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.

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.

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.

Apresento neste trabalho uma derivação alternativa da hamiltoniana efetiva para um elétron na banda de condução de uma heteroestrutura semicondutora de rede Zincblende. Partindo do modelo de Kane 8 × 8 e da aproximação das funções envelope, esta hamiltoniana efetiva foi obtida com a linearização dos denominadores (dependentes das autoenergias) presentes na equação para a banda de condução, sob a hipótese de que o gap de energia seja muito maior que todas as demais diferenças de energia envolvidas (verdade para a maioria das estruturas Zincblende). A partir de um procedimento introduzido previamente1,3, desenvolvi um procedimento mais geral que implementa sistematicamente esta linearização até segunda ordem no inverso do gap de energia e que corrige a normalização do spinor da banda de condução usando as bandas de valência. Este procedimento é idêntico à expansão em série de potência no inverso da velocidade da luz utilizada para se obter aproximações relativísticas da equação de Dirac. Uma vantagem deste procedimento é a arbitrariedade na forma dos potenciais, o que implica na validade da hamiltoniana resultante para poços, fios e pontos quânticos. Evidencio também as consequências de cada termo desta hamiltoniana efetiva para os autoestados eletrônicos em poços retangulares, incluindo termos independentes de spin inéditos (Darwin e interação momento linearcampo elétrico). Estes resultados estão de acordo com os estudos anteriores4. A fim de estudar transições ópticas dentro da banda de condução, mostro que o acoplamento mínimo pode ser realizado diretamente na hamiltoniana de Kane se os campos externos variam tão lentamente quanto as funções envelope. Repetindo a linearização dos denominadores de energia, derivo uma hamiltoniana efetiva para a banda de condução com acoplamentos elétron-fótons. Um destes acoplamentos, induzido exclusivamente pela banda de valência, origina transições mediadas pelo spin eletrônico. Estas transições assistidas por spin possibilitam mudanças, opticamente induzidas, na orientação do spin eletrônico, um fato que talvez possa ser útil na construção de dispositivos spintrônicos. Por fim, as taxas de transição deste acoplamento apresentam saturação e linhas de máximos e mínimos no espaço recíproco. Espero que estas acoplamentos ópticos possam auxiliar na observação dos efeitos dos acoplamentos spin-órbita intra (Rashba) e intersubbandas. / In this work, I present an alternative derivation of the conduction band effective hamiltonian for Zincblende semiconductor heterostructures. Starting from the 8×8 Kane model and envelope function approximation, this effective hamiltonian was obtained by means of a linearization in the eigenenergy-dependent denominators present the conduction band equation, under the hypothesis that the energy gap is bigger than any other energy difference in the system (true for mostly every Zincblende semiconductor bulk or heterostructure). Based on a previous procedure1,3, I have developed a more general procedure that implements sistematicaly (i) this linearization and (ii) renormalizes the conduction band spinor using the valence bands, both (i) and (ii) up to second order in the inverse of the energy gap. This procedure is identical to the expansion in power series of the inverse of the light speed used to derive non-relativistic approximations of the Dirac equation. One advantage of this procedure is the generality of the potentials adopted in our derivation: the same results hold for quantum wells, wires and dots. I show the consequences of each term of this hamiltonian for the electron eigenstates in retangular wells, including novel spin-independent terms (Darwin and linear momentumelectric field couplings). These resulties agree with previous works4. In order to study conduction band optical transitions, I show that the minimal substitution can be performed directly in the Kane hamiltonian if the external fields vary slowly (at least, as slowly as the envelope functions). Repeating the linearization of the energy denominators, I derive a new effective hamiltonian, up to second order in the inverse of the energy gap, with electron-photons couplings. One of these couplings, induced exclusively by the valence bands, gives rise to optical transitions mediated by the electron spin. This spin-assisted coupling enable optically-induced spin flipps in conduction subband transitions, which can be useful in the construction of spintronic devices. Finaly, the spin-assisted transitions rates show saturation and lines of maxima and minima in the reciprocal lattice. I hope that these optical couplings can be of any help in the observation of interesting effects induced by the intra and intersubband spin-orbit coupling.

This thesis uses ferromagnetic resonance to explore the current-induced torques (CITs) in two different systems, namely YIG/heavy metal bilayers and bulk NiMnSb, at room temperature. We apply a microwave current to the sample while sweeping the external magnetic field, and measure the longitudinal DC voltage. From a symmetry analysis of the ferromagnetic resonance lineshape, the amplitudes and directions of the CITs parameterised by an effective magnetic field are accurately estimated. In Chapter 4, YIG samples of different thickness, capped by either Pt or Ta, are studied. The resonance is driven by both spin-transfer torque and Oersted field, and the DC voltage is attributed to both spin rectification and spin pumping. The CITs can be well analysed from the lineshape of the voltage and its dependence on YIG thickness, from which we deduce that the Oersted field dominates over the spin-transfer torque in driving magnetization dynamics. In Chapter 5, we characterise the CITs in bulk NiMnSb induced by the relativistic spin-orbit coupling effect. Both field-like and antidamping-like spin-orbit torques are observed and analysed in detail. At the end of this chapter, we study the spin-wave resonance driven by the CITs, from which the exchange stiffness of NiMnSb is determined. In Chapter 6, we extrapolate a new form of magnetoresistance in NiMnSb: unidirectional spin-orbit magnetoresistance (USOMR). USOMR scales linearly with the current and has opposite sign when the magnetization is reversed. Similar to the giant magnetoresistance in magnetic multilayers, USOMR can be used to distinguish between two opposite magnetization directions directly in the bulk of the ferromagnet.

<div>The quantum phase transitions and exotic excitations are exciting and important topics of nowadays condensed matter theory. Topologically protected excitations are of great interest for potential applications in quantum computing. This Thesis explores two examples of exotic topologically protected excitations, Majorana fermions and parafermions in hybrid superconductor/semiconductor systems.</div><div><br></div><div>In the first part of the thesis, after a brief review of ideas on Majorana zero modes in solid state systems obtained by researchers over the past decade, I present our study of the emergence of Majorana fermions in charge carrier holes doped quantum wires. Study of Majorana modes in this system requires understanding Luttinger holes in low dimensions, which is also crucial for numerous spin-dependent phenomena, emerging field of spintronics and nanotechnology. We find that hole-doped quantum wires that are proximity coupled to a conventional s-wave superconductor is a promising system for the observation of Majorana fermions. We advanced understanding of Luttinger holes in quantum wells and quantum wires. We have shown that the vast majority of earlier treatments of Luttinger holes ignored an important effect, a mutual transformation of heavy and light holes at the heteroboundaries. We have derived the effective hole Hamiltonians in the ground size-quantized sub-bands of quantum wells and quantum wires. The effect of mutual transformation of holes is crucial for understanding Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole-doped quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems and show that GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, providing additional opportunities for its control compared to intensively studies InSb and InAs electron systems.</div><div><br></div><div>In the second part of the thesis, I first introduce the basic facts of the current theoretical understanding of the fractional quantum Hall effect and a theoretical model of parafermion excitations. Parafermion zero modes are promising for universal quantum computing. However, physical systems that are predicted to host these exotic excitations are rare and difficult to realize in experiments. I present our work on modeling domain walls on the boundary between gate-induced polarized and unpolarized domains of the fractional quantum Hall effect system near the spin transitions, and the emergence of the parafermion zero modes when such domain wall is proximity coupled to an s-wave superconductor. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves formation of the counter-propagating edge states with different spin polarizations at the boundaries between areas of the electron liquid in polarized and unpolarized filling factor $\nu=2/3$ phases. By analytical and numerical methods we find the conditions for emergence of parafermion zero modes in hybrid fractional quantum Hall/s-wave superconductor system. The phase diagram indicates that the parafermionic phase, which is represented by the six-fold ground state degeneracy, is separated from other phases by a topological phase transition. Such parafermion modes are experimentally feasible. They present a vital step toward the realization of Fibonacci anyons that allow a full universal set of quantum operations with topologically protected quasiparticles.</div><div><br></div>

acase@tulane.edu

The problem of spin manipulation via the spin-orbit interaction in nonmagnetic semiconductors in the absence of magnetic fields is investigated in this work. We begin with a review of the literature on spin dynamics in semiconductors, then discuss the semi-empirical k ⋅ p method of calculating direct-gap semiconductor properties, which we use to estimate material parameters significant for manipulation of spin even in the absence of a magnetic field. The total effective magnetic fields and precession lengths are calculated for a variety of quantum well orientations, and a class of devices are proposed that will allow for all-electric arbitrary manipulation of spin orientations. The strain- and momentum-dependent spin splitting coefficient C3 has been calculated using a fourteen band Kane k⋅p model for a variety of III-V semiconductors as well as ZnSe and CdSe. It is observed that the spin-splitting parameters C3 and γ, corresponding to the strain-induced spin-orbit interaction and Dresselhaus coefficient, are sensitive to the value of the inter-band spin-orbit coupling Δ− between the p valence and p̄ second conduction band in all cases. The value of Δ− has therefore been recalculated in these materials using a tight-binding model and modern experimental values of the valence and second conduction band spin-orbit splittings. The total effective magnetic field and precession length of spins in strained quantum wells in the (001), (110), and (111) planes are derived with consideration for all known effective magnetic fields except those due to interface effects in non- common-atom heterostructures (native inversion asymmetry). The orientation of the k-linear Dresselhaus field and the strain-dependent fields vary strongly with the growth axis of the quantum well. The precession length in the (110) and (001) cases can achieve infinite anisotropy, while the precession length of (111) quantum wells is always isotropic. We find that the electronic spin rotation induced by drift transport around a closed path in a wide variety of nonmagnetic semiconductors at zero magnetic field depends solely on the physical path taken. Physical paths that produce any possible spin rotation due to transport around a closed path are constructed for electrons experiencing strain or electric fields in (001), (110), or (111)-grown zinc blende semiconductor quantum wells. Spin decoherence due to travel along the path is negligible compared to the background spin decoherence rate. The small size of the designed paths (< 100 nm scale in GaAs) may lead to applications in nanoscale spintronic circuits.

In the recent years, interest in TM oxides with 5d valence electrons has grown immensely due to the realization of novel spin-orbit coupled ground states. In these compounds, e.g., iridates and osmates, the intriguing situation arises where the spin-orbit and electron-electron interactions meet on the same energy scale. This has created a new window of interest in these compounds since the interplay of crystal field effects, local multiplet physics, spin-orbit couplings, and intersite hopping can offer novel types of correlated ground states and excitations. In 5d5 iridates, a spin-orbit entangled j = 1/2 Mott insulating state has been realized recently. A remarkable feature of such a ground state is that it gives rise to anisotropic magnetic interactions. The 2D honeycomb-lattice 213 iridium oxides, A2IrO3 (A=Li,Na), have been put forward to host highly anisotropic bond-dependent spin-spin interactions that resemble the Kitaev spin model, which supports various types of topological phases relevant in quantum computing. The 2D square-lattice 214 iridates Sr2IrO4 and Ba2IrO4 are, on the other hand, appealing because of their perceived structural and magnetic simi- larity to La2CuO4, the mother compound of the cuprate high-Tc superconductors. This has promoted the latter iridium oxide compounds as novel platforms for the search of high-Tc superconductivity. To put such considerations on a firm footing, it is essential to quantify the different coupling strengths and energy scales, as they for instance appear in effective Hamiltonian descriptions of these correlated systems. Moreover, it is important to correctly describe their effects. In this thesis, the electronic structure and magnetic properties of 5d5 (mainly 214 and 213) iridates are studied using wave-function-based quantum chemistry methods. These methods are fully ab initio and are capable of accurately treating the electron-electron interactions without using any ad hoc parameters. The spin-orbit entangled j = 1/2 ground state in 214, 213 and other lower symmetry Sr3CuIrO6 and Na4Ir3O8 iridates is first analyzed in detail, by studying the local electronic structure of the 5d5 Ir4+ ion. We establish that the longer-range crystal anisotropy, i.e., low-symmetry fields related to ionic sites beyond the nearest neighbor oxygen cage, strongly influence the energies of Ir d levels. The ground state in all the compounds studied is j = 1/2 like with admixture from j ≃ 3/2 states ranging from 1 – 15 %. Further, the average j ≃ 1/2 → j ≃ 3/2 excitation energy we find is around 0.6 eV. The NN magnetic exchange interactions we computed for 214 iridates are predominantly isotropic Heisenberg-like with J ~ 60 meV, 3 – 4 times smaller than found in isostructural copper oxides. However, the anisotropic interactions are an order of magnitude larger than those in cuprates. Our estimates are in excellent agreement with those extracted from experiments, e.g., resonant inelastic x-ray scattering measurements. For the 213 honeycomb-lattice Na2IrO3 our calculations show that the relevant spin Hamiltonian contains further anisotropic terms beyond the Kitaev-Heisenberg model. Nevertheless, we predict that the largest energy scale is the Kitaev interaction, 10 to 20 meV, while the Heisenberg superexchange and off-diagonal symmetric anisotropic couplings are significantly weaker. In the sister compound Li2IrO3, we find that the structural inequivalence between the two types of Ir-Ir links has a striking influence on the effective spin Hamiltonian, leading in particular to two very different NN superexchange pathways, one weakly AF (~ 1 meV) and another strongly FM (−19 meV). The latter gives rise to rigid spin-1 triplets on a triangular lattice.