Spin-orbit coupling (SOC) reduces the spatial symmetry of ferromagnetic solids. That is, the physical properties of ferromagnetic materials are anisotropic, depending on the magnetization direction. In this thesis, by means of numerical calculations with full-relativistic density functional theory, we studied two kinds of physical properties: surface magnetic anisotropy energy (MAE) and anisotropic thermoelectric power due to Lifshitz transitions. After a short introduction to the full-relativistic density functional theory in Chapter 2, the MAE of ferromagnetic thin films is studied in Chapter 3. For such systems, separation of different contributions, such as bulk magnetocrystalline anisotropy (MCA) energy, shape anisotropy energy, and surface/interface anisotropy energy, is crucial to gain better understanding of experiments. By fitting our calculating results for thick slabs to a phenomenological model, reliable surface MAE could be obtained. Following this idea, we have studied the MAE of Co slabs with different geometries, focusing on the effects of orbital polarization correction (OPC). We found that the surface anisotropy is mainly determined by the geometry. While OPC gives better results of orbital moments, it overestimates the MAE. In the second part of Chapter3, the effects of electric fields on the MAE of L10 ferromagnetic thin films are studied. Using a simple model to simulate the electric field, our calculations are in good agreement with previous experimental results. We predicted that for CoPt, even larger effects exist. Moreover, we found that it is the amount of screening charge that determines the magnetoelectric coupling effects. This gives us some clue about how to achieve electric field control of magnetization direction. In Chapter 4, Lifshitz transitions in L10 FePt caused by a canted magnetic field are studied. We found several Lifshitz transitions in ordered FePt with tiny features in DOS. Using a two-band model, it is demonstrated that at such transitions, the singular behaviour of kinetic properties is due to the interband scattering, and the singularity itself is proportional to the derivative of the singular DOS. For FePt, such singularity will be smeared into anomaly by chemical disorder. Using CPA, we studied the effects of energy level broadening for the critical bands in FePt. We found that for experimentally available FePt thin films, Lifshitz transitions would induce up to a 3% increase of thermopower as the magnetization is rotated from the easy axis to the hard axis. / Spin-Bahn-Kopplung reduziert die Symmetrie ferromagnetischer Festkörper. Das bedeutet, dass die physikalischen Eigenschaften ferromagnetischer Stoffe anisotrop bezüglich der Magnetisierungsrichtung sind. In dieser Dissertation werden mittels numerischer voll-relativistischer Dichtefunktional-Rechnungen zwei Arten physikalischer Eigenschaften untersucht: magnetische Oberflächen-Anisotropieenergie (MAE) und anisotrope Thermokraft durch Lifshitz-Übergänge. Nach einer kurzen Einführung in die relativistische Dichtefunktional-Theorie in Kapitel 2 wird in Kapitel 3 die MAE ferromagnetischer dünner Filme untersucht. In diesen Systemen ist es für ein Verständnis experimenteller Ergebnisse wichtig, verschiedene Beiträge zu separieren: Volumenanteil der magnetokristallinen Anisotropie (MCA), Formanistropie und Oberflächen bzw. Grenzflächenanisotropie. Durch Anpassen berechneter Daten für dicke Schichten an ein phänomenologisches Modell konnten verlässliche Oberflächen Anisotropien erhalten werden. In dieser Weise wurde die MAE von Co- Schichten mit unterschiedlichen Geometrien untersucht, wobei der Einfluss von Orbitalpolarisations-Korrekturen (OPC) im Vordergrund stand. Es wurde gefunden, dass die Oberflächenanisotropie hauptsächlich von der Geometrie bestimmt wird. Während OPC bessere Ergebnisse für die Orbitalmomente liefert, wird die MAE überschätzt. Im zweiten Teil von Kapitel 3 wird der Einfluss elektrischer Felder auf die MAE von dünnen ferromagnetischen Filmen mit L10-Struktur untersucht. Unter Verwendung eines einfachen Modells zur Simulation des elektrischen Feldes liefern die Rechnungen gute Übereinstimmung mit vorliegenden experimentellen Ergebnissen. Es wird vorhergesagt, dass für CoPt ein noch größerer Effekt existiert. Weiterhin wurde gefunden, dass die magnetoelektrische Kopplung von der Größe der Abschirmladung bestimmt wird. Dies ist eine wichtige Einsicht, um die Magnetisierungsrichtung durch ein elektrisches Feld kontrollieren zu können. In Kapitel 4 werden Lifshitz-Übergänge untersucht, die ein gekantetes Magnetfeld hervorruft. Es wurden mehrere Lifshitz-Übergänge in geordnetem FePt gefunden, welche kleine Anomalien in der Zustandsdichte hervorrufen. Mit Hilfe eines Zweiband-Modells wird gezeigt, dass an solchen Übergängen das singuläre Verhalten kinetischer Eigenschaften durch Interband- Streuung verursacht wird und dass die Singularität proportional zur Ableitung der singulären Zustandsdichte ist. In FePt wird durch chemische Unordnung diese Singularität zu einer Anomalie verschmiert. Der Einfluss einer Verbreiterung der Energieniveaus der kritischen Bänder in FePt wurde mittels CPA untersucht. Es wurde gefunden, dass in experimentell verfügbaren dünnen FePt-Filmen Lifshitz-Übergänge bis zu 3% Erhöhung der Thermokraft erzeugen, wenn die Magnetisierung von der leichten in die harte Richtung gedreht wird.

Title: Theoretical study of spin-orbit coupling on spectra and photophysics of rhenium complexes Author: RNDr. Radka Heydová Department: Physical and Macromolecular Chemistry Supervisor: Ing. Stanislav Záliš, CSc., JHI AS CR, v.v.i. Supervisor's e-mail address: stanislav.zalis@jh.inst-cas.cz Abstract: Relativistic effects, especially spin-orbit coupling (SOC), play an essential role in transition metal chemistry and SOC treatment is indispensable for a correct theoretical description. To demonstrate the importance of SOC, the energies and oscillator strengths of vertical transitions for a series of [ReX(CO)3(2,2'-bipyridine)] (X = Cl, Br, I) and [Re(imidazole)(CO)3(1,10-phenanthroline)]+ complexes were calculated in the spin-free (SF) and spin-orbit (SO) conceptual frameworks. Two different computational approaches were adopted: SO-MS-CASPT2 where SOC was added a posteriori using a configuration interaction model (SO-RASSI), and the approximate perturbative SO-TD-DFT method. Relativistic effects were included via the two-component Douglas-Kroll-Hess transformation and the zeroth-order regular approximation in the former and the latter technique, respectively. The SF (i.e. accounting only for the scalar relativistic effects) and SO results from both methods were compared with each other and to available...

In the investigation of correlated electron systems which are characterized by strong spin-orbit coupling, one of the central challenges is the description of the complex interplay of different microscopic energy scales and the elucidation of its influence on the formation of exotic electronic phases like complex ordering phenomena and superconductivity. In the present thesis, exemplary three case studies of iridium-based compounds are presented, in which the effects of such an interplay have been investigated employing state-of-the-art synchrotron-based techniques. The particular focus is set on experimental possibilities to influence this equilibrium utilizing external parameters. In the first study, magnetic excitations are investigated in iridate double perovskites, which exhibit a nonmagnetic ground state. Upon increasing the influence of kinetic contributions, the potential condensation of these excitations is predicted to drive a novel kind of magnetic transitions, called ’excitonic magnetism’. A comprehensive investigation of the dynamics of these excitations via resonant inelastic x-ray scattering allows for an estimation of the relevant energy scales. These results indeed reveal that the influence of kinetic contributions is too small to drive such a transition under ambient conditions. Therefore the influence of excitonic magnetism on the macroscopic properties of the investigated compounds can be excluded. In the second case, the development of a new experimental setup is presented, facilitating the investigation of complex ordering phenomena at low temperatures as a function of pressure via resonant elastic x-ray scattering. This setup has been developed and implemented as part of this work in strong collaboration with the staff of the beamline P09 at the synchrotron PETRAIII (DESY). The functionality of this setup has been illustrated by measurements of the resonant magnetic x-ray scattering in the spin-orbit coupled Mott-insulator Sr 2IrO4. Since the magnetic ground state and magnetic order in iridates result from a complex interplay of different microscopic energy scales, these systems are particularly susceptible to external influences like hydrostatic pressure. In the third case, structural phase transitions are investigated in the iridium-based dichalcogenide IrTe2. Despite the macroscopic itinerant properties of IrTe2, the phase transitions are characterized by the formation of strongly localized states. These transitions have been investigated in the course of this work using single crystal x-ray diffraction experiments as a function of hydrostatic pressure and temperature. The presented experimental data show that these strongly localized states are stabilized with increasing pressure, which is observed as an increased density of Ir-Ir dimer bonds.

No description available.

No description available.

No description available.

<p>Bose-Einstein condensates (BECs) in light-induced synthetic gauge fields and spaces can provide a highly-tunable platform for quantum simulations. Chapter 1 presents a short introduction to the concepts of BECs and our BEC machine. Chapter 2 introduces some basic ideas of how to use light-matter interactions to create synthetic gauge fields and spaces for neutral atoms. Three main research topics of the thesis are summarized below.</p> <p>Chapter 3: Recently, using bosonic quasiparticles (including their condensates) as spin carriers in spintronics has become promising for coherent spin transport over macroscopic distances. However, understanding the effects of spin-orbit (SO) coupling and many-body interactions on such a spin transport is barely explored. We study the effects of synthetic SO coupling (which can be turned on and off, not allowed in usual materials) and atomic interactions on the spin transport in an atomic BEC.</p> <p>Chapter 4: Interplay between matter and fields in physical spaces with nontrivial geometries can lead to phenomena unattainable in planar spaces. However, realizing such spaces is often impeded by experimental challenges. We synthesize real and curved synthetic dimensions into a Hall cylinder for a BEC, which develops symmetry-protected topological states absent in the planar counterpart. Our work opens the door to engineering synthetic gauge fields in spaces with a wide range of geometries and observing novel phenomena inherent to such spaces.</p> <p>Chapter 5: Rotational properties of a BEC are important to study its superfluidity. Recent studies have found that SO coupling can change a BEC's rotational and superfluid properties, but this topic is barely explored experimentally. We study rotational dynamics of a SO-coupled BEC in an effective rotating frame induced by a synthetic magnetic field. Our work may allow for studying how SO coupling modify a BEC's rotational and superfluid properties.</p> <p>Chapter 6 presents some possible future directions.</p>

Le travail théorique présenté dans cette thèse concerne la formation de molécules ultra-froides bialcalines et le contrôle de leurs degrés de liberté externes et internes. Cette étude est motivée par les nombreuses expériences en cours visant à l'obtention d'un gaz quantique dégénéré de molécules dans leur état fondamental absolu. Le schéma de formation étudié repose sur le processus de transfert adiabatique stimulé (STIRAP) réalisé en présence d'un potentiel optique de piégeage (réseau optique) des atomes et des molécules.Nous avons déterminé les paramètres du réseau optique (intensité et fréquence du champ laser) qui permettent de piéger efficacement des dimères d'alcalins en évaluant la polarisabilité dynamique acquise par les molécules soumises à un champ externe. Ces calculs reposent en particulier sur la connaissance détaillée de la structure électronique des molécules. Nous avons identifié des plages de longueur d'ondes dites « magiques » où la polarisabilité est la même pour chaque niveau peuplé au cours du transfert adiabatique, permettant ainsi un transfert optimal. Ce formalisme nous a également permis d'obtenir les coefficients Van der Waals de l'interaction à longue portée nécessaires pour étudier les taux de collisions entre molécules.Nous avons réalisé une étude plus détaillée de la molécule RbCs. En étudiant précisément la probabilité de transition de la molécule vers un niveau excité, nous avons proposé un schéma STIRAP pour transférer des molécules de RbCs, initialement dans un niveau vibrationnel excité, vers leur état rovibrationnel fondamental.Ces travaux ont montré l'importance de la connaissance précise de la structure hyperfine de l'état électronique moléculaire excité pour réaliser un gaz dégénéré de molécules dans un état quantique bien défini. Un modèle asymptotique nous a permis d'obtenir une première estimation de la structure hyperfine des courbes d'énergies potentielles des premiers états moléculaires excités des molécules Cs2 et RbCs. / The theoretical work presented in this thesis is focused on the formation of ultracold bialcaline molecules and on the control of their external and internal degrees of freedom. This study is motivated by the increasing number of experiments aiming at obtaining a quantum degenerate gas of molecules in their absolute ground state. The formation scheme we worked on is based on the Stimulated Raman Adiabatic Passage (STIRAP) technique operated while molecules are trapped inside an optical lattice.We have determined the parameters of the optical lattice (intensity and wavelength of the laser) that allow for an efficient trapping of the alkali dimers by evaluating the dynamic polarizability of molecules in the presence of an external field. Such calculations require the accurate knowledge of the electronic structure of the molecules. We have identified the so-called ``magic'' wavelength for which all levels populated during the STIRAP sequence have the same polarizability, thus ensuring an optimal transfer. The same approach has also been used to compute the strength of the long-range interaction between polar bialkali molecules needed to evaluate collision rates.The particular case of the RbCs molecule has been investigated. We have selected a radiative transition allowing for an efficient STIRAP scheme yielding molecules in their rovibrational ground state. These works have raised the need for the precise knowledge of the hyperfine structure of the excited electronic molecular state involved in the STIRAP scheme. We have developed an asymptotic model to obtain a first estimate of the hyperfine structure for the potential curves of the lowest excited states of Cs2 and RbCs.

Em sistemas com acoplamento spin-órbita (SO) é possível manipular eletricamente o spin do elétron via a aplicação de um campo elétrico.1 Isso permite a potencial aplicação do grau de liberdade de spin (Spintronica) no desenvolvimento de novos dispositivos e tecnologias, como por exemplo na tecnologia da informação (computação quântica).2,3 No entanto, sabe-se que a interação SO causa efeitos indesejáveis, como por exemplo a relaxação e o defasamento de spin.4 Dessa maneira, do ponto de vista de aplicações, torna-se desejável maximizar o tempo de vida do spin. Neste trabalho, investigamos a relaxação de spin dos elétrons de condução em poços quânticos com duas sub-bandas5 crescidos ao longo das direções [001] e [110] via o mecanismo de D\'yakonov-Perel\'.6 Combinando teoria de grupos, o método k.p, a aproximação da função envelope e teoria de perturbação de Löwdin obtemos um Hamiltoniano efetivo para os elétrons da banda de condução na presença das interações SO de Rashba e Dresselhaus. Aqui, diferentemente de alguns trabalhos anteriores,7,8 além de incluir o termo cúbico de Dresselhaus, também levamos em conta as contribuições devido à influência da segunda sub-banda de mais baixa energia do poço. A partir deste Hamiltoniano derivamos expressões para os tempos de relaxação do spin e analisamos como estas novas contribuições (termos do acoplamento com a segunda sub-banda) afetam os tempos de vida dos spins. Comparamos os tempos de relaxação para as direções [001] com os calculados para a direção [110]. Nossos resultados mostram que as contribuições devido à segunda sub-banda são desprezíveis para ambas as direções. Mostramos também que o tempo de relaxação para a direção [110] é mais longo que o da [001], resultado consistente com experimentos9,10 e outros trabalhos teóricos anteriores.7 / In systems with spin-orbit (SO) coupling, it is possible to electrically manipulate the electron spin via applied gate voltages.1 This allows for the potential use of the spin degree of freedom (Spintronics) in the development of new devices and technologies, for instance information technology (quantum computing).2,3 It is known however, that the SO interaction leads to the undesired effect of causing spin relaxation and spin dephasing.4 Thus from the point of view of applications, it is desirable to maximize the spin lifetimes. Here, we investigate the spin relaxation of the conduction electrons in quantum wells with two sub-bands5 grown along the [001] and [110] directions via the D\'yakonov-Perel\' mechanism.6 By combining group theory, the k.p method, the envelope function approach and the Löwdin perturbation theory, we obtain an effective Hamiltonian for the conduction electrons in the presence of the Rashba and Dresselhaus SO interactions. Differently from some early works,7,8 in addition to the cubic Dresselhaus term, we also account for the contributions arising from the second lowest sub-band of the well. We derive expressions for the spin relaxation times and analyze how the new contributions (second sub-band terms) affect the spin lifetimes. We compare the relaxation times obtained in the [001] direction with those calculated for the [110] direction. Our results show that the contributions from the second sub-band are negligible for both directions. We also find that the relaxation time in the [110] direction is longer than the one in the [001], a result consistent with experiments9,10 and earlier theoretical works.7

Cette thèse est consacrée à la description de la physique à une particule ainsi qu'à celle de fluides quantiques bosoniques dans des systèmes topologiques. Les deux premiers chapitres sont introductifs. Dans le premier, nous introduisons des éléments de théorie des bandes et les quantités géométriques et topologiques associées : tenseur métrique quantique, courbure de Berry, nombre de Chern. Nous discutons différents modèles et réalisations expérimentales donnant lieu à des effets topologiques. Dans le second chapitre, nous introduisons les condensats de Bose-Einstein ainsi que les excitons-polaritons de cavité.La première partie des résultats originaux discute des phénomènes topologiques à une particule dans des réseaux en nid d'abeilles. Cela permet de comparer deux modèles théoriques qui mènent à l'effet Hall quantique anormal pour les électrons et les photons dû à la présence d'un couplage spin-orbite et d'un champ Zeeman. Nous étudions aussi l'effet Hall quantique de vallée photonique à l'interface entre deux réseaux de cavités avec potentiels alternés opposés.Dans une seconde partie, nous discutons de nouveaux effets qui émergent due à la présence d'un fluide quantique interagissant décrit par l’équation de Gross-Pitaevskii dans ces systèmes. Premièrement, il est montré que les interactions spin anisotropes donnent lieu à des transitions topologiques gouvernées par la densité de particules pour les excitations élémentaires d’un condensat spineur d’exciton-polaritons.Ensuite, nous montrons que les tourbillons quantifiés d'un condensat scalaire dans un système avec effet Hall quantique de vallée, manifestent une propagation chirale le long de l'interface contrairement aux paquets d'ondes linéaires. La direction de propagation de ces derniers est donnée par leur sens de rotation donnant lieu à un transport de pseudospin de vallée protégé topologiquement, analogue à l’effet Hall quantique de spin.Enfin, revenant aux effets géométriques linéaires, nous nous sommes concentrés sur l’effet Hall anormal. Dans ce contexte, nous présentons une correction non-adiabatique aux équations semi-classiques décrivant le mouvement d’un paquet d’ondes qui s’exprime en termes du tenseur géométrique quantique. Nous proposons un protocole expérimental pour mesurer cette quantité dans des systèmes photonique radiatifs. / This thesis is dedicated to the description of both single-particle and bosonic quantum fluid Physics in topological systems. After introductory chapters on these subjects, I first discuss single-particle topological phenomena in honeycomb lattices. This allows to compare two theoretical models leading to quantum anomalous Hall effect for electrons and photons and to discuss the photonic quantum valley Hall effect at the interface between opposite staggered cavity lattices.In a second part, I present some phenomena which emerge due to the interplay of the linear topological effects with the presence of interacting bosonic quantum fluid described by mean-field Gross-Pitaevskii equation. First, I show that the spin-anisotropic interactions lead to density-driven topological transitions for elementary excitations of a condensate loaded in the polariton quantum anomalous Hall model (thermal equilibrium and out-of-equilibrium quasi-resonant excitation configurations). Then, I show that the vortex excitations of a scalar condensate in a quantum valley Hall system, contrary to linear wavepackets, can exhibit a robust chiral propagation along the interface, with direction given by their winding in real space, leading to an analog of quantum spin Hall effect for these non-linear excitations. Finally, coming back to linear geometrical effects, I will focus on the anomalous Hall effect exhibited by an accelerated wavepacket in a two-band system. In this context, I present a non-adiabatic correction to the known semiclassical equations of motion which can be expressed in terms of the quantum geometric tensor elements. We also propose a protocol to directly measure the tensor components in radiative photonic systems.