predict photoluminescence, reactivity and structural properties of organic and transition metal complexes. With the rise of methods including relativity, these studies have been expanded to the accurate modeling of luminescence spectra of complexes with considerable spin-orbit splitting due to heavy metal centers as well as the reaction pathways for these complexes to produce natural products such as hydrogen gas. These advances have led to the synthesis and utility of more effective catalysis as well as the development of more effective organic light emitting diodes (OLEDs) through the incorporation of organometallic complexes as emitters instead of typical organic emitters. In terms of significant scientific advancement presented in this work is in relation to the discovery of significant spin-orbit splitting in a gold(I) alkylphosphine complex, where the splitting results in the states that emit in different colors of the visible region of the electromagnetic spectrum. This work also reveals the discovery both computationally and experimentally, of a genuine polar-covalent bond between two-closed shell metals. This work highlights a complex with an incredibly short gold(I) – copper(I) intermetallic distance leading to a vibrational frequency and dissociation energy that is on par with those of other systems with single-bonded metal centers. Lastly, this work outlines a strategy for the production of hydrogen gas through the use of trinuclear cyclic coinage metal complexes as catalysis to split hydrohalic acids.

This thesis experimentally demonstrates four approaches of frequency control of magnetic auto-oscillations in spin Hall nano-oscillators (SHNOs). The frequency can be changed in the GHZ-range by external magnetic fields as shown in this work. This approach uses large electromagnets, which is inconvenient for future applications. The nonlinear coupling between oscillator power and frequency can be used to control the latter one by changing the applied direct current to the SHNO. The frequency can be controlled over a range of several 100 MHz as demonstrated in this thesis. The first part of the experimental chapter demonstrates the synchronization (injection-locking) between magnetic auto-oscillations and an external microwave excitation. The additionally applied microwave current generates a modulation of the effective magnetic field, which causes the interaction with the auto-oscillation. Both synchronize over a range of several 100 MHz. In this range, the auto-oscillation frequency can be controlled by the external stimulus. An increase of power and a decrease of line width is achieved in the synchronization range. This is explained by the increased coherence of the auto-oscillations. A second approach is the synchronization of auto-oscillations to an alternating magnetic field. This field is generated by a freestanding antenna, which is positioned above the SHNO. The second part of the experimental chapter introduces a bipolar concept of SHNOs and its experimental demonstration. In contrast to conventional SHNOs, bipolar SHNOs generate auto-oscillations for both direct current polarities and both directions of the external magnetic field. This is achieved by combining two ferromagnetic layers in an SHNO. The combination of two different ferromagnetic materials is used to switch between two frequency ranges in dependence of the direct current polarity since it defines the layer showing auto-oscillations. This approach can be used to change the frequency in the GHz-range by switching the direct current polarity. / Diese Arbeit demonstriert experimentell vier verschiedene Methoden der Frequenzkontrolle magnetischer Auto-Oszillationen in Spin Hall Nano-Oszillatoren (SHNOs). Durch externe magnetische Felder kann die Frequenz im GHz-Bereich geändert werden, wie es in dieser Arbeit gezeigt wird. Dies erfordert jedoch große Elektromagneten, deren Nutzung für zukünftige Anwendungen der SHNOs nicht geeignet sind. Aufgrund der nichtlinearen Kopplung zwischen Oszillatorleistung und Oszillatorfrequenz, lässt sich letztere durch den Versorgungsstrom beeinflussen. Dies ist typischerweise in einem Bereich von mehreren 100 MHz möglich, wie es an mehreren Stellen dieser Arbeit gezeigt wird. Im ersten Abschnitt des Ergebnisteils wird die Synchronisation der magnetischen Auto-Oszillationen zu einer externen Mikrowellenanregung demonstriert. Der zusätzlich eingespeiste Mikrowellenstrom erzeugt eine Modulation des effektiven Magnetfelds, was zur Wechselwirkung mit den Auto-Oszillationen führt. Diese synchronisieren über eine Frequenzdifferenz von mehreren 100 MHz. In diesem Bereich lässt sich die Frequenz der Auto-Oszillation mit der äußeren Frequenz steuern. Innerhalb des Synchronisationsbereichs wird außerdem eine Erhöhung der Leistung und eine Verringerung der Linienbreite der Auto-Oszillationen festgestellt. Dies wird mit einer Erhöhung der Kohärenz der Auto-Oszillationen erklärt. Neben der zusätzlichen Einspeisung eines Mikrowellenstroms können die Auto-Oszillationen auch zu einem magnetischen Wechselfeld synchronisieren, welches von einer frei beweglichen Antenne erzeugt wird, die über dem SHNO positioniert wird. Im zweiten Abschnitt des Ergebnisteils wird ein bipolares Konzept eines SHNO vorgestellt und seine Funktionsfähigkeit experimentell nachgewiesen. Im Vergleich zu konventionellen SHNOs erzeugen bipolare SHNOs Auto-Oszillationen für beide Polaritäten des elektrischen Versorgungsstroms und beide Richtungen des externen Magnetfelds. Dies wird durch die Kombination zweier ferromagnetischer Lagen in einem SHNO erreicht. Die Kombination unterschiedlicher ferromagnetischer Materialien kann genutzt werden, um die Mikrowellenfrequenz in Abhängigkeit der Stromrichtung zu ändern, da diese bestimmt in welcher Lage die Auto-Oszillationen erzeugt werden können. Durch eine geeignete Materialkombination kann die Frequenz im GHz-Bereich geändert werden, wenn die Strompolarität umgekehrt wird.

Topological insulators (TIs) are semiconductors with protected electronic surface states that allow dissipation-free transport. TIs are envisioned as ideal materials for spintronics and quantum computing. In Bi14Rh3I9, the first weak 3D TI, topology presumably arises from stacking of the intermetallic [(Bi4Rh)3I]2þ layers, which are predicted to be 2D TIs and to possess protected edge-states, separated by topologically trivial [Bi2I8]2+ octahedra chains. In the new layered salt Bi12Rh3Cu2I5, the same intermetallic layers are separated by planar, i.e., only one atom thick, [Cu2I4]2- anions. Density functional theory (DFT)-based calculations show that the compound is a weak 3D TI, characterized by Z2 ¼ ð0; 0001Þ, and that the topological gap is generated by strong spin–orbit coupling (Eg,calc.~ 10 meV). According to a bonding analysis, the copper cations prevent strong coupling between the TI layers. The calculated surface spectral function for a finite-slab geometry shows distinct characteristics for the two terminations of the main crystal faces 〈001〉, viz., [(Bi4Rh)3I]2þ and [Cu2I4]2-. Photoelectron spectroscopy data confirm the calculated band structure. In situ four-point probe measurements indicate a highly anisotropic bulk semiconductor (Eg,exp.¼ 28 meV) with pathindependent metallic conductivity restricted to the surface as well as temperatureindependent conductivity below 60 K.

Transition metal oxides (TMO) have proven to exhibit novel properties such as high temperature superconductivity, magnetic ordering, charge and spin density waves, metal to insulator transitions and colossal magnetoresistance. Among these are a spin-orbit coupling (SOC) induced Mott insulator Sr2IrO4. The electric transport properties of this material remain finite even at cryogenic temperatures enabling its complex electronic structure to be investigated by a scanning tunneling microscope. At T = 77 K, we observed two features which represent the Mott gap with a value of 2D ~ 615 meV. Additionally an inelastic loss feature was observed inside this gap due to a single magnon excitation at an energy of ~ 125 meV. These features are consistent with similar measurements with other probes. In addition to these features, at T = 4.2 K lower energy features appear which are believed to be due to additional magnetic ordering. Another material that exhibits a unique physical behavior is the sliding charge density wave (CDW) material TaS3. It is a quasi-one dimensional material that forms long narrow ribbon shaped crystals. It exhibits anomalies including non-ohmic conductivity, a decrease in the Young’s modulus, a decrease in the shear modulus and voltage induced changes in the crystal’s overall length. In addition, we have observed the torsional piezo-like response, voltage induced torsional strain (VITS), in TaS3 which was first discovered by Pokrovskii et. al. in 2007. Our measurements were conducted with a helical resonator. The VITS response has a huge effective piezoelectric coefficient of ~ 104 cm/V. In addition we have concluded that the VITS is a very slow response with time constants of ~ 1 s near the CDW depinning threshold, that these time constants are dependent on the CDW current, and we suggest that the VITS is due to residual twists being initially present in the crystal.

This thesis presents details of x-ray and neutron scattering experiments used to probe quantum magnets with strong spin-orbit interaction. The first of these systems are the three-dimensional iridate compounds, in which the three-fold co-ordination of IrO₆ octahedra has been theoretically hypothesized to stabilize anisotropic exchange between Ir⁴⁺ ions. This novel interaction between these spin-orbital entangled, J_eff=1/2 moments is described by a Hamiltonian first proposed by Kitaev, and would be the first physical realization of this Hamiltonian in a condensed matter system. This thesis details the determination of the structure of a new polytype within these compounds, the 'stripyhoneycomb' &gamma;-Li₂IrO₃. Furthermore, through resonant magnetic x-ray diffraction experiments on single crystals of &beta;-Li₂IrO₃ and &gamma;-Li₂IrO₃, an incommensurate, non-coplanar structure with counter-rotating moments is found. The counter-rotating moment structure is a rather counter-intuitive result, as it is not stabilizied by Heisenberg exchange between magnetic sites, however, the Kitaev exchange naturally accounts for this feature. As such, these experiments reveal, for the first time, systems which exhibit dominant Kitaev interactions. The ordering wavevector of both &beta;- and &gamma;-Li₂IrO₃ polytypes are found to be identical, suggesting that the same magnetic interactions are responsible for stabilizing magnetic order in both materials, despite their different lattice topologies. Following this, the spinel FeSc₂S₄ is considered. Here, despite the presence of strong exchange between Fe<sup>2+,/sup>, and the fact that these ions sit in a Jahn-Teller active environment, the system does not order in the spin or orbital degrees of freedom. A 'spin-orbital singlet' has been theoretically proposed to describe the groundstate of this system, and here inelastic neutron scattering (INS) is used to probe the resulting triplon excitations. This allows determination of microscopic parameters in the single ion and exchange Hamiltonians, and moreover experiments in external magnetic field reveal the true spin-and-orbital nature of these triplon excitations. Finally, Ba₃CoSb₂O₉, a physical realization of the canonical triangular antiferromagnet model is explored with INS and the high energy excitations from the 120 degree magnetic structure are found to display significant differences from those calculated by linear spin wave theory, suggesting the presence of quantum dynamics not captured in the 1/S linear spin wave expansion.

Nesta dissertação são estudados Condensados de Bose-Einstein de átomos com pseudo-spin 1/2 cuja dinâmica orbital está acoplada a estes dois níveis de energia internos. A geração de tal sistema é possível induzindo transições entre os subníveis m_f = -1 e m_f = 0 do estado hiperfino atômico f = 1 usando um arranjo de lasers, os quais também introduzem junto uma dependência espacial dada por suas fases, as quais estão relacionadas a posição do átomo no campo, levando assim à interação acoplando spin e órbita. É considerado então um sistema unidimensional efetivo na mesma direção do acoplamento dos lasers, onde são estudado diferentes observáveis do estado fundamental, para uma varredura dos parâmetros presentes na equação, dando origem a três fases diferenciadas pela distribuição do momento. Foram determinadas estas fases do estado fundamental para interação atrativa, sendo elas modulada(striped), onda plana e de momento nulo, mostrando a localização onde cada uma ocorre no domínio de parâmetros da equação, através de diagramas de fase. São também mostrados, separadamente, observáveis relevantes como momento e desbalanço entre os estados internos nestas transições, os quais apresentaram variações bruscas, ditando valores críticos nos parâmetros, onde ocorrem. Posteriormente é estudado a dinâmica através de soluções do tipo sóliton, as quais não se propagam linearmente e são ditadas por oscilações do centro de massa e das populações, explorando diferentes situações iniciais. / In the present dissertation it has been studied Bose-Einstein Condensation of atoms with 1/2 pseudo-spin whose the orbital dynamics is coupled to these two internal energy levels. The generation of such a system is done by inducing transitions between the sub-levels m_f = -1 and m_f = 0 from the hyperfine atomic state f = 1 using an arrangement of lasers, that also introduce a spacial dependence due to their phases, that changes accordingly the atom\'s position in the light field, conducting in this way to a interaction that couples orbital motion with spin. It is then considered an effective one dimensional system in the same direction of the laser coupling, where it has been studied different ground state observables, making a sweeping in the equation parameters, showing three typical phases based on momentum distribution. So far, it was determined these phases for attractive interactions, named striped, plane wave and zero momentum, determining as well the location where each one occurs in the equation\'s parameters through a phase diagram. It is also reported, separately, a few relevant observables as individual momentum of each population and the unbalance between the internal spin states, in the transition among these phases, whose the values present abrupt variations, dictating critical values for the parameters, where it occurs. Lately is presented a dynamical study with soliton like solutions, that do not linearly propagate and instead, shows a center of mass and unbalance oscillation, probing different initial conditions.

Nesta dissertação são estudados Condensados de Bose-Einstein de átomos com pseudo-spin 1/2 cuja dinâmica orbital está acoplada a estes dois níveis de energia internos. A geração de tal sistema é possível induzindo transições entre os subníveis m_f = -1 e m_f = 0 do estado hiperfino atômico f = 1 usando um arranjo de lasers, os quais também introduzem junto uma dependência espacial dada por suas fases, as quais estão relacionadas a posição do átomo no campo, levando assim à interação acoplando spin e órbita. É considerado então um sistema unidimensional efetivo na mesma direção do acoplamento dos lasers, onde são estudado diferentes observáveis do estado fundamental, para uma varredura dos parâmetros presentes na equação, dando origem a três fases diferenciadas pela distribuição do momento. Foram determinadas estas fases do estado fundamental para interação atrativa, sendo elas modulada(striped), onda plana e de momento nulo, mostrando a localização onde cada uma ocorre no domínio de parâmetros da equação, através de diagramas de fase. São também mostrados, separadamente, observáveis relevantes como momento e desbalanço entre os estados internos nestas transições, os quais apresentaram variações bruscas, ditando valores críticos nos parâmetros, onde ocorrem. Posteriormente é estudado a dinâmica através de soluções do tipo sóliton, as quais não se propagam linearmente e são ditadas por oscilações do centro de massa e das populações, explorando diferentes situações iniciais. / In the present dissertation it has been studied Bose-Einstein Condensation of atoms with 1/2 pseudo-spin whose the orbital dynamics is coupled to these two internal energy levels. The generation of such a system is done by inducing transitions between the sub-levels m_f = -1 and m_f = 0 from the hyperfine atomic state f = 1 using an arrangement of lasers, that also introduce a spacial dependence due to their phases, that changes accordingly the atom\'s position in the light field, conducting in this way to a interaction that couples orbital motion with spin. It is then considered an effective one dimensional system in the same direction of the laser coupling, where it has been studied different ground state observables, making a sweeping in the equation parameters, showing three typical phases based on momentum distribution. So far, it was determined these phases for attractive interactions, named striped, plane wave and zero momentum, determining as well the location where each one occurs in the equation\'s parameters through a phase diagram. It is also reported, separately, a few relevant observables as individual momentum of each population and the unbalance between the internal spin states, in the transition among these phases, whose the values present abrupt variations, dictating critical values for the parameters, where it occurs. Lately is presented a dynamical study with soliton like solutions, that do not linearly propagate and instead, shows a center of mass and unbalance oscillation, probing different initial conditions.