This dissertation focuses on the study of spin-dependent transport in systems with strong spin-orbit coupling within their band structure. In particular we focus on the anomalous Hall effect, the spin Hall effect, and the Aharonov-Casher effect whose origins, are linked to the presence of spin-orbit coupling. Given the theoretical controversy surrounding these effects we further simplify our studies to semiconductor systems where the band structure is much simpler than in metallic systems with heavy elements. To obtain finite analytical results we focus on reduced dimensions (two and one dimensions) which can be explored experimentally. To set the stage, we discuss the origins of the strong spin-orbit coupling in semiconductors deriving the effective interaction from the Dirac equation. We discuss in detail the skew scattering contribution to the anomalous Hall effect in two-dimensional systems, which is dominant for systems with low impurity concentrations, and find that it is reduced when the two chiral subbands are partially occupied in an electron gas and vanishes for a hole gas, regardless of the band filling. We also present calculations for all contributing mechanisms. We propose a device to test this prediction and study the crossover from the intrinsic to the extrinsic anomalous Hall effect. We calculate all contributions to the anomalous Hall effect in electron systems using the Kubo-Streda formalism. We find that all contributions vanish when both subbands are occupied and that the skew scattering contribution dominates when only the majority subband is occupied. We calculate the interference effects due to spin-orbit interaction in mesoscopic ring structures patterned from HgTe quantum wells related to the Aharonov-Casher effect and the spin Hall effect. We find that the transport properties are affected by the carrier density as well as the spin orbit interaction. We find that the conductivity is larger in hole gas systems. We also show that devices with inhomogenous spin orbit interaction exhibit an electrically controlled spin-flipping mechanism.

In this Thesis we discussed ultracold Fermi gas with an s-wave interaction and synthetic spin-orbit coupling under a variety of conditions. We considered the system in both three and two spatial dimensions, with equal-Rashba-Dresselhaus type or Rashba-only type of spin-orbit-coupling, and with or without an artificial Zeeman field. We found competing effects on Fermionic superfluidity from spin-orbit coupling and Zeeman fields, and topologically non-trivial states in the presence of both fields. We gave an outlook on the many-body physics in the last.

This thesis focuses on the interplay of the spin-orbit coupling, the electronic correlations and the bandwidth energy scales, along with the lattice distortions seen in perovskite iridates. In particular, we study the magnetic phases in these materials and the insulator to metal transition that occurs as the dimensionality of the system is changed. Motivated by the novel magnetic phases seen in the Sr2IrO4 system, we study the band structures of three materials in the Sr(n+1)Ir(n)O(3n+1) Ruddlesden-Popper series by use of a tight-binding model. From the effect of spin-orbit coupling, we see that the relevant bands near the Fermi energy are indeed made of effective J=1/2 states. This spin-orbit separation of the bands creates effectively smaller bandwidth which can then be split via magnetic ordering driven by electronic correlations. By the use of a self-consistent mean-field theory, we derive the ordering for each of the three materials studied and show that the nature of the magnetic ordering is highly dependent on the lattice structure. The ordering in the bilayer Sr3Ir2O7, which has been a topic of debate in recent experimental studies, is understood within the current approach to be a collinear antiferromagnetic order, in agreement with the latest results. Given that the iridate systems have large spin-orbit coupling, and that the topic of topological insulators has become a very popular subject of research, we discuss the proximity of the perovskite iridates to topological insulators. Since the SrIrO3 material displays a semimetal structure with nodal dispersion near the Fermi level, we looked at an extra term in the Hamiltonian that could lift the nodal lines and turn the system into an insulator. Further studies of the parity eigenvalues of the bands at each time reversal invariant momentum point confirms that for a range of this extra term, a topological phase can be achieved. A discussion on material realization of such a phase is also given where we suggest that a Sr2IrRhO6 superstructure might be a good candidate to achieve this state.

This thesis focuses on the interplay of the spin-orbit coupling, the electronic correlations and the bandwidth energy scales, along with the lattice distortions seen in perovskite iridates. In particular, we study the magnetic phases in these materials and the insulator to metal transition that occurs as the dimensionality of the system is changed. Motivated by the novel magnetic phases seen in the Sr2IrO4 system, we study the band structures of three materials in the Sr(n+1)Ir(n)O(3n+1) Ruddlesden-Popper series by use of a tight-binding model. From the effect of spin-orbit coupling, we see that the relevant bands near the Fermi energy are indeed made of effective J=1/2 states. This spin-orbit separation of the bands creates effectively smaller bandwidth which can then be split via magnetic ordering driven by electronic correlations. By the use of a self-consistent mean-field theory, we derive the ordering for each of the three materials studied and show that the nature of the magnetic ordering is highly dependent on the lattice structure. The ordering in the bilayer Sr3Ir2O7, which has been a topic of debate in recent experimental studies, is understood within the current approach to be a collinear antiferromagnetic order, in agreement with the latest results. Given that the iridate systems have large spin-orbit coupling, and that the topic of topological insulators has become a very popular subject of research, we discuss the proximity of the perovskite iridates to topological insulators. Since the SrIrO3 material displays a semimetal structure with nodal dispersion near the Fermi level, we looked at an extra term in the Hamiltonian that could lift the nodal lines and turn the system into an insulator. Further studies of the parity eigenvalues of the bands at each time reversal invariant momentum point confirms that for a range of this extra term, a topological phase can be achieved. A discussion on material realization of such a phase is also given where we suggest that a Sr2IrRhO6 superstructure might be a good candidate to achieve this state.

We study the spin dynamics in a high-mobility two dimensional electron gas (2DEG) system with generic spin-orbit interactions (SOIs). We derive a set of spin dynamic equations which capture the purely exponential to the damped oscillatory spin evolution modes observed in different regimes of SOI strength. Hence we provide a full treatment of the D'yakonov-Perel's mechanism by using the microscopic linear response theory from the weak to the strong SOI limit. We show that the damped oscillatory modes appear when the electron scattering time is larger than half of the spin precession time due to the SOI, in agreement with recent observations. We propose a new way to measure the scattering time and the relative strength of Rashba and linear Dresselhaus SOIs based on these modes and optical grating experiments. We discuss the physical interpretation of each of these modes in the context of Rabi oscillation. In the finite temperature, We study the spin dynamics in the presence of impurity and electron-electron (e-e) scattering in a III-V semiconductor quantum well. Starting from the Keldysh formalism, we develop the spin-charge dynamic equation at finite temperature in the presence of inelastic scattering which provide a new approach to describe the spin relaxation from the weak to the strong spin-orbit coupling (SOC) regime. In the weak SOC regime, our theory shows that when the system is near the SU(2) symmetry point, because the spin relaxation due to DP mechanism is suppressed dramatically, the spin relaxation is dominated by the Elliott-Yafet (EY) mechanism in a wide temperature regime. The non-monotonic temperature dependence of enhanced-lifetime of spin helix mode is due to the competition between the DP and EY mechanisms. In the strong SOC regime, the our theory is consistent to the previous theoretical results at zero temperature.

La spintronique est principalement basée sur le phénomène d’accumulation de spin, inhérent à la circulation d’un courant électrique aux interfaces entre des matériaux ferromagnétiques et non magnétiques. Ces accumulations sont classiquement obtenues dans des empilements multicouches pour lesquels les épaisseurs des couches sont inférieures aux longueurs caractéristiques du transport dépendant en spin. Il est ainsi possible de générer dans ces multicouches des effets de magnétorésistance ou de transfert de spin.Le développement de procédés de nanofabrication permet aujourd’hui de créer des nanodispositifs dont les dimensions latérales sont inférieures aux longueurs caractéristiques du transport dépendant en spin, et donc de mettre en jeu ces mêmes phénomènes. Au cours de ma thèse j’ai étudié différentes nanostructures latérales F/N, montrant qu’il est possible de tirer avantage de la géométrie tridimensionnelle des structures et des différentes orientations possibles des spins injectés. Des études de transport ont en particulier été réalisées dans les régimes colinéaires et non colinéaires, afin d’étudier les conséquences de la non-colinéarité sur les effets d’accumulation de spin et de magnétorésistance.Après un chapitre d’introduction au transport électronique dépendant en spin, le second démontre l’intérêt de l’utilisation de l’alliage CoFe dans la réalisation de structures latérales. Le troisième chapitre explore les nouvelles opportunités offertes par les structures latérales dans le cas du transport colinéaire. Le cas non-colinéaire du transport de spin au travers d’un matériau ferromagnétique est ensuite examiné à l’aide de mesures d’absorption de spin et de mesures d’effet Hanle. Enfin, l’exploitation des purs courants de spin en vue de réaliser des structures fonctionnelles à effets de magnétorésistance est étudiée au cours des Chapitres V et VI. Des nanostructures dont la géométrie tire parti des trois directions de l’espace, basées sur un transport de spin à la fois vertical et latéral, sont notamment présentée dans le Chapitre VI. / Spintronics is mainly based on the phenomenon of spin accumulation, which is inherent to the circulation of an electric current at the interfaces between ferromagnetic and non-magnetic materials. These accumulations are conventionally obtained in multilayers for which the thicknesses of the layers are smaller than the characteristic lengths of the spin-dependent transport. It is thus possible to generate in these multilayers magnetoresistances or spin transfer effects.The development of nanofabrication processes makes it nowadays possible to create nanodevices whose lateral dimensions are less than the characteristic lengths of the spin-dependent transport, and thus to bring into play these same phenomena. During my thesis I studied different F / N lateral nanostructures, showing that it is possible to take advantage of the three-dimensional geometry of the structures, and of the different possible orientations of the injected spins. In particular, transport studies have been carried out in collinear and non-collinear regimes, in order to study the consequences of the non-collinearity on the spin accumulations and magnetoresistances.After an introductory chapter on spin-dependent electron transport, the second chapter demonstrates the interest of the CoFe alloy in lateral structures. The third chapter explores the new opportunities offered by lateral structures in the case of collinear transport. The non-collinear case of spin transport through a ferromagnetic material is then examined using spin absorption measurements and Hanle measurements. Finally, the exploitation of pure spin currents in order to realize functional devices is studied in Chapters V and VI. In particular, new nanostructures whose geometry takes advantage of the three directions of space (based on both vertical and lateral spin transport) are presented in Chapter VI.

Magnetic random­access memory (MRAM) devices have been widely studied since the 1960s. During this time, the size of spintronic devices has continued to decrease. Conse quently, there is now an urgent need for new low­dimensional magnetic materials to mimic the traditional structures of spintronics at the nanoscale. We also require new effective mechanisms to conduct the main functions of memory devices, which are: reading, writ ing, and storing data. To date, most research efforts have focused on MRAM devices based on magnetic tun nel junction (MTJ), such as a conventional field­driven MRAM and spin­transfer torque (STT)­MRAM devices. Consequently, many efforts are currently focusing on new alterna tives using different techniques, such as spin­orbit torque (SOT) and magnetic skyrmions (a skyrmion is the smallest potential disruption to a uniform magnet required to obtain more effective memory devices). The most promising memory devices are SOT­MRAMs and skyrmion­based memories. This study investigates the magnetic properties of 1T­phase vanadium dichalcogenide (VXY) Janus monolayers, where X, Y= S, Se, or Te (i.e., monolayers that exhibit inversion symme try breaking due to the presence of different chalcogen elements). This study is developed along four directions: (I) the nature of the magnetism and the SOT effect of Janus mono layers; (II) the Dzyaloshinskii Moriya interaction (DMI); (III) investigation of stability en hancement by adopting practical procedures for industry; and (IV) study of the effect of a hexagonal boron nitride (h­BN) monolayer as an insulator on the magnetism of the VXY monolayer. This study provides a clear perspective for the next generation of memory de vices, such as SOT­MRAMs based on transition metal dichalcogenide monolayers.

In the search for low power operation of microelectronic devices, spin-based solutions have attracted undeniable increasing interest due to their intrinsic magnetic nonvolatility. The ability to electrically manipulate the magnetic order using spin-orbit interaction, associated with the recent emergence of topological spintronics with its promise of highly efficient charge-to-spin conversion in solid state, offer alluring opportunities in terms of system design. Although the related technology is still at its infancy, this thesis intends to contribute to this engaging field by investigating the nature of the charge and spin transport in spin-orbit coupled and topological systems using quantum transport methods. We identified three promising building blocks for next-generation technology, three classes of systems that possibly enhance the spin and charge transport efficiency: (i)- topological insulators, (ii)- spin-orbit coupled magnonic systems, (iii)- topological magnetic textures (skyrmions and 3Q magnetic state). Chapter 2 reviews the basics and essential concepts used throughout the thesis: the spin-orbit coupling, the mathematical notion of topology and its importance in condensed matter physics, then topological magnetism and a zest of magnonics. In Chapter 3, we study the spin-orbit torques at the magnetized interfaces of 3D topological insulators. We demonstrated that their peculiar form, compared to other spin-orbit torques, have important repercussions in terms of magnetization reversal, charge pumping and anisotropic damping. In Chapter 4, we showed that the interplay between magnon current jm and magnetization m in homogeneous ferromagnets with Dzyaloshinskii-Moriya (DM) interaction, produces a field-like torque as well as a damping-like torque. These DM torques mediated by spin wave can tilt the imeaveraged magnetization direction and are similar to Rashba torques for electronic systems. Moreover, the DM torque is more efficient when magnons are thermally driven. Chapters 5 and 6 carry throughout tight-binding studies on the topological charge-spin transport in two-dimensional lattices with ferromagnetic skyrmions and 3Q magnetic structure. We use the Landauer-Buttiker formalism and evaluate the robustness of the topological signals. For the 3Q state, a spin-polarized quantum anomalous Hall state with chiral edge modes, unaffected by deformation and disorder, is reachable in zero net magnetization. We finish with concluding remarks and perspectives.

In the past two decades, the interest in materials with strong spin-orbit coupling has attracted substantial attention because of the novel physical mechanisms they display and their potential for applications. The interface displaying large spin-orbit coupling has been recognized as a powerful platform to investigate the spin transport in ferromagnetic, antiferromagnetic, and non-magnetic materials, as well as their interfaces. Besides its rich physics, the related applications are also worth studying. The current-induced spin-orbit-torque arising from angular momentum transfer from the lattice to the spin system has substantial potential in recent state-of-art spin-orbit torque magnetic random access memory. In this dissertation, we have been interested in better understanding and characterizing the spin-orbit torque and spin Hall transport in various heterostructures of interest. We used the second harmonic method to determine the magnitude of the spin currents generation and transmission in Cu-Au alloy and Ir-Mn compound, respectively. We also characterized the device performance in selected heterostructures displaying either perpendicular MgO-based tunnel magnetoresistance or unusual surface states. Finally, we used these properties to approach spin-orbit torque magnetic random access memory through designing, fabricating, and characterizing the devices that focused on current-induced spin-orbit-torque magnetization switching.

The spin of an electron often misleadingly interpreted as the classical rotationof a particle. The quantum spin distinguishes itself from classicalrotation by possessing quantized states and can be detected by its magneticmoment. The properties of spin and its collective behavior with otherfundamental properties are fascinating in basic sciences. In many aspectsit offers scope for designing new materials by manipulating the ensemblesof spin. In recent years attention towards high density storage devices hasdriven the attention to the fundamental level were quantum physics rules.To understand better design of molecule based storage materials, studies onspin degrees of freedom and their coupling properties can not be neglected. To account for many body effect of two or more electrons consistent withrelativity, an approximation like the Breit Hamiltonian(BH) is used in modernquantum chemical calculations, which is successful in explaining the splitin the spectra and corresponding properties associated with it. Often differenttactics are involved for a specific level of computations. For example themulti-configurational practice is different from the functional based calculations,and it depends on the size of the system to choose between resourcesand accuracy. As the coupling terms offers extra burden of calculating theintegrals it is literally challenging. One can readily employ approximations as it suits best for the applicationoriented device computations. The possible methods available in the literatureare presented in chapter 2. The theoretical implementations of couplingfor the multi-reference and density functional method are discussed in detail.The multi-reference method precedes the density functional methodin terms of accuracy and generalizations, however it is inefficient in dealingvery large systems involving many transition elements, which is vital formolecule based magnets as they often possess open shell manifolds. On theother hand existing density functional method exercise perturbations techniqueswhich is extremely specialized for a specific system - highly coupledspins. The importance of spin-spin coupling(SSC) in organic radical-Oxyallyl(OXA)was systematically studied with different basis sets and compared with asimilar isoelectronic radical(TMM). The method of spin-spin coupling implementationsare also emphasized. Similar coupling studies were carriedivout for the species HCP and NCN along with spin-orbit coupling(SOC).The splitting of the triplet states are in good agreement with experiments / QC 20110210