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No. of bitstreams: 1 Dissertação- Cleverton Oliveira Dias.pdf: 1220759 bytes, checksum: a90af3e1cf4a80152ef01c95168c9138 (MD5) Previous issue date: 2015-11-25 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This dissertation presents systematically the traditional superconductors, taking into account its discovery, properties that characterize the theory describing and changes taking place in their thermodynamic properties when subject to spin-orbit interaction Rashba. In the rst part are the key topics discussed related to phenomenon of superconductivity. It begins with a chapter 1 approach of the historical evolution of superconductivity and presentation properties that characterize a conventional superconductor, in addition to de ne superconductors Type I (conventional) and type II. The Chapter 2 is intended for an explanation of the microscopic BCS theory whose application is associated with type I superconductors, although this chapter argue about the interaction of electrons with the network, thus forming what is called Cooper pairs. The Chapter 3 is intended to introduce the Rashba model, which can be veri ed in two ways: by spontaneous generation of electric eld the junction interface of two materials or because application of the an external electric eld. In work not take into account the so that will be produced this electric eld. In Chapter 4 it shows the model Hamiltonian that constitutes the junction BCS Hamiltonian with the Hamiltonian of Rashba, from this model it is intended to calculate the e ect of Rashba interaction on the gap energy using the method of canonical transformations, consisting to assess the evolution of the operator concerned by a equation of dynamic evolution, allowing us nd the self energy carriers and their respective eigenvalues and associates them to gaps of energy. As a result of Chapter 4, Chapter 5 determine the gap superconductor function of temperature and the parameter R Rashba and as the thermodynamic properties of the model studied in this chapter also opens a space for comments and discussions. We end with Chapter 6, presenting partial conclusions, Related analytical curve made from certain data numerical, these curves will analyze the variation in thermodynamic properties of superconductors because the e ect Rashba. / A presente dissertação consiste em apresentar de forma sistemática os supercondutores tradicionais, levando em consideração sua descoberta, as propriedades que o caracterizam, a teoria que os descrevem e as mudanças que ocorrem em suas propriedades termodinâmicas quando submetidos a interação spin- orbita de Rashba. Na primeira parte são discutidos os t ópicos fundamentais referentes ao fenômeno da supercondutividade. Inicia-se o capítulo 1 com uma abordagem da evolução hist orica da supercondutividade e a apresentação das propriedades que caracterizam um supercondutor convencional, al em de de nir supercondutores tipo I (convencionais) e tipo II. O cap tulo 2 destina-se a uma explana c~ao da teoria microscópica BCS, cuja aplicação está associada a supercondutores de tipo I, ainda neste capítulo argumenta-se sobre a interação dos elétrons com a rede, formando assim o que chamamos de pares de Cooper. O capiítulo 3 destina-se a apresentar o modelo de Rashba, que pode ser verificado de duas maneiras: por geração espontânea de campo elétrico na interface da junção de dois materiais ou em razão da aplicação de um campo elétrico externo. No trabalho não se levar a em conta a maneira que ser a produzido esse campo elétrico. No capítulo 4 apresenta-se o Hamiltoniano do modelo, que consiste na junção do Hamiltoniano BCS com o Hamiltoniano de Rashba, a partir deste modelo pretende-se calcular o efeito da intera ção de Rashba, sobre os gaps de energia utilizando o m etodo das transforma ções canônicas, que consiste em avaliar a evolu ção temporal do operador em questão por meio de uma equa ção de evolução dinâmica, o que nos permitir a encontrar os autovetores de energia e seus respectivos autovalores e associa-los aos gaps de energia. Como consequência do capítulo 4, no cap tulo 5 determinaremos o gap do supercondutor em fun ção da temperatura e do parâmetro de Rashba R, bem como as propriedades termodinâmicas do modelo estudado, neste cap tulo tamb em abre-se um espa co para comentarios e discussões. Finalizamos com o cap tulo 6, apresentando conclusões parciais, relacionadas a an alise de algumas curvas feitas a partir de dados num ericos, estas curvas permitirão analisar a varia ção nas propriedades termodinâmicas dos supercondutores devido o efeito Rashba.

In modern technology exciting developments are related to the ability to understand and control interfaces. Particularly, magnetic interfaces revealing spindependent electron transport are of great interest for modern spintronic devices, such as random access memories and logic devices. From the technological point of view, spintronic devices based on magnetic interfaces enable manipulation of the magnetism via an electric field. Such ability is a result of the different quantum effects arising from the magnetic interfaces (for example, spin transfer torque or spin-orbit torque) and it can reduce the energy consumption as compared to the traditional semiconductor electronic devices. Despite many appealing characteristics of these materials, fundamental understanding of their microscopic properties and related phenomena needs to be established by thorough investigation. In this work we implement first principles calculations in order to study the structural, electric, and magnetic properties as well as related phenomena of two types of interfaces with large potential in spintronic applications: 1) interfaces between antiferromagnetic 3d-metal-oxides and ferromagnetic 3d-metals and 2) interfaces between non-magnetic 5d(4d)- and ferromagnetic 3d-metals. A major difficulty in studying such interfaces theoretically is the typically large lattice mismatch. By employing supercells with Moir e patterns, we eliminate the artificial strain that leads to doubtful results and are able to describe the dependence of the atomic density at the interfaces on the component materials and their thicknesses. After establishing understanding about the interface structures, we investigate the electronic and magnetic properties. A Moir e supercell with transition layer is found to reproduce the main experimental findings and thus turns out to be the appropriate model for simulating magnetic misfit interfaces. In addition, we systematically study the magnetic anisotropy and Rashba band splitting at non-magnetic 5d(4d) and ferromagnetic 3d-metal interfaces and their dependences on aspects such as interdiffusion, surface oxidation, thin film thickness and lattice mismatch. We find that changes of structural details strongly alter the electronic states, which in turn influences the magnetic properties and phenomena related to spin-orbit coupling. Since the interfaces studied in this work have complex electronic structures, a computational approach has been developed in order to estimate the strength of the Rashba band splitting below and at the Fermi level. We apply this approach to the interfaces between a Co monolayer and 4d (Tc, Ru, Rh, Pd, and Ag) or 5d (Re, Os, Ir, Pt, and Au) transition metals and find a clear correlation between the overall size of the band splitting and the charge transfer between the d-orbitals at the interface. Furthermore, we show that the spin splitting at the Fermi surface scales with the induced orbital moment weighted by the strength of the spin-orbit coupling.

Neste trabalho de mestrado apresentamos um estudo sobre a manifestação do efeito Rashba em isolantes topológicos na ausência de simetria de inversão estrutural. Os cálculos das propriedades atomísticas, energéticas e as estruturas eletrônicas são abordados através de métodos de primeiros princípios baseados na teoria do funcional da densidade. E seus resultados foram utilizados para o desenvolvimento de hamiltoniana efetiva baseado no modelo de Zhang. Realizamos o estudo de dois sistemas: 1) Bi$_2$Se$_3$ com átomos de Sn depositados na superfície: Este sistema pode ser entendido através da manifestação do efeito Rashba sobre um isolante topológico dada a quebra de simetria de inversão estrutural. Para um sítio de deposição específico, os átomos de Sn causam uma reconstrução da superfície e um terceiro cone de Dirac é observado na estrutura eletrônica. Este terceiro cone é não localizado na superfície e pode ser entendido como a manifestação do efeito Rashba. 2) PbBiI: Reportado aqui como um novo isolante topológico 2D com efeito Rashba. Descobrimos este sistema por um estudo sistemático sobre uma família de materiais formados por átomos tipo IV, V, e VII, cuja estrutura cristalina é hexagonal e não centrossimétrica. Mostramos que o PbBiI possui: i) Estabilidade mecânica, ii) Spin-splitting Rashba de 60 meV, iii) um gap de energia não trivial de 0.14 eV, iv) retroespalhamento proibido entre os estados de borda e v) retroespalhamento proibido entre os estados do bulk no entorno do nível de Fermi. Estas propriedades fazem do PbBiI um candidato para construção de dispositivos de spintrônica que atenua a perda de energia. / In this work, were studied the Rashba effect in topological insulators without structural inversion symmetry. We performed a first principles study based on density functional theory to calculate the atomistic properties, formation energy and electronic structure. These results were used to development a effective Hamiltonian based on Zhang model. They were studied two systems: 1) Bi$_2$Se$_3$ with Sn atoms deposited on the surface: This system can be seen as the Rashba effect manifestation on a topological insulator due to the structural inversion symmetry breaking. For a specific deposition site, the Sn atoms cause a reconstruction of the surface and display a third Dirac cone in the electronic structure. This third cone is not located on the surface and can be understood as the giant Rashba effect manifestation. 2) We propose a new non-centrosymmetric honeycomb-lattice QSH insulator family formed by the IV, V, and VII elements. The system formed by Bi, Pb and I atoms is reported here as a new 2D topological insulator with Rashba effect. We show that this system has: i) Mechanical stability, ii) spin-splitting Rashba of 60 meV, iii) nontrivial energy gap of 0.14 eV, iv) backscattering forbidden for both edge and bulk conductivity channels in the nanoribbon band structure. These properties make PbBiI a good candidate to construct spintronic devices with less energy loss.

This thesis is focused on the electronic, spin-dependent and dynamical properties of thin magnetic systems. Photoemission-related techniques are combined with synchrotron radiation to study the spin-dependent properties of these systems in the energy and time domains. In the first part of this thesis, the strength of electron correlation effects in the spin-dependent electronic structure of ferromagnetic bcc Fe(110) and hcp Co(0001) is investigated by means of spin- and angle-resolved photoemission spectroscopy. The experimental results are compared to theoretical calculations within the three-body scattering approximation and within the dynamical mean-field theory, together with one-step model calculations of the photoemission process. From this comparison it is demonstrated that the present state of the art many-body calculations, although improving the description of correlation effects in Fe and Co, give too small mass renormalizations and scattering rates thus demanding more refined many-body theories including nonlocal fluctuations. In the second part, it is shown in detail monitoring by photoelectron spectroscopy how graphene can be grown by chemical vapour deposition on the transition-metal surfaces Ni(111) and Co(0001) and intercalated by a monoatomic layer of Au. For both systems, a linear E(k) dispersion of massless Dirac fermions is observed in the graphene pi-band in the vicinity of the Fermi energy. Spin-resolved photoemission from the graphene pi-band shows that the ferromagnetic polarization of graphene/Ni(111) and graphene/Co(0001) is negligible and that graphene on Ni(111) is after intercalation of Au spin-orbit split by the Rashba effect. In the last part, a time-resolved x-ray magnetic circular dichroic-photoelectron emission microscopy study of a permalloy platelet comprising three cross-tie domain walls is presented. It is shown how a fast picosecond magnetic response in the precessional motion of the magnetization can be induced by means of a laser-excited photoswitch. From a comparision to micromagnetic calculations it is demonstrated that the relatively high precessional frequency observed in the experiments is directly linked to the nature of the vortex/antivortex dynamics and its response to the magnetic perturbation. This includes the time-dependent reversal of the vortex core polarization, a process which is beyond the limit of detection in the present experiments. / Diese Dissertation beschäftigt sich mit den elektronischen, spinabhängigen und dynamischen Eigenschaften dünner magnetischer Systeme. Auf dem Photoeffekt basierende Untersuchungsmethoden werden zusammen mit Synchrotronstrahlung eingesetzt, um die spinabhängigen Eigenschaften dieser Systeme im Energie- und Zeitbereich zu untersuchen. Im ersten Teil dieser Arbeit wird mit spin- und winkelaufgelöster Photoemission die Stärke von Elektronenkorrelationseffekten in der spinabhängigen elektonischen Struktur von ferromagnetischerm bcc Fe(110) und hcp Co(0001) untersucht. Die experimentellen Ergebnisse werden verglichen mit theoreteischen Berechnungen im Rahmen der Näherung der Drei-Körper-Streuung und der dynamischen Molekularfeldtheorie, zusammen mit Berechnungen des Photoemissionsprozesses im Rahmen des Ein-Stufen-Modells. Ausgehend von diesem Vergleich wird gezeigt, dass die gegenwärtig fortgeschrittensten Rechnung, obgleich sie die Beschreibung von Korrelationseffekten in Fe und Co verbessern, zu kleine Massenrenormalisierungen und Streuraten ergeben, was zu der Forderung nach verfeinerten Vielteilchentheorien unter Einbeziehung von nichtlokalen Fluktuationen führt. Im zweiten Teil wird unter Kontrolle durch die Photoelektronenspektroskopie im Detail gezeigt, wie Graphen durch chemische Gasphasenabscheidung auf den Übergangsmetall-Oberflächen Ni(111) und Co(0001) aufgebracht und mit einer Monolage Au interkaliert werden kann. Für beide Systeme wird eine lineare E(k)-Dispersion masseloser Dirac-Fermionen im Graphen-pi-Band in der Nähe der Fermi-Energie beobachtet. Spinaufgelöste Photoemission des Graphen-pi-Bandes zeigt, dass die ferromagnetische Polarisation von Graphen/Ni(111) und Graphen/Co(0001) vernachlässigbar ist und dass Graphen/Ni(111) nach Interkalation mit Au eine Spin-Bahn-Aufspaltung aufgrund des Rashba-Effekts zeigt. Im letzten Teil wird eine zeitaufgelöste Studie des Röntgenzirkulardichroismus mit Photoelektronenmikroskopie präsentiert, die an einer Permalloy-Probe durchgeführt wurde, die drei als Stachelwände ausgebildete Domänenwände enthält. Es wird gezeigt, wie eine schnelle magnetische Antwort auf der Pikosekundenskala in der Präzessionsbewegung der Magnetisierung durch einen laserangesteuerten Photoschalter erzeugt werden kann. Durch Vergleich mit einer mikromagnetischen Rechnung wird gezeigt, dass die relativ hohe Präzessionsfrequenz, die im Experiment beobachtet wird, in unmittelbarer Beziehung steht zu den Eigenschaften der Vortex/Antivortex-Dynamik und ihrer Antwort auf die magnetische Störung. Das schließt die zeitabhängige Umkehr der Vortexkernpolarisation ein, einem Vorgang der jenseits der Nachweisgrenze der gegenwärtigen Experimente liegt.

Ce travail de thèse est consacré à l’étude et au contrôle des propriétés de spin des électrons dans des structures à base de semi-conducteurs GaAs : GaAsN, GaAsBi et InGaAs. L'objectif est de donner une description fine de leurs propriétés électronique afin d'appréhender leur potentiel pour des applications en optoélectronique et spintronique. Nous avons focalisé l'étude des propriétés de spin des semi-conducteurs à base de nitrure dilué GaAsN sur les propriétés de l'interaction hyperfine entre l'électron et les noyaux des centres paramagnétiques naturellement présents dans ces matériaux. L'étude est réalisée par des expériences de photoluminescence pompe-sonde, en tirant parti du mécanisme de filtrage de spin par les centres paramagnétiques profonds présents dans le GaAsN massif : la recombinaison dépendante du spin (SDR). Nous démontrons, via l'enregistrement de la dynamique de la photoluminescence bande à bande, une nouvelle technique de détection des oscillations de spin cohérentes électron-noyau dues à l'interaction hyperfine. Ces oscillations sont observées dans l'application d'un champ magnétique externe et sans la nécessité d'utiliser les techniques de résonance de spin électronique. La caractérisation des matériaux bismures dilués GaAsBi en couches massives et en puits quantiques élaborés par épitaxie par jet moléculaire avec différentes concentrations de bismuth avec des expériences de spectroscopie de photoluminescence résolue en temps et en polarisation permet l’étude des propriétés de spin des électrons. Les résultats expérimentaux ont révélé une nette diminution du temps de relaxation de spin des électrons lorsque la fraction de bismuth augmente. Cette réduction significative du temps de relaxation de spin est liée à l'augmentation du couplage spin-orbite dans le matériau GaAsBi. La dynamique de relaxation observée est en bon accord avec le modèle de D'yakonov-Perel. Une troisième étude a porté sur le contrôle et la manipulation de spin des électrons dans les puits quantiques à semi-conducteurs III-V InGaAs/GaAs. Les hétérostructures élaborées sur des substrats d'orientation (111) présentent des propriétés de symétries particulières, qui combinées aux propriétés piézoélectriques, permettent sans application d’un champ électrique externe, de bloquer ou accélérer la dynamique de relaxation de spin. Ces observations démontrent la possibilité de contrôler le spin des porteurs à l'aide des propriétés intrinsèques de structures à puits quantiques, ce qui en fait de très bons candidats pour des applications futures de traitement et de stockage de l'information quantiques. / This thesis is devoted to the study of the electron spin properties for optoelectronic and spintronic applications of different GaAs-based semiconductor systems: GaAsN, GaAsBi, and InGaAs.The investigation of the spin properties of dilute nitride GaAsN-based semiconductors is centered on the properties of the hyperfine interaction between the electron and the nuclei at the paramagnetic centers naturally present in these compounds. The study is carried out, in the temporal domain, by a photoluminescence-based pump-probe technique and taking advantage of the spin-dependent relaxation mechanism via deep paramagnetic centers in GaAsN bulk. We demonstrate a novel detection scheme of the coherent electron-nuclear spin oscillations related to the hyperfine interaction and revealed by the band-to-band photoluminescence in zero external magnetic field and without the need of electron spin resonance techniques. GaAsBi semiconductors provide new opportunities for many optoelectronic applications thanks to possibility of greatly modulate the band gap and the spin-orbit interaction with the bismuth concentration. Using time-resolved photoluminescence spectroscopy experiment, we have characterized the optical and spin properties of bulk and quantum well GaAsBi structures elaborated by molecular beam epitaxy in a wide range of Bi-content. The experimental results revealed, on the one hand, the localization effect of exciton at low temperature and, on the other hand, the marked decrease of electron spin relaxation time when bismuth content increases. These results are consistent with Dyakonov-Perel spin relaxation mechanism whose efficiency is enhanced by the strong spin-orbit coupling interaction in GaAsBi alloy. The third study is focused on the demonstration of the control of the electron spin relaxation time in the III-V semiconductors by taking advantage of the symmetry properties allied to the piezoelectric effects in InGaAs (111)B heterostructures, without the need of any external electric field. We show that, in this system, the particular direction (111) associated with parameters related to InGaAs quantum wells such as indium concentration and quantum well width allows the control of spin electron relaxation time via piezoelectric field induced by the strain amplitude in the well. These observations demonstrate the possibility of monitoring electron spin relaxation process using intrinsic quantum confined structures, making them ideal candidates for use in quantum information storage and processing devices.

Neste trabalho de mestrado apresentamos um estudo sobre a manifestação do efeito Rashba em isolantes topológicos na ausência de simetria de inversão estrutural. Os cálculos das propriedades atomísticas, energéticas e as estruturas eletrônicas são abordados através de métodos de primeiros princípios baseados na teoria do funcional da densidade. E seus resultados foram utilizados para o desenvolvimento de hamiltoniana efetiva baseado no modelo de Zhang. Realizamos o estudo de dois sistemas: 1) Bi$_2$Se$_3$ com átomos de Sn depositados na superfície: Este sistema pode ser entendido através da manifestação do efeito Rashba sobre um isolante topológico dada a quebra de simetria de inversão estrutural. Para um sítio de deposição específico, os átomos de Sn causam uma reconstrução da superfície e um terceiro cone de Dirac é observado na estrutura eletrônica. Este terceiro cone é não localizado na superfície e pode ser entendido como a manifestação do efeito Rashba. 2) PbBiI: Reportado aqui como um novo isolante topológico 2D com efeito Rashba. Descobrimos este sistema por um estudo sistemático sobre uma família de materiais formados por átomos tipo IV, V, e VII, cuja estrutura cristalina é hexagonal e não centrossimétrica. Mostramos que o PbBiI possui: i) Estabilidade mecânica, ii) Spin-splitting Rashba de 60 meV, iii) um gap de energia não trivial de 0.14 eV, iv) retroespalhamento proibido entre os estados de borda e v) retroespalhamento proibido entre os estados do bulk no entorno do nível de Fermi. Estas propriedades fazem do PbBiI um candidato para construção de dispositivos de spintrônica que atenua a perda de energia. / In this work, were studied the Rashba effect in topological insulators without structural inversion symmetry. We performed a first principles study based on density functional theory to calculate the atomistic properties, formation energy and electronic structure. These results were used to development a effective Hamiltonian based on Zhang model. They were studied two systems: 1) Bi$_2$Se$_3$ with Sn atoms deposited on the surface: This system can be seen as the Rashba effect manifestation on a topological insulator due to the structural inversion symmetry breaking. For a specific deposition site, the Sn atoms cause a reconstruction of the surface and display a third Dirac cone in the electronic structure. This third cone is not located on the surface and can be understood as the giant Rashba effect manifestation. 2) We propose a new non-centrosymmetric honeycomb-lattice QSH insulator family formed by the IV, V, and VII elements. The system formed by Bi, Pb and I atoms is reported here as a new 2D topological insulator with Rashba effect. We show that this system has: i) Mechanical stability, ii) spin-splitting Rashba of 60 meV, iii) nontrivial energy gap of 0.14 eV, iv) backscattering forbidden for both edge and bulk conductivity channels in the nanoribbon band structure. These properties make PbBiI a good candidate to construct spintronic devices with less energy loss.

The search for novel technologies like spin-based electronics and suitable materials for respective devices requires a profound understanding of fundamental interactions regarding electron spin and related properties. In the same context, with ongoing device miniaturisation, surface-related phenomena become increasingly important. Here, we study the electronic and magnetic properties of quasi-2D electron states at a metallic surface under the influence of the Rashba effect and exchange coupling to localised 4f moments that order magnetically at low temperatures. Particularly, in the considered systems, both interactions are of similar strengths, a case which is rather unexplored in the literature. Our model system is the (001) surface of intermetallic LnIr2Si2 compounds with ThCr2Si2 structure, where Ln = lanthanide. With this work, we continue our long-term systematic study of the LnT2Si2 compounds with T = Rh, where the Rashba-like spin-orbit coupling is about a hundred times weaker than the exchange interaction. Using ARPES and DFT we explore with GdIr2Si2 and EuIr2Si2 two representatives of the LnIr2Si2 family, which are both characterised by the insensitivity of the 4f shell to the crystal electric field. On the other hand, they have fundamentally different bulk properties. GdIr2Si2 is a robust bulk antiferromagnet with a high ordering temperature of 87 K, whereas EuIr2Si2 is a mixed-valent material with a non-magnetic ground state in the bulk. The mean Eu valency is strongly temperature dependent, changing continuously from a nearly divalent magnetic configuration at room temperature to a nearly trivalent non-magnetic Eu state below 50K. Studying the surface states in both compounds we find that the magnitude of the Rashba-like spin-orbit interaction increases tremendously in comparison to the isoelectronic Rh compounds. This is reflected in a huge splitting of the surface state bands and emphasizes the importance of atomic spin-orbit coupling in high Z elements for the strength of the Rashba effect. Employing DFT, which reproduces the measured band structure very accurately, we find the same exotic triple winding of the electron spin along the isoenergy contours of the surface state bands as reported in terms of a cubic Rashba effect for the Rh compounds. This proves the generic nature of the surface states and their universal properties in the considered LnT2Si2 compounds. With the ordering of the 4f moments at low temperatures, spin structure and surface band dispersion undergo significant changes induced by the exchange interaction. Pronounced asymmetries emerge in the band dispersion, which allow for the determination of the magnetisation axis. We demonstrate that this is even possible if spectral structures originating from different magnetic domains overlap in the spectra. Remarkably, we find respective asymmetries in EuIr2Si2, too, despite the almost trivalent, and thus non-magnetic Eu state at low temperatures. With complementary experimental techniques like x-ray absorption, x-ray linear and circular dichroism as well as by taking photoelectron diffraction into account, we demonstrate that in the surface Si–Ir–Si–Eu four-layer block Eu is nearly divalent and magnetically active. The associated Eu moments order ferromagnetically below 49K. In the case of Eu termination, we find that the 4f moments of the divalent Eu ions at the surface order ferromagnetically below 10K, too, and unveil thus another occurrence of 2D surface-related magnetism in the same non-magnetic bulk compound. Simultaneously, the mixed-valent properties of EuIr2Si2 and the strong temperature dependence of the mean Eu valency are clearly reflected in the electronic structure of the bulk in a smooth expansion of the Doughnut Fermi surface sheet with increasing temperature, which is interpreted as a band-filling effect. Our results show the high tunability of the electron spin by combining spin-orbit coupling and structural inversion asymmetry with the exchange interaction, which is at the heart of spintronics applications. The disclosure of controllable 2D magnetism at the surface of a non-magnetic bulk compound, which is enabled by an instability in the 4f shell, nominates valence fluctuating 4f compounds, especially with Eu and Sm, to be promising candidates for fundamental studies and applications. Our study moreover demonstrates the richness and versatility of 4f physics that may differ significantly at the surface and in the bulk.:1. Introduction 2. Preliminary Studies 2.1. Short introduction to lanthanides and 4f physics 2.2. LnT2Si2 compounds 3. Foundations 3.1. Band structure 3.2. Bulk states, surface states and surface resonances 3.3. The principles of photoelectron spectroscopy 3.4. Angle-resolved photoelectron spectroscopy 3.5. Photoabsorption and resonant photoelectron spectroscopy 3.6. X-ray absorption spectroscopy 3.6.1. X-ray magnetic circular dichroism 3.6.2. X-ray magnetic linear dichroism 3.7. Photoelectron diffraction 3.8. Synchrotron and synchrotron radiation 3.9. Density functional theory 4. Methods 4.1. Experimental details 4.2. DFT calculations 5. GdIr2Si2 5.1. Introduction 5.2. Results and discussion 5.2.1. Paramagnetic phase 5.2.2. Magnetically ordered phase 5.3. Summary 6. EuIr2Si2 6.1. Introduction 6.2. Results and discussion 6.2.1. Photoemission from the Eu 4f shell 6.2.2. ARPES on the Si-terminated surface 6.2.3. X-ray magnetic linear and circular dichroism 6.2.4. Eu termination 6.2.5. Determination of the mean Eu valency in the subsurface layers 6.2.6. Bulk properties 6.3. Summary 7. Conclusion / Die Suche nach neuartigen Technologien wie spinbasierte Elektronik sowie nach geeigneten Materialien für entsprechende Bauteile erfordert ein tiefgreifendes Verständnis der Wechselwirkungen des Elektronenspins und damit verbundener Materialeigenschaften. Mit der zunehmenden Miniaturisierung von Bauteilen gewinnen in diesem Zusammenhang auch Oberflächenphänomene zunehmend an Bedeutung. In dieser Arbeit untersuchen wir die elektronischen und magnetischen Eigenschaften quasizweidimensionaler elektronischer Zustände an metallischen Oberflächen unter dem Einfluss des Rashba-Effekts und der Austauschwechselwirkung mit lokalisierten 4f Momenten, die bei tiefen Temperaturen magnetisch ordnen. Dabei liegt die Besonderheit der untersuchten Systeme darin, dass beide Wechselwirkungen von vergleichbarer Stärke sind. Dieser Fall ist in der Fachliteratur bislang unterrepräsentiert. Unser Modellsystem ist die (001)-Oberfläche intermetallischer LnIr2Si2 Verbindungen mit ThCr2Si2 Struktur, wobei Ln ein Lanthanoidenelement darstellt. Dabei führen wir die langjährige und systematische Untersuchung von LnT2Si2 Verbindungen mit T = Rh fort, in denen die Rashba-artige Spin-Bahn-Kopplung ungefähr 100-mal schwächer als die Austauschwechselwirkung ist. Mit Hilfe von winkelaufgelöster Photoelektronenspektroskopie (ARPES) und Dichtefunktionaltheorie (DFT) erkunden wir mit GdIr2Si2 und EuIr2Si2 zwei Vertreter der LnT2Si2 Familie, die beide durch die Insensibilität der 4f Schale gegenüber dem Kristallfeld ausgezeichnet sind. Zugleich haben sie grundsätzlich verschiedene Volumeneigenschaften. GdIr2Si2 ist ein robuster Volumenantiferromagnet mit einer hohen Ordnungstemperatur von 87K, wohingegen EuIr2Si2 eine gemischtvalente Verbindung mit einem nicht-magnetischen Volumengrundzustand ist. Die mittlere Eu Valenz ist stark temperaturabhängig, sie ändert sich kontinuierlich von einer nahezu zweiwertigen Konfiguration bei Raumtemperatur zu einem beinahe dreiwertigen, nicht-magnetischen Eu Zustand unterhalb von _ 50K. Die Untersuchung der Oberflächenzustände in beiden Verbindungen zeigt, dass die Stärke der Rashba-artigen Spin-Bahn-Kopplung gegenüber den isoelektronischen Rh Verbindungen erheblich zunimmt. Dies spiegelt sich in einer riesigen Aufspaltung der Oberflächenbänder wider und unterstreicht die Bedeutung der atomaren Spin-Bahn-Kopplung in Elementen mit großer Kernzahl Z für die Stärke des Rashba-Effekts. Unsere DFT Rechnungen reproduzieren die gemessene Bandstruktur mit hoher Genauigkeit und offenbaren dieselbe Dreifachwindung des Spins entlang der Konturen konstanter Energie, die schon als kubischer Rashba-Effekt in den Rh Verbindungen beobachtet wurde. Hierin zeigt sich das allgemeingültige Wesen der Oberflächenzustände und deren universelle Eigenschaften in den betrachteten LnT2Si2 Verbindungen. Das Ordnen der 4f Momente bei niedrigen Temperaturen führt zu starken Veränderungen in der Spinstruktur und der Dispersion der Oberflächenbänder durch die einsetzende Austauschwechselwirkung. In der Bandstruktur bilden sich starke Asymmetrien, aus denen die Magnetisierungsachse bestimmt werden kann. Wir zeigen, dass dies sogar dann noch möglich ist, wenn sich spektrale Strukturen überlagern, die von unterschiedlichen magnetischen Domänen stammen. Besonders bemerkenswert ist, dass entsprechende Asymmetrien auch in EuIr2Si2 auftreten, trotz des nahezu dreiwertigen und damit nicht-magnetischen Eu bei tiefen Temperaturen. Mit komplementären experimentellen Methoden wie Röntgenabsorption, linearem und zirkularem Röntgendichroismus als auch durch die Berücksichtigung von Beugungseffekten in der Photoelektronenspektroskopie zeigen wir, dass Eu im Si–Ir–Si–Eu Oberflächenblock beinahe zweiwertig und magnetisch aktiv ist. Die zugehörigen Eu Momente ordnen unterhalb von 49K ferromagnetisch. Im Fall der Eu-Terminierung stellen wir fest, dass auch die 4f Momente der zweiwertigen Eu-Ionen an der Oberfläche unterhalb von 10K ferromagnetisch geordnet sind, und enthüllen damit ein weiteres Vorkommen zweidimensionalen, oberflächenbezogenen Magnetismus in derselben, nichtmagnetischen Volumenverbindung. Gleichzeitig spiegeln sich die gemischtvalenten Eigenschaften von EuIr2Si2 deutlich in der elektronischen Volumenbandstruktur in einer kontinuierlichen Ausdehnung der Doughnut-Fermifläche mit steigender Temperatur wider. Dies interpretieren wir als Bandfüllungseffekt. Unsere Ergebnisse zeigen die hohe Einstellbarkeit des Elektronenspins durch die Kombination von Spin-Bahn-Kopplung und struktureller Inversionsasymmetrie mit der Austauschwechselwirkung, was die Grundlage für Anwendungen in der spinbasierten Elektronik bildet. Die Enthüllung von kontrollierbarem, zweidimensionalem Magnetismus an der Oberfläche einer Verbindung mit instabiler 4f Schale, die im Volumen nicht-magnetisch ist, nominiert gemischtvalente 4f Verbindungen, insbesondere mit Eu und Sm, als vielversprechende Kandidaten für Grundlagenforschung und Anwendungen. Unsere Studie zeigt zudem den Reichtum und die Vielseitigkeit von 4f Systemen, deren Eigenschaften sich an der Oberfläche deutlich vom Volumen unterscheiden können.:1. Introduction 2. Preliminary Studies 2.1. Short introduction to lanthanides and 4f physics 2.2. LnT2Si2 compounds 3. Foundations 3.1. Band structure 3.2. Bulk states, surface states and surface resonances 3.3. The principles of photoelectron spectroscopy 3.4. Angle-resolved photoelectron spectroscopy 3.5. Photoabsorption and resonant photoelectron spectroscopy 3.6. X-ray absorption spectroscopy 3.6.1. X-ray magnetic circular dichroism 3.6.2. X-ray magnetic linear dichroism 3.7. Photoelectron diffraction 3.8. Synchrotron and synchrotron radiation 3.9. Density functional theory 4. Methods 4.1. Experimental details 4.2. DFT calculations 5. GdIr2Si2 5.1. Introduction 5.2. Results and discussion 5.2.1. Paramagnetic phase 5.2.2. Magnetically ordered phase 5.3. Summary 6. EuIr2Si2 6.1. Introduction 6.2. Results and discussion 6.2.1. Photoemission from the Eu 4f shell 6.2.2. ARPES on the Si-terminated surface 6.2.3. X-ray magnetic linear and circular dichroism 6.2.4. Eu termination 6.2.5. Determination of the mean Eu valency in the subsurface layers 6.2.6. Bulk properties 6.3. Summary 7. Conclusion

In the research field of spintronics, it is essential to have a deep understanding of the relaxation mechanisms of the spin degree of freedom. To this end, we study the spin relaxation in semiconductor nanostructures with spin-orbit interaction. First we analyze the spin decay and dephasing in graphene quantum dots within the framework of the Bloch-Redfield theory. We consider a gate-tunable circular graphene quantum dot where the intrinsic and Rashba spin-orbit interactions are operative. We derive an effective Hamiltonian via the Schrieffer-Wolff transformation describing the coupling of the electron spin to potential fluctuations generated by the lattice vibrations. The spin relaxation occurs with energy relaxation provided by the electron-phonon coupling and the spin-flip transition assisted by spin-orbit interactions. We predict a minimum of the spin relaxation time T1 as a function of the external magnetic field Bext caused by the Rashba spin-orbit coupling-induced anticrossing of opposite spin states. By constrast, the intrinsic spin-orbit interaction leads to monotonic behavior of T1 with Bext due to direct spin-phonon coupling. We also demonstrate that the spin decoherence time T2 = 2T1 in graphene is dominated by relaxation processes up to leading order in the spin-orbit interaction and the electron-phonon coupling mechanisms. Secondly, we develop a numerical model to account for the D´yakonov-Perel spin relaxation mechanism in multisubband quantum wires. We consider the elastic spin-conserving scattering events in the time-evolution operator and then evaluate the time-dependent expectation value of the spin operators. After averaging these results over an ensemble, we can extract the spin relaxation time as a function of Bext. We observe a non-monotonic behavior for the spin relaxation time with Bext aligned perpendicularly to the quantum wire. This effect is called ballistic spin resonance. In our model, the ballistic spin resonance occurs near the subband anticrossing induced by the subband-spin mixing spin-orbit interaction term. In systems with weak spin-orbit coupling strenghts, no spin resonance is observed when Bext is parallel to the channel. Nevertheless, we also predict the emergence of anomalous resonances plateaus in systems with strong spin-orbit couplings even when Bext is aligned with the quantum wire. Finally, we predict the emergence of a robust spin-density helical crossed pattern in two-dimensional electron gas with Rashba α and Dresselhaus β spin-orbit couplings. This pattern arises in a quantum well with two occupied subbands when the spin-orbit coupling strenghts are tuned to have equal absolute strengths but opposite signs, e.g., α1 = +β1 e α2 = −β2 for the first v = 1 and second v = 2 subbands. We named this novel pattern as crossed persistent spin helices. We analyze the spin-charge coupled diffusion equations in order to investigate the lifetime of the crossed persistent spin helices and the feasibility of probing the crossed persistent spin helix mode. We also study the inteband spin-orbit interaction effects on the crossed persistent spin helices, energy anticrossings and spin textures induced by the interband spin-orbit coupling / No campo de pesquisa denominado spintrônica é de fundamental importância o entendimento dos mecanismos de relaxação de spin. A fim de contribuir com esse objetivo, estudamos a relaxação de spin em nanoestruturas semicondutoras na presença da interação spin-órbita. Primeiramente, analisamos o decaimento e defasamento do spin eletrônico em pontos quânticos formados no grafeno usando a teoria de Bloch-Redfield. Consideramos um ponto quântico circular com as interações spin-órbita intrínseca e de Rashba. A relaxação de spin ocorre via relaxacação de energia pela interação elétron-fônon acompanhado do mecanismo de spin-flip auxiliado pela interação spin-órbita. Previmos a presença de um mínimo no tempo de relaxação de spin T1 em função do campo magnético externo Bext causado pelo acoplamento spin-órbita de Rashba que por sua vez leva a cruzamento evitado de níveis de energia com spins opostos. Em contraste, a interação spin-órbita intrínseca gera um comportamento monotônico de T1 com Bext devido ao acoplamento direto spin-fônon. Demonstramos também que o tempo de decoerência de spin T2 = 2T1 é dominado por contribuições dos mecanismos de relaxação em primeira ordem na interação spin-órbita e na interação elétron-fônon. Desenvolvemos também um modelo numérico que leva em conta o mecanismo de relaxação de spin de D´yakonov-Perel em fios quânticos com múltiplas subbandas. Consideramos espalhamentos elásticos, que conservam a orientação do spin, no operador evolução temporal. Em seguida, calculamos o valor esperado dos operadores de spin dependentes do tempo para um ensemble de elétrons. Por fim, extraímos o tempo de relaxação de spin em função do campo magnético externo Bext. Observamos um comportamento não-monotônico da relaxação de spin para um campo Bext alinhado perpendicularmente ao fio quântico. Em sistemas com acoplamento spin-órbita fracos, nenhuma ressonância de spin é encontrada quando Bext está alinhado paralelamento ao fio quântico. No entanto, previmos o aparecimento de ressonâncias de spin anômalas em sistemas com forte acoplamento spin-órbita mesmo quando Bext está alinhado ao canal balístico. Por fim, estudamos a formação de uma densidade de spin helicoidal cruzada e robusta contra espalhamento por impurezas em um gás bi-dimensional de elétrons na presença das interações spin-órbita de Rashba α and Dresselhaus β. Generalizamos o efeito previsto para um poço quântico com uma subbanda para duas subbandas ocupadas quando as interações spin-órbita assumem o mesmo valor em intensidade mas sinais opostos, e.g., α1 = +β1 e α2 = −β2 para a primeira v = 1 e segunda v = 2 subbandas. Denominamos esse novo padrão de helicóides de spin persistentes e cruzadas. Analisamos as equações de difusão com carga e spin acoplados com o intuito de investigarmos o tempo de vida das densidades de spin helicoidais cruzadas e a possibilidade de medi-las com os experimentos atuais. Estudamos também o efeito da interação spin-órbita interbanda na relaxação dos modos helicoidais de spin, espectro de energia com cruzamentos evitados e texturas de spin

Diese Arbeit befasst sich mit der Untersuchung und Manipulation von Halbleitern, bei denen die Spin-Bahn-Kopplung (SBK) in Kombination mit einem Bruch der strukturellen Inversionssymmetrie zu einer impulsabhängigen Spinaufspaltung der Bandstruktur führt. Von besonderem Interesse ist hierbei der Zusammenhang zwischen der spinabhängigen elektronischen Struktur und der strukturellen Geometrie. Dieser wird durch eine Kombination komplementärer, oberflächensensitiver Messmethoden - insbesondere Rastertunnelmikroskopie (STM) und Photoelektronenspektroskopie (PES) - an geeigneten Modellsystemen untersucht. Der experimentelle Fokus liegt dabei auf den polaren Halbleitern BiTeX (X =I, Br, Cl). Zusätzliche Experimente werden an dünnen Schichten der topologischen Isolatoren (TI) Bi1,1-xSb0;9+xSe3 (x = 0. . . 1,1) und Bi2Te2Se durchgeführt. Die inversionsasymmetrische Kristallstruktur in BiTeX führt zur Existenz zweier nicht-äquivalenter Oberflächen mit unterschiedlicher Terminierung (Te oder X) und invertierter atomarer Stapelfolge. STM-Aufnahmen der Oberflächen gespaltener Einkristalle belegen für BiTeI(0001) eine Koexistenz beider Terminierungen auf einer Längenskala von etwa 100 nm, die sich auf Stapelfehler im Kristallvolumen zurückführen lassen. Diese Domänen sind groß genug, um eine vollständig entwickelte Banddispersion auszubilden und erzeugen daher eine Kombination der Bandstrukturen beider Terminierungen bei räumlich integrierenden Messmethoden. BiTeBr(0001) und BiTeCl(0001) hingegen zeichnen sich durch homogene Terminierungen auf einer makroskopischen Längenskala aus. Atomar aufgelöste STM-Messungen zeigen für die drei Systeme unterschiedliche Defektdichten der einzelnen Lagen sowie verschiedene strukturelle Beeinflussungen durch die Halogene. PES-Messungen belegen einen starken Einfluss der Terminierung auf verschiedene Eigenschaften der Oberflächen, insbesondere auf die elektronische Bandstruktur, die Austrittsarbeit sowie auf die Wechselwirkung mit Adsorbaten. Die unterschiedliche Elektronegativität der Halogene resultiert in verschieden starken Ladungsübergängen innerhalb der kovalent-ionisch gebundenen BiTe+ X- Einheitszelle. Eine erweiterte Analyse der Oberflächeneigenschaften ist durch die Bedampfung mit Cs möglich, wobei eine Änderung der elektronischen Struktur durch die Wechselwirkung mit dem Alkalimetall studiert wird. Modifiziert man die Kristallstruktur sowie die chemische Zusammensetzung von BiTeI(0001) nahe der Oberfläche durch Heizen im Vakuum, bewirkt dies eine Veränderung der Bandstruktur in zwei Schritten. So führt zunächst der Verlust von Iod zum Verlust der Rashba-Aufspaltung, was vermutlich durch eine Aufhebung der Inversionsasymmetrie in der Einheitszelle verursacht wird. Anschließend bildet sich eine neue Kristallstruktur, die topologisch nichttriviale Oberflächenzustände hervorbringt. Der Umordnungsprozess betrifft allerdings nur die Kristalloberfläche - im Volumen bleibt die inversionsasymmetrische Einheitszelle erhalten. Einem derartigen Hybridsystem werden bislang unbekannte elektronische Eigenschaften vorausgesagt. Eine systematische Untersuchung von Dünnschicht-TIs, die mittels Molekularstrahlepitaxie (MBE) erzeugt wurden, zeigt eine Veränderung der Morphologie und elektronischen Struktur in Abhängigkeit von Stöchiometrie und Substrat. Der Vergleich zwischen MBE und gewachsenen Einkristallen offenbart deutliche Unterschiede. Bei einem der Dünnschichtsysteme tritt sogar eine lokal inhomogene Zustandsdichte im Bindungsenergiebereich des topologischen Oberflächenzustands auf. / This thesis is about the analysis and manipulation of semiconductor surfaces, for which Spin-Orbit-Coupling (SOC) in combination with a break of structural symmetry leads to a k-dependent spin separation in the electronic structure. Therefore, the relation between the spin-dependent electronic structure and the atomic geometry is of particular interest. Suitable model systems have been investigated by a combination of complementary surface-sensitive measuring methods, e.g. Scanning Tunneling Microscopy (STM) and Photoelectron Spectroscopy (PES). In this work, the main experimental focus is on the BiTeX (X =I, Br, Cl) polar semiconductors. Additional experiments have been carried out on thin films of topological insulators (TI) Bi1,1-xSb0,9+xSe3 (X = 0. . . 1.1) and Bi2Te2Se. The non-centrosymmetric crystal structure of BiTeX results in two non-equivalent surfaces with different terminations (Te or X) and inverted layer structure. STM measurements of the surface of cleaved single crystals show a coexistence of both terminations for BiTeI(0001) on a length scale of around 100 nm, which is caused by bulk stacking faults. These domains are large enough to show a fully developed band dispersion and therefore yield a combined band structure of both terminations when investigated with spatially integrating methods. By contrast, BiTeBr(0001) and BiTeCl(0001) show homogeneous terminations on a macroscopic scale. Atomically resolved STM measurements on each of the three systems reveal different defect densities for each of the atomic layers as well as different structural influences of the halogens. PES measurements show a strong influence of the termination on several surface properties, e.g. electronic band structure, work function and absorbate interaction. The different electronegativities of the halogens result in a varying degree of charge transfer within the covalently-ionically bonded BiTe+ X- unit cell. A more detailed study of the surface properties has been facilitated by Cs deposition and the subsequent investigation of alterations of the electronic structure resulting from interactions with the alkali metal. A surface modification of the crystal structure and chemical properties of BiTeI(0001) by vacuum annealing results in a variation of the band structure in two steps. At first, the loss of I causes a disappearance of the Rashba-splitting, which might be caused by the loss of non-centrosymmetry of the unit cell. In a second step, a new unit cell forms at the surface, which generates non-trivial topological surface states. This reordering only affects the surface while the unit cells of the crystal bulk remain non-centrosymmetric. Hybrid systems like this are expected to exhibit novel electronic properties. A systematic analysis of thin _lm TIs grown by molecular beam epitaxy (MBE) shows changes in morphology and electronic structure as a function of stoichiometry and substrate. The comparison of MBE and grown single crystals reveals a considerable difference between sample properties. One particular system even shows a locally inhomogeneous density of states within the binding energy regime of the topological surface state.

This dissertation describes the theoretic studies of magnetic moment and spinorbit interaction in vacuum (Dirac wavepacket) and solid state systems, such as semiconductors. The semiclassical approach developed here provides a simple and intuitive picture for the origin of spin and spin-orbit coupling. In the Dirac model, the spin magnetic moment is originated from the self-rotating Dirac wavepacket with a correct g-value. The spin-orbit interaction is related to Berry connection (gauge potential) and the model is generalized to solid state systems. The Rashba effect caused by the spin-orbit coupling in a crystal with asymmetric potential in heterostructure quantum well is calculated by semiclassical spindependent scattering. The exact treatment of interface phase accumulation provides a justification of spin-dependent boundary condition at interface derived in previous treatment using Löwdin decomposition. Other spin-orbit coupling related phenomena in solid state system are also discussed in this thesis. / text