Quantum spin liquids represent a novel phase of magnetic matter where quantum fluctuations are large enough to suppress the formation of local order parameters, even down to zero temperature. Quantum spin liquid states can emerge from frustrated quantum magnets. These states show several peculiar properties, such as topological order, fractional excitations, and long-range entanglement. The Kitaev spin model on the honeycomb lattice is one of the few models proposed which can exactly show the existence of a $\mathbb{Z}_2$ quantum spin liquid. The model describes spins featuring frustrated compass interactions, and it exhibits a quantum spin liquid ground state. The model's ground state can be found exactly by representing spins in terms of Majorana fermions. It turns out that spin excitations fractionalize into two degrees of freedom: spinless matter fermions and flux excitations of the emergent $\mathbb{Z}_2$ gauge theory. Recently, possible solid-state realizations of Kitaev quantum spin liquids have been proposed in a class of frustrated Mott insulators. Unfortunately, experiments can not unambiguously identify quantum spin liquids, due to their elusive nature. Nevertheless, indirect observations on a spin liquid state can be done by looking at its excitations. Along this line, thermal transport investigations provide for an option to study heat-carrying excitations, and thus the properties of the related spin liquid state. In this doctoral thesis work, I performed a study of longitudinal thermal transport properties in the two-dimensional Kitaev spin model. This study aims to advance the understanding of transport in prototypical frustrated quantum magnets that might harbor Kitaev physics, and in particular quantum spin liquid states. For this purpose, I explored the model for varying exchange coupling regimes $-$ to underline the impact of anisotropy on transport $-$ and I studied transport over a wide range of temperatures. Transport properties have been explored within the formalism of the linear response theory. Based on the latter, thermal transport coefficients can be evaluated by calculating dynamical energy-current auto-correlation functions. First, I performed an analytical study of the uniform gauge sector of the model $-$ where excitations of gauge degrees of freedom are neglected. Analytical findings for the energy-current correlations, and their related transport coefficients, imply a finite-temperature ballistic heat conductor in terms of free matter fermion excitations $-$ independent of exchange couplings. Second, thermal transport has been studied at finite temperatures, considering thermal gauge excitations off the uniform gauge sector. For this purpose, I made use of two complementary numerical methods able to treat finite-temperature systems. On the one hand, I resorted on the exact diagonalization of the Kitaev Hamiltonian given in terms of fermions and a real-space dependent $\mathbb{Z}_2$ gauge potential, to study relatively small systems. On the other hand, I used an approximate method based on a mean-field treatment of thermal gauge fluctuations. The method allowed to extend the study of thermal transport to systems with up to $\sim\mathcal{O}(10^4)$ spinful sites. It made possible the computation of correlation functions by reducing the exact trace over all gauge states to an average over dominant gauge states suited to a given temperature range. The reliability of the method has been checked by comparing to numerically exact thermodynamics of systems. Based on the thermodynamic analysis, the method has been restricted to a temperature range where the mean-field treatment of gauge fluctuations is acceptable. Within such temperature range, the method succeeded in well reproducing exact results. The prime advantage of this method is its capability to reveal important features in the energy-current correlation spectra, not captured by the exact diagonalization approach because of finite-size effects. I found that the energy-current correlation spectra, in the presence of thermal gauge excitations, show clear signatures of spin fractionalization. In particular, the low-energy part of spectra displays features arising from a temperature-dependent matter-fermion density relaxation off an emergent thermal gauge disorder. This static gauge disorder also leads to the appearance of a pseudogap in the zero-frequency limit, which closes in the thermodynamic limit. The extracted dc heat conductivity is consequently influenced by this interplay between matter fermions and gauge degrees of freedom. The anisotropy in the exchange couplings moves Kitaev systems through gapless and gapped phases of the matter fermion sector. Effects of anisotropy are visible in the dc conductivities which display a low-temperature dependence crossing over from power-law to exponentially activated behavior upon entering the gapped phase. Therefore, I found that in the thermodynamic limit, two-dimensional Kitaev systems feature dissipative transport, regardless of exchange couplings. This finding is in contrast to the ballistic transport found discarding gauge excitations in the uniform gauge sector, which underlines the relevance of gauge degrees of freedom in thermal transport properties of Kitaev systems.

Spin resonance of a two-dimensional electron system confined in a GaN/AlGaN heterostructure grown by molecular beam epitaxy was resistively detected over a wide range of magnetic field and microwave frequency. Although the spin-orbit interaction is strong in this type of heterostructure at zero magnetic field, surprisingly the width of the detected spin resonance line was very narrow—down to 6.5 mT at 13.3 T. The spin depolarization time extracted from the resonance linewidth was estimated to be 2 ns. The electron g-factor was measured with high accuracy, resembling a value close to the free-electron value and its dependence on the magnetic field was studied.

The general theme of the thesis is the interplay between magnetization dynamics and spin transport. The main presentation is divided into three parts. The first part is devoted to deepening our understanding on magnetic damping of ferromagnetic metals, which is one of the long-standing issues in conventional spintronics that has not been completely understood. For a nonuniformly-magnetized ferromagnetic metal, we find that the damping is nonlocal and is enhanced as compared to that in the uniform case. It is therefore necessary to generalize the conventional Landau-Lifshitz-Gilbert equation to include the additional damping. In a different vein, the decay mechanism of the uniform precession mode has been investigated. We point out the important role of spin-conserving electron-magnon interaction in the relaxation process by quantitatively examining its contribution to the ferromagnetic resonance linewidth. In the second part, a transport theory is developed for magnons which, in addition to conduction electrons, can also carry and propagate spin angular momentum via the magnon current. We demonstrate that the mutual conversion of magnon current and spin current may take place at magnetic interfaces. We also predict a novel magnon-mediated electric drag effect in a metal/magnetic-insulator/metal trilayer structure. This study may pave the way to the new area of insulator-based spintronics. In the third part of thesis, particular attention is paid to the influence the spin orbit coupling on both charge and spin transport. We theoretically investigate magnetotransport anisotropy and the conversion relations of spin and charge currents in various magnetic systems, and apply our results to interpret recent experiments.

A unique feature of the 5d-iridates is that the spin-orbit interaction (SOI) and Coulomb interactions U are of comparable strength and therefore compete vigorously. The relative strength of these interactions stabilizes new exotic ground states that provide a fertile ground for studying new physics. SOI is proportional to Z^4 (Z is the atomic number), and it is now recognized that strong SOI can drive novel narrow-gap insulating states in heavy transition metal oxides such as iridates. Indeed, strong SOI necessarily introduces strong lattice degrees of freedom that become critical to new physics in the iridates. This dissertation thoroughly examines a wide array of newly observed novel phenomena induced by adjusting the relative strengths of U and SOI interactions via slight chemical doping and application of hydrostatic pressure in the layered iridates, particularly, BaIrO3 and Sr2IrO4.

<p>Highly correlated quantum chemical methods have been appliedto study the photophysical properties of substituted benzenes.With the inclusion of spin-orbit coupling, the phosphorescencesof these molecules have been calculated usingMulti-CongurationalSelf- Consistent Field (MCSCF) quadraticresponse theory. The Herzberg-Teller approximation has beenadopted to evaluate the vibronic contributions tophosphorescence.</p><p>The performance of hybrid density functional theory (DFT) atthe B3LYP level is examined in comparison to the MP2, CCSD andCCSD(T) methods for the geometry and permanent dipole moment ofp-aminobenzoic acid. The time-dependent DFT/B3LYP method isapplied to calculate the two-photon absorption of a series ofZinc-porphyrin derivatives in combination with a two-statemodel. The transitions between excited singlet and tripletstates of Zinc and Platinum based organometallic compounds havebeen computed using DFT quadratic response theory. The resultsare used to simulate the non-linear propagation of laser pulsesthrough these materials utilizing a dynamical wave propagationmethod.</p>

Mesoscopic devices, such as nano-wires, are of interest for the next step in creating spintronic devices. With the ability to manipulate electrons and their spin, spintronic devices may be realised. To that end the different effects found in low-dimensional devices must be studied and understood. In this thesis  the influence that lateral spin-orbit coupling (LSOC) has on a nanowire, with asymmetrical confinement potential, is studied. The nanowire is studied through a numerical approach, using the Hartree-Fock method with Dirac interactions to solve the eigenvalue problem of an idealised infinite nanowire. The nanowire has a split-gate that generates the electrostatic asymmetrical confinement potential. It is found that the lateral spin-orbit coupling has little to no effect without any longitudinal effects in the wire, such as source-drain bias. The electrons will spontaneously create spin-rows in the device due to spin polarization. The spin polarization is triggered by using LSOC, numerical noise or from a weak magnetic field. / Mesoskopiska anordningar, som nano-trådar, tros vara ett viktigt steg för att skapa spinnelektronik. För att kunna skapa spinnelektronik behövs kunskap om hur elektroner kan manipuleras. Generellt måste därför existerande fenomen i nanoelektronik studeras. I denna avhandling studeras hur ''lateral spin-orbit koppling'' (LSOC) influerar en nanotråd som har en asymmetrisk potentialbarriär. Hartree-Fock metoden, med Dirac potential för elektron-elektron interaktioner, användes för att beräkna energinivåerna för en idealisk, oändligt lång nanotråd. Nanotråden har en split-gate som alstrar den elektrostatiska, asymmetriska potentialbarriären. "Lateral spin-orbit koppling" visar sig ha minimal effekt då longitudinella effekter, exempelvis spänning, saknas. Elektronerna placerar sig spontant i spinn-rader i tråden vid spontan spinn polarisation. Spinn polarisationen sätts igång av LSOC, numeriska störningar eller från svagt pålagt magnetfält.

Atomic clusters are attractive candidates for building motifs for new nano-assembled materials with desirable properties. At this nano-regime of matter, the size, shape, and composition of clusters changes their electronic structure and hence their properties. Computational modeling must work hand in hand with experiment to provide robust descriptions of the geometries and energetics of atomic clusters and how they might behave in a nano-assembled material. To this end, we have investigated three distinct species as model systems: antimony oxides SbxOy (x = 1, 2; y = 0 - 3), metal ion-solvent complexes Mm(NH3)n (M = Bi, Pb; m = 1 - 2, n = 0 - 4), and quantum dots Z10H16 (Z = Si, Ge) and β-Sn12H24. Their geometries and electronic structures have been determined using gradient-corrected density functional theory. The relative stabilities for antimony oxides have been examined by the respective comparison of highest-occupied and lowest-unoccupied molecular orbital (HOMO-LUMO) gaps and atomization energies. The superior electronic stability of Sb2O3 is indicated by its closed shell structure, wide HOMO-LUMO gap calculated to be 3.11 eV, and high atomization energy of 4.21 eV. Spin-orbit corrections were necessary for accurate calculation of the metal-solvent energetics, closing the gap between experimental and theoretical values by 1.05 eV for the electron affinity of the Pb atom. Quantum dot modeling of the well-established Si and Ge as well as the less-investigated Sn illuminated the accuracy of the CEP basis sets and the B3LYP functional over other DFT computational routes for clusters containing elements beyond the third row. Throughout, the results correlate well with experiment and higher order ab initio methods where data is available. These comparisons validate the accuracy of the computational routes used. This document was prepared in the Linux Ubuntu Open Office Suite 2.4.1.

We investigate two medium-facilitated interactions between properties of light upon propagation through optical fiber. The first is interaction between the spin and intrinsic orbital angular momentum in a linear optical medium. This interaction gives rise to fine structure in the longitudinal momenta of fiber modes and manifests in rotational beating effects. We probe those beating effects experimentally in cutback experiments, where small segments are cut from the output of a fiber to probe the evolution of both output polarization and spatial orientation, and find agreement between theoretical predictions and measured behavior. The second is nonlinear optical interaction due to cross- and self-phase modulation between the complex-valued temporal amplitude profile of pump pulses and the amplitude profiles of generated signal and idler pulses in optical fiber photon-pair sources utilizing the four-wave mixing process named modulation instability. We develop a model including the effects of these nonlinear phase modulations (NPM) describing the time-domain wave function of the output biphoton in the low-gain regime. Assuming Gaussian temporal amplitude profiles for the pump pulse, we numerically simulate the structure of the biphoton wave function, in symmetric and asymmetric group velocity matching configurations. Comparing the overlap of the joint temporal amplitudes with and without NPM indicates how good of an approximation neglecting NPM is, and we investigate the effects of NPM on the Schmidt modes. We find that effects of NPM are small on temporally separable sources utilizing symmetric group velocity matching, but appreciably change the state of temporally entangled sources with the same group velocity matching scheme. For sources designed to produce entangled biphotons, our simulations suggest that NPM increases the Schmidt number, which may increase entanglement resource availability with utilization of a phase-sensitive detection scheme. We find that NPM effects on temporally separable sources designed with asymmetric group velocity matching produce non-negligible changes in the state structure. The purity is unaffected at perfect asymmetric group velocity matching, but if the pump is detuned from the correct wavelength, the purity degrades. The largest changes to the state due to NPM occur in long fibers with long pulse durations and low repetition rates.

Spin-dependent phenomena in semiconductor nanowires have recently gained a lot of attention, in special because these nanostructures can be a viable setup to study exotic states of matter like the Majorana fermions. One of the key ingredients to accommodate the Majorana zero modes is the spin-orbit coupling in the nanowires, which has been usually treated with two-band Hamiltonians. The spin-orbit coupling in semiconductors arise from two distinct sources being the bulk inversion asymmetry, when the unit cell does not present inversion symmetry, e.g. when the crystal unit cell is composed by two different atoms, and the structural inversion asymmetry, when the whole system does not have a mirror symmetry. To describe the system these effective models take as input, parameters that are dependent on the system configuration and measurement setups. Although these effective models have been successful in determine relevant physical properties, a more realistic description of the interacting energy bands is required, specially in quantum confined systems where the interplay between both sources of spin-orbit coupling can change the systems properties in non-trivial ways. For instance, in quantum wells there is an anisotropy of the g-factor due to the quantum confinement and structural inversion asymmetry. Furthermore, the in-plane g-factor also have an anisotropy which is due to the intrinsic spin-orbit coupling and it is not captured by these effective models. In this study, we use realistic multiband k &middot; p Hamiltonians, including both spin-orbit coupling mechanisms, to determine the band structure of zincblende InSb and wurtzite InAs nanowires under a transverse electric field. We analyze the effects of the lateral quantum confinement for a hexagonal cross-section geometry and of the change in growth directions, extracting the relevant physical parameters for the first conduction subband. We found that the g-factors are heavily dependent on the quantum confinement and nanowire orientation, with in-plane/out-of-plane anisotropies up to 3%. We also found that for zinc-blende nanowires the extrinsic spin-orbit coupling is dominant over the intrinsic one whereas, for wurztize, the opposite behavior holds. In order to assess if the nanowires could host the aforementioned Majorana zero modes we investigate under which circumstances the topological phase transition occurs, using the Bogoliubov-de Gennes formalism to couple the nanowire with a superconductor, and we found that using realistic and experimental feasible parameters, indeed, the phase transition occurs. In conclusion, our systematic investigation of nanowires shows that the spin-orbit coupling energy can be fine tuned by the external electric field in experimentally achievable setups that ultimately could guide the search for the elusive Majorana modes. Moreover, our numerical approach is not restricted to a specific material or dimensionality and can be used to study others systems to provide useful insights into the electronic and spintronic fields. / Recentemente, fenômenos dependentes de spin em nanofios semicondutores se tornaram uma área de pesquisa ativa especialmente porque essas nanoestruturas podem ser viáveis para o estudo de estados exóticos da matéria como, por exemplo, os férmions de Majorana. Um dos ingredientes chave para que esses modos de excitação possam existir em nanofios é o acoplamento spin-órbita, o qual tem sido usualmente tratado com modelos de duas bandas. O acoplamento spin-órbita em semicondutores aparece de duas fontes distintas sendo elas a assimetria de inversão no bulk, quando a célula unitária do cristal não possui simetria de inversão, por exemplo, quando é formada por dois átomos diferentes, e a assimetria de inversão estrutural, quando o sistema como um todo não possui simetria de inversão. Para descrever o sistema, os modelos efetivos de duas bandas usam como entrada parâmetros que dependem tanto do sistema específico quanto da configuração do arranjo experimental. Apesar desses modelos terem sucesso em descrever algumas das propriedades físicas relevantes, uma descrição mais realística da interação entre as bandas de energia se faz necessária, especialmente em sistemas com confinamento quântico onde a ação combinada das duas fontes de acoplamento spin-órbita muda as propriedades do sistema de maneira não-trivial. Por exemplo, o fator giromagnético em poços quânticos é anisotrópico devido aos efeitos de ambos, confinamento quântico e a assimetria de inversão estrutural. Ademais, o fator giromagnético ao longo do plano também possui uma anisotropia, a qual tem origem no acoplamento spin-órbita intrínseco do sistema e não é capturada por esses modelos efetivos. Nesse estudo, nós usamos Hamiltonianos k &middot; p multibanda, incluindo ambos os mecanismos de acoplamento spin-órbita, para determinar a estrutura de bandas de nanofios de InSb na fase blenda de zinco e InAs na fase wurtzita sob a ação de um campo elétrico transversal. Nós analisamos os efeitos do confinamento quântico lateral, para fios com seção transversal hexagonal, e diferentes direções de crescimento, extraindo parâmetros físicos relevantes para a primeira sub-banda de condução. Nós encontramos que os fatores giromagnéticos são fortemente influenciados pelo confinamento quântico e orientação dos nanofios, com anisotropias no plano e fora do plano de até 3%. Nós também encontramos que para nanofios de InSb na fase blenda de zinco, o acoplamento spin-órbita extrínseco domina o intrínseco enquanto que, em nanofios de InAs na fase wurtzita, vale o oposto. Para avaliar se os nanofios podem hospedar os modos de Majorana de energia zero nós investigamos sob quais circunstâncias a transição de fase topológica ocorre usando o formalismo de Bogoliubov-de Gennes para acoplar o nanofio a um supercondutor, e encontramos que usando nossos parâmetros e em condições experimentalmente factíveis, de fato, a transição de fase ocorre. Em conclusão, nossa investigação sistemática nos nanofios mostrou que o acoplamento spin-órbita pode ser ajustado por fontes externas, tais como um campo elétrico aplicado, e em configurações experimentais factíveis e que ultimamente pode guiar à busca dos elusivos modos de Majorana. Além do mais, nossa abordagem numérica não é restrita a esses materiais em específico e nem a nanofios, podendo ser usada para estudar outros sistemas provendo intuições úteis nos campos de eletrônica e spintrônica.

Thesis advisor: Stephen D. Wilson / Spin-orbit intertwined order gives rise to many novel phenomena with a broad phase space spanned by the competing energy scales within a system. This dissertation synthesized and studied two such systems demonstrating different manifestations of spin-orbit interactions, originating from orbital degeneracy effects, on geometrically frustrated magnetic lattices. Firstly, strong spin-orbit coupling in the hyperkagome lattice, Na4Ir3O8, and secondly, the layered material, α-NaMnO2, where single-ion anisotropy and a cooperative Jahn-Teller distortion drive magnetism to the quasi-1D limit. The magnetic ground state of the Jeff = 1/2 spin-liquid candidate, Na4Ir3O8, is explored via combined bulk magnetization, muon spin relaxation, and neutron scattering measurements. A short-range, frozen, state comprised of quasi-static moments develops below a characteristic temperature of TF = 6 K, revealing an inhomogeneous distribution of spins occupying the entirety of the sample volume. Quasi-static, short-range, spin correlations persist until at least 20 mK and differ substantially from the nominally dynamic response of a quantum spin liquid. Much of this dissertation focuses on the second spin-orbit intertwined system, α-NaMnO2, where a cooperative Jahn-Teller distortion of the MnO6 octahedra arising from an orbital degeneracy in the Mn3+ cations directly affects the electronic (ferro-orbital) and magnetic (antiferromagnetic) order, which results in an intriguing study of low-dimensional magnetism. Intricacies of the structure, static magnetic order, and magnon dynamics are presented, which heavily relied on neutron scattering techniques. In particular, a longitudinally polarized bound magnon mode is characterized through the use of polarized neutron scattering. / Thesis (PhD) — Boston College, 2018. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Physics.