Dissertations / Theses on the topic 'Quantum magnetism'

This thesis describes neutron scattering experiments on strongly correlated systems exhibiting a range of emergent phenomena: antiferromagnetism, charge order, superconductivity and multiferroicity. I have examined the La_{2}CoO_{4} compound which is a Mott insulator and orders antiferromagnetically near room temperature. The La_{2}CoO_{4} sample was studied using spherical neutron polarimetry and I present magnetic structure models to describe the two antiferromagnetic phases of the compound. Furthermore, the magnetic fluctuations have been investigated using neutron time-of-flight technique. This has allowed us to extract the dominant exchange interactions in the system. More interestingly, the work on La_{2}CoO_{4} presented in this thesis provides a basis for the experimental evidence of an hourglass dispersion in La_{5/3}Sr_{1/3}CoO_{4}, previously only observed in the copper oxide based superconductors. This dispersion has been understood in terms of a stripe ordered magnetic phase and was found to be well described by a linear spin-wave model. Neutron scattering experiments were also carried out on the new iron-based high-temperature superconductors, FeSe_{x}Te_{1−x}. A range of compositions were studied, including both antiferromagnetically ordered and superconducting. Below the superconducting phase transition temperature, a spin resonance mode was found centred on the antiferromagnetic wavevector. This is an important feature shared by many unconventional superconductors. The spin resonance intensity was found to reflect the order parameter of the superconducting state. Polarised inelastic neutron scattering experiments have revealed a small anisotropy between the in-plane and out-of-plane magnetic fluctuations at the resonance. This anisotropy cannot be readily explained by the usual anisotropic terms in the Hamiltonian. This could be evidence of new physics in the FeSe_{x}Te_{1−x} superconductors. Finally, I have studied CuO – a high-temperature multiferroic. Analysis of polarised neutron diffraction experiments shows that the magnetic domain population can be varied using an externally applied electric field. This unambiguously demonstrates coupling between the magnetic and ferroelectric degrees of freedom. Using representation analysis I derive the incommensurate magnetic structure in the multiferroic phase. The origin of the magnetoelectric coupling is consistent with models based on the inverse Dzyaloshinskii-Moriya interaction.

Quantum dots offer a number of advantages over standard fluorescent dyes for monitoring biological systems including high luminescence, stability against photobleaching, and a wide range of fluorescence wavelengths from blue to infrared depending on the particle size. In this work, we investigated in using the protein cage apoferritin as a template for the synthesis of colloidal quantum dots. We obtained apoferritin after reductive dissolution of the ferritin iron core and showed that the protein structure was left intact during this process. We further studied the solubility of ferritin, apoferritin and cationized ferritin in organic and fluorinated solvents by hydrophobic ion pairing methodology in order to expand the possibility of using an apoferritin template for the synthesis of quantum dots in organic media. We then focused on the synthesis and fluorescence properties of PbS quantum dots in aqueous solution. PbS dots are thermally stable and emit in the range 1,100 to 1,300 nm depending on their size. We demonstrated the encapsulation of these PbS quantum dots within the cavity of the iron storage protein apoferritin using two routes: 1) the disassembly/reassembly of apoferritin subunits trapping previously synthesised PbS quantum dots; and 2) use of the channels present in the protein shell to allow the entrance of Pb2+ and S2- ions leading to formation of quantum dots in the apoferritin cavity. We show that PbS-apoferritin composites emit in the near infrared region which make them promising labels for biological applications. Furthermore, we demonstrated that PbS QDs can be excited via a bioluminescence resonance energy transfer (BRET) using luciferin from Luciola mingrelica which could be developed into a self-illuminating labelling system. Finally, in order to make PbS-apoferritin composites selectively attachable to biomolecules during labelling experiments, the apoferritin was modified by the incorporation of analogues of methionine introducing azido groups absent in the proteins. The azido groups can then be selectively modified in complex mixtures e.g. cell lysates using `bio-orthogonal' reactions such as the Cu(I) catalysed Staudinger ligation and Huisgen cycloaddition. This would allow highly selective addition of receptor targeting or cellular permeation of peptides to the outer surface of the apoferritin shell.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 168-185).
In this thesis, two sets of experimental studies in bosonic and fermionic gases are described. In the first part of the thesis, itinerant ferromagnetism was studied in a strongly interacting Fermi gas of ultracold atoms. The observation of nonmonotonic behavior of lifetime, kinetic energy, and size for increasing repulsive interactions provides strong evidence for a phase transition to a ferromagnetic state. Our observations imply that itinerant ferromagnetism of delocalized fermions is possible without lattice and band structure, and our data validate the most basic model for ferromagnetism introduced by Stoner. In the second part of the thesis, the coherence properties of a Bose-Einstein condensate (BEC) was studied in a radio frequency induced double-well potential implemented on a microfabricated atom chip. We observed phase coherence between the separated condensates for times up to 200 ms after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. Furthermore, the effect of phase fluctuations on an atom interferometer was studied in an elongated BEC. We demonstrated that the atom interferometer using the condensates is robust against phase fluctuations; i.e., the relative phase of the split condensates is reproducible despite axial phase fluctuations. Finally, phase-sensitive recombination of two BECs was demonstrated on an atom chip. The recombination was shown to result in heating, caused by the dissipation of dark solitons, which depends on the relative phase of the two condensates. This heating reduces the number of condensate atoms and provides a robust way to read out the phase.
by Gyu-Boong Jo.
Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2014.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 191-198).
The geometry of the kagome lattice leads to exciting novel magnetic behavior in both ferromagnetic and antiferromagnetic systems. The collective spin dynamics were investigated in a variety of magnetic materials featuring spin-1/2 and spin-1 moments on kagome lattices using neutron scattering and thermodynamic probes. Both ferromagnetic and antiferromagnetic systems were studied. Cu(1,3-bdc) is an organometallic material, where the Cu2+ ions form a ferromagnetic S = 1/2. kagomé system. Synthesis techniques were developed to produce -mg-sized deuterated single crystals, and ~2,000 crystals were partially coaligned to create a sample for neutron scattering measurements. Elastic neutron scattering measurements show the existence of long range magnetic ordering below T = 1.77 K. Integrated Bragg peak intensities were analyzed to determine the structure of ordered magnetic moments. Inelastic neutron scattering measurements show the magnon dispersion spectrum, which consists of a flat high energy band and two dispersive, lower energy bands. The application of a magnetic field perpendicular to the kagome plane opens gaps between these three bands and distorts the flatness of the highest energy band. The system was modelled as a nearest-neighbor Heisenberg ferromagnet with Dzyaloshinskii-Moriya(DM) interaction. The model dispersion and scattering structure factor were calculated and fit to the data to precisely determine the strengths of the nearest-neighbor coupling and DM interaction. The observed manon band structure is a bosonic analog to the band structure of the topological insulator systems. Antiferromagnetic kagome systems can exhibit novel magnetic ground states such as quantum spin liquids and spin nematics. Thermodynamic measurements were performed on the antiferromagnetic kagome materials MgxCu₄-x(OH)₆ Cl₂ , featuring S = 1/2 moments. These measurements reveal magnetic ordering at low values of x that is suppressed with increasing x. At x = 0.75, this ordering is not fully suppressed, but susceptibility and specific heat measurements reveal behavior similar to that of the quantum spin liquid candidate herbertsmithite. Thermodynamic and neutron scattering measurements were performed on the kagome lattice material BaNi₃(OH)₂(VO₄)₂, which features S = 1 moments. These measurements reveal competing interactions, which result in a spin glass ordering transition.
by Robin Michael Daub Chisnell.
Ph. D.

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Sandoildo Freitas Tenório, Antônio; Domingues Coutinho Filho, Maurício. Phase transitions and thermodynamics of quasione- dimensional quantum rotor and spin systems. 2009. Tese (Doutorado). Programa de Pós-Graduação em Física, Universidade Federal de Pernambuco, Recife, 2009.

This thesis presents different strategies for the design of molecular complexes with the requirements to be used as two-qubit quantum gates. The approaches followed towards the preparation of potential qubit systems have been carried out focusing on the synthesis of ligands with β-diketone coordination units, which are very versatile for the design of metallocluster assemblies. One of the main advantages of using this kind of ligands is that they can be easily prepared through simple Claisen condensation, providing different combinations and possibilities for the addition of big variety of donor atoms and pockets. Each ligand has been designed for the preparation of predefined magnetic coordination complexes that can fulfill the conditions of a two-qubit molecular quantum gate. The different complexes synthesized within this thesis can be defined in two different categories: Molecular pairs of well-defined and weakly coupled metal clusters, and complexes of two dissimilar and weakly coupled anisotropic metal ions. In addition, the use of the designed ligands for the preparation of metallo-helicates has been also carried out. The description and study of their helicoidal structure is also shown, using the ligand H4L1 with trivalent and tetravalent metal ions like FeIII, GaIII or UIV. - Molecules featuring two weakly coupled clusters: The approach is based on the design of molecules featuring two well defined coordination clusters that could represent ideal systems for realizing two-qubit quantum gates, as long as each cluster exhibits the appropriate spin properties. Two different ligand-based strategies have been followed for the preparation of such molecular pairs of well-defined metal clusters. The first one is based on the design of poly-β-diketone ligands exhibiting two groups of coordination pockets, which serve to aggregate metals in close proximity. Following this approach, the ligand is responsible for having metals grouped into two clusters, as well as for keeping each metal group together within each subsystem. The structural characteristics of H4L1 provides the requirements for the construction of this kind of clusters, since it might align and separate metals into two dimetallic entities. The goal has been achieved by using the deprotonated ligand that organizes the metals in two groups within molecular linear arrays, saturating the equatorial positions. Compounds with NiII, CuII and CoII metal ions are described and studied. The second strategy is based on the preparation of poly-β-diketone ligands with an additional X donor atom in the middle for acting as a “template” for the aggregation of metals into linear clusters, further linked as molecular pairs by auxiliary ligands Organic ligands like H4L2 or H2L3 fulfill the requirements to aggregate closely spaced metals, which can be then used as building blocks to be linked into molecular pairs by other bifunctional external ligands. An example using CoII is described and studied. - Dinuclear complexes of anisotropic metal ions: The synthesis of complexes of two dissimilar and weakly coupled lanthanides has been used as approach for the construction of molecular prototypes of CNOT quantum gates. The ligand-based strategy considers the design of non-symmetric ligands as a possible way of having two inequivalent lanthanide qubits within a molecule. The ligand H3L4 exhibits a collection of donor groups disposed to favor the aggregation of two metals in different coordination environments. The use of lanthanide ions are good candidates for encoding quantum information following such approach, since they can exhibit strong anisotropy and very well isolated ground state doublets ±mJ (effective S = ½). In addition, lanthanide ions have been proved to have spin states with long decoherence, with T2 timescales that can reach values up to 7 μs.[41] A detailed study of a vast number of dinuclear homo- and heterometallic lanthanide coordination complexes is exposed, including an exhaustive study for some of them to prove their possibilities as CNOT and √SWAP quantum gates.
El trabajo realizado en esta tesis doctoral se basa en el diseño, la síntesis y el estudio de complejos de coordinación, centrándose en la comprensión de sus propiedades magnéticas y la posibilidad de su aplicación en la computación cuántica. Para el diseño de estos materiales moleculares, tres diferentes propuestas han sido llevadas a cabo. En primer lugar, se han desarrollado ligandos capaces de agregar metales paramagnéticos en dos grupos diferentes, definiendo de esta manera los dos posibles bits cuánticos de una puerta lógica. Complejos de coordinación homo- y heterometálicos con NiII, CoII y CuII han sido sintetizados y caracterizados para tal efecto. La segunda estrategia seguida ha estado centrada en el diseño de complejos de coordinación lineales para su posterior ensamblaje en parejas de compuestos. Se han desarrollado ligandos que favorezcan la complejación de este tipo de topología, obteniéndose un compuesto de CoII con las propiedades estructurales idóneas para su ensamblaje. Utilizando el ligando bifuncional 4.4’-bipiridina, se ha podido unir dos entidades [Co4] obteniendo así otro prototipo de “parejas moleculares”. La tercera estrategia se ha centrado en el diseño de moléculas asimétricas para facilitar la definición de cada bit cuántico dentro de la entidad molecular. Para ello, se ha sintetizado un ligando no simétrico, que ha sido utilizado para obtener complejos dinucleares homo- y heterometálicos de iones lantánido. Se ha obtenido compuestos con todos los elementos de la serie de los lantánidos. Su estudio magnético y estructural ha mostrado que los dos centros metálicos de estas entidades moleculares son distintos, lo que ha permitido definir el espín de cada ion lantánido como un bit cuántico. El estudio magnético a muy bajas temperaturas de un compuesto de dos átomos de terbio(III), por ejemplo, ha permitido definir dos puertas lógicas: la CNOT y la √SWAP. Utilizando el espectro de energías de los estados magnéticos de la molécula, se han observado las transiciones entre dichos estados en relación a las dos operaciones lógicas.

Neutron scattering measurements were used to investigate the magnetic and crystal structure and magnetic excitations of three compounds characterized as low-dimensional quantum magnets. The materials are frustrated systems with low spin quantum number. The first was a powder sample of AgNiO₂. The Ni ions form a triangular lattice antiferromagnet in which, according to the published crystal structure, both the orbital order and magnetic couplings are frustrated. However, it is shown here that there was a small distortion of the crystal structure at 365 K, which is proposed to result from charge disproportionation and this relieves the orbital frustration. The magnetic structure was investigated and, below 20 K, the triangular lattice of electron-rich Ni sites was observed to order into antiferromagnetic stripes. Investigations of the magnetic excitations showed that the main dispersions were within the triangular plane, indicating a strong two-dimensionality. The dispersion was larger along the stripes than between the stripes of collinear spins. The second material investigated was CoNb₂O₆, a quasi Ising-like ferromagnet. It was studied with a magnetic field applied transverse to the Ising direction. The magnetic field introduced quantum fluctuations which drove a phase transition at a field comparable to the main exchange interaction. The phase diagram of the magnetic order was mapped outs and a transition from an ordered phase to a paramagnetic phase was identified at high field. This low-temperature high-field phase transition was further investigated by inelastic neutron scattering measurements to observe the change in the energy gap and magnetic excitation spectrum on either side of the transition. The spectrum had two components in the ordered phase and had sharp magnon modes in the paramagnetic phase. The third material was the spin-half layered antiferromagnet CuSb₂O₆. It has a square lattice of Cu²⁺ ions in which the main interaction is across only one diagonal of the square. The magnetic structure was studied by neutron scattering with a field applied along the direction of the zero-field ordered moment. A spin-flop was observed at low field and there was evidence for a high-field transition. The magnetic excitation spectrum was unusual in that it had an intense resonance at 13 meV at the magnetic Brillouin zone boundary.

Molecular nanomagnets have attracted the attention of the scientific community since they represent model systems to study many quantum phenomena, such as quantum entanglement and decoherence. They are also interesting for their envisaged technological applications, including magnetic refrigeration, high-density information storage and quantum information processing. Driven by these motivations, the present Thesis focuses on the study of magnetic properties and spin dynamics of different classes of molecular nanomagnets, with the purpose to understand their quantum behavior and their potential applications in future technologies. Magnetic frustration is at the origin of many exotic phenomena in matter. Here frustration-induced properties are studied and analyzed for the clusters Ni7, Fe7, Fe6 and Mn6, together with their effects on phonon-induced relaxation dynamics. Indeed, the comprehension of relaxation mechanisms is crucial in order to address the implementation of these systems in the fields of quantum information processing or information storage. Molecular nanomagnets are also promising materials for very-low-temperature magnetic refrigeration due to a potentially enhanced magnetocaloric effect. By explicitly considering Carnot refrigeration cycles, the theoretical recipe to design the best molecules for cryogenic magnetic refrigeration is identified. Another important class of molecular nanomagnets is that of antiferromagnetic rings. Of these, Cr7Ni is of great importance for applications in quantum information processing. The local spin density distribution in Cr7Ni is here obtained from 53Cr-NMR and confirmed by theoretical calculations. The origin of magnetic anisotropy of these rings grafted on surfaces is investigated using XMCD and theoretical calculations. Antiferromagnetic “purple” rings are completely characterized by the comparison of our calculations with inelastic neutron scattering and EPR data. The characterization of purple rings represents a first step in the description of a new family of “purple-green” entangled dimers, which represent model systems to study spin entanglement and its application in the field of quantum computation.

This thesis describes an experimental investigation and analysis of two topical problems in condensed matter physics: 1.) the effect of a magnetic field on quantum states of an electron bound to a shallow donor impurity in a quantum well heterostructure and 2.) the breakdown of the quasi-dissipationless state of the integer quantum Hall effect. Two introductory chapters describe important material parameters and the experimental equipment and techniques used. Magneto-tunneling spectroscopy (MTS) is used to probe the spatial form of the eigenfunction of electrons bound in the ground state of a shallow Si-donor impurities in a GaAs/(A1Ga)As quantum well. An in-plane magnetic field, B[subscript] |, acts to tune the k-vector of the tunnelling electron through the effect of the Lorentz force. The variation with B [subscript] | of the tunnel current through the donor ground state provides a map of the Fourier transform, |ψ(k)| [superscript]2, of the probability density of the ground state donor wavefunction in real space. By applying a strong magnetic field component, B [subscript] ||, parallel to the direction of tunnel current, it is possible to magneto-compress the donor function in real space. The magneto-compression is investigated using MTS and the data are analysed in terms of a simple model, which is critically discussed. The breakdown of the integer quantum Hall effect is investigated by measuring the variation of the voltage drop Vxx along the direction of current flow for a range of currents and magnetic fields and for a number of sample geometries including Hall bars with narrow channels. The data are discussed in terms of two complementary models of breakdown: the bootstrap electron heating model and magneto-exciton formation at a charged impurity. Evidence is found for both types of breakdown depending on the type of sample used and on experimental parameters. For samples with constrictions, it is found that in the breakdown region the value of Vxx measured across a pair of contacts on one side of the Hall bar can differ substantially from that measured on the other side. A model based on magneto-exciton formation at impurities is proposed to explain this unexpected effect. The thesis concludes with a brief summary and suggestions for future work.

Die magnetischen Eigenschaften von Li2CuO2 sind seit mehr als zwei Jahrzehnten Gegenstand theoretischen und experimentellen Interesses. Über die genaue Natur der magnetischen Wechselwirkungen in diesem Isolator konnte jedoch keine Einigkeit erzielt werden. Während das Material von Seiten theoretischer Untersuchungen als quasi-eindimensionaler Magnet mit starken ferromagnetischen Kopplungen entlang der Kette verstanden wurde, legten experimentelle Studien dominierende dreidimensionale Zwischenkettenkopplungen nahe. Im Rahmen dieser Dissertation werden auf der Grundlage von Untersuchungen des magnetischen Anregungsspektrums mittels inelastischer Neutronenstreuung und dessen Analyse innerhalb eines Spinwellenmodels die führenden magnetischen Wechselwirkungen in Li2CuO2 bestimmt. Es wird zweifelsfrei nachgewiesen, dass das Material eine quasi-eindimensionale Spinkettenverbindung darstellt. Insbesondere kann die Konkurrenz von ferro- und antiferromagnetischen Wechselwirkungen entlang der Ketten nachgewiesen werden. Die Anwendbarkeit einer Spinwellenanalyse dieses niedrigdimensionalen Spin-1=2 Systems wird gezeigt. Das magnetische Phasendiagramm wird mittels Messungen von spezifischer Wärme, thermischer Ausdehnung und Magnetostriktion sowie der Magnetisierung in statischen und gepulsten Magnetfeldern untersucht und im Bezug auf die Austauschwechselwirkungen diskutiert. Aufgrund seiner einfachen kristallographischen und magnetischen Struktur stellt Li2CuO2 ein potentiell wertvolles Modellsystem in der Klasse der Spinkettenverbindungen mit konkurrierenden ferro- und antiferromagnetischen Wechselwirkungen dar
The magnetic properties of Li2CuO2 have attracted interest since more than two decades, both in theory and experiment. Despite these efforts, the precise nature of the magnetic interactions in this insulator remained an issue of controversial debate. From theoretical studies, the compound was understood as a quasi-one-dimensional magnet with strong ferromagnetic interactions along the chain, while in contrast, experimentally studies suggested dominant three-dimensional inter-chain interactions. In this thesis, the leading magnetic exchange interactions of Li2CuO2 are determined on the basis of a detailed inelastic neutron scattering study of the magnetic excitation spectrum, analyzed within spin-wave theory. It is unequivocally shown, that the material represents a quasi-one-dimensional spin-chain compound. In particular, the competition of ferro- and antiferromagnetic interactions in the chain has been evidenced. The applicability of a spin-wave model for analysis of this low-dimensional spin-1=2 system is shown. The magnetic phase diagram of Li2CuO2 is studied by specific heat, thermal expansion and magnetostriction measurements as well as magnetization measurements in both static and pulsed magnetic fifields. The phase diagram is discussed with respect to the exchange interactions. With its simple crystallographic and magnetic structure, Li2CuO2 may serve as a worthwhile model system in the class of spin-chain compounds with competing ferromagnetic and antiferromagnetic interactions

This thesis explores the synthesis and characterisation of a range of molecular wheels containing unpaired electron spins. These molecular spin systems are of considerable interest, both for the insight they provide into the physics of such systems and for their potential as quantum bits ("qubits") in a quantum information processing device. In particular, this thesis explores using these wheels to meet criteria 1 and 5 of the DiVincenzo criteria. The synthesis of a novel homometallic and nonametallic ring of CrIII ions is introduced, along with extensive physical characterisation. Inelastic Neutron Scattering measurements suggest that the molecule has an almost degenerate S = 1/2 ground state with only 0.1 meV separation, making this ring a near perfect example of a Type I frustrated spin system. Chemical modification of the heterometallic {Cr7M} family of wheels with both hard and soft Lewis base functionality is also explored. Using a triphenylphosphine derivative, the coordination chemistry of a highly sterically hindered mono-substituted triphenylphosphine derivative with gold is explored, yielding new arrangements of the wheels. Changes in the electronic and steric properties of the system are studied by a combination of 31P NMR spectroscopy and DFT modelling, revealing dramatic changes in the phosphorus donor properties. The effect of this ligand substitution on the anisotropy tensor of CoII contained in a heterometallic {Cr7Co} ring is explored using variable temperature 1H NMR spectroscopy. Using a combination of the experimentally observed 1H NMR dipolar shifts and computational modelling, a significant change in the anisotropy tensor of the cobalt is found. Finally, as part of a g-engineering approach to qubit design the chemistry of the octametallic {Cr7Ni} ring functionalised with triphenylphosphine oxide is introduced. Initial efforts towards developing a hybrid {Cr7Ni}2Ln (Ln = Gd, Eu) qubit system, along with characterisation by EPR and luminescence spectroscopy, suggest that this may be a route to developing a qubit with the capacity for optical control of the communication.

Propriedades dinâmicas de sistemas quânticos de muitos corpos é um tópico de grande interesse em física da matéria condensada. Estas propriedades nos dão informação sobre a propagação de excitações elementares e de mecanismos de relaxação em sistemas interagentes. Neste contexto, as funções de correlação tem se tornado ainda mais relevantes devido a experimentos em sistemas de átomos frios e íons armadilhados que medem diretamente no domínio temporal os comportamentos assintóticos no tempo. No entanto, até o momento a maioria dos estudos em cadeias de spin quânticas focaram-se em correlações de um único spin. Utilizando a cadeia de spin XX unidimensional, nós estudamos métodos exatos para calcular as funções de correlação das componentes do tensor de dois spins, Tabi,j = SaiSbj. Estes operadores aparecem, por exemplo, como a resposta da seção de choque de espalhamento inelástico de raios X. Baseados no teorema de Wick, nós mostramos que algumas funções de correlação das componentes locais do tensor de dois operadores de spins de sítios vizinhos, na representação de férmions, podem ser escritas como uma combinação de funções de Green de uma única partícula. Utilizamos diagramas de Feynman para organizar esta combinação e calcular as funções de correlação. Em seguida, considerando esses propagadores para tempos longos e grandes distâncias ao longo do cone de luz, encontramos o comportamento dessas funções de correlação como leis de potência oscilatórias que decaem com o tempo e distância. Uma aplicação direta das funções de correlação é para o estudo de quantidades conservadas e não conservadas, uma análise sobre algumas dessas quantidades foi feita. Discutimos também as funções de correlação das componentes do tensor que não são locais na representação fermiônica. Nesse caso os cálculos foram mais desafiadores, mas usamos o fato que funções de correlação dependente do tempo podem ser expressadas em termos dos determinantes de Fredholm.
Dynamical properties of quantum many body systems is a major topic of interest in condensed matter physics. These properties tell us about the propagation of elementary excitation and mechanisms of relaxation in interacting systems. In this context correlation functions have became even more relevant due the experiments in systems of cold atoms and trapped ions that measure real time dependence directly out to relatively long times. However, most studies in quantum spins chains so far have focused on correlations of single spins. Using the one dimensional XX spin chain, we study exact methods to calculate the correlation functions of the components of the tensor operator involving two spins, Tabi,j = SaiSbj. This operator appear, for example, as a response of inelastic x-ray scattering cross section. Based on Wick\'s theorem, we show that some correlation functions of local components of the tensor operator of two pairs of neighbor sites, in the fermion space, can be written as a combination of Greens functions of a single particle. We have used Feynman diagrams to organize this combination and calculate the correlation functions. Then, considering these propagators for long times and large distances along the light cone, we found the behavior of these correlation functions as a oscillatory and power law decay on time. A direct application of correlation functions is to study conserved and non-conserved quantities, and such analysis has been made. We also considered other two-spin operators which are not local in the fermionic representation. In this case the calculation is more challenging, but the time-dependent correlation functions can be expressed in terms of Fredholm determinants.

La quantité d'information générée chaque année ne cesse de croitre tout comme la complexité des problèmes à résoudre. Ces nouveaux défis ont conduit au développement de nouveaux paradigmes, tels que l'information quantique, qui utilise des ordinateurs quantiques basés sur des bits quantiques (qubits). Les molécules magnétiques sont des candidats intéressants pour coder des qubits de spin. Parmi les défis de la recherche sur les molécules paramagnétiques en tant que qubit, se trouve l'obtention de longs temps de relaxation (T₁ et T₂) ainsi que le couplage de qubit entre eux.Un qubit de spin est un système de deux niveaux quantiques qui peuvent être mis en superposition suffisamment longtemps pour être observé et manipulé. Ceci peut être réalisé avec des molécules ayant un électron célibataire (comme un radical organique) avec un spin ½ ou en concevant des molécules avec un spin entier (S = 1 pour les complexes Ni(II)) pour lever la dégénérescence en champ nul (ZFS). La transition entre ces niveaux, connue sous le nom de transition d'horloge (CT), est protégée des fluctuations magnétiques, ce qui allonge le temps de relaxation T₂. Durant cette thèse, nous avons étudié divers composés de nickel et essayé de prédire le signe de l'anisotropie axiale à partir de leur structure. Nous avons mesuré les spectres RPE de ces composés pour accéder aux paramètres ZFS et avons rationalisé les résultats par le calcul. La modulation de la sphère de coordination par des effets stériques et électroniques des complexes de Ni(II) a donné lieu à des composés avec des transitions d'horloge accessibles. L'étude RPE pulsée de ces complexes a mis en évidence différentes stratégies pour augmenter le T₁ et a démontré la robustesse d'un CT contre les fluctuations magnétiques. Nous nous sommes également orientés vers l'étude de complexes avec une valeur de spin S=1/2, qui possèdent des temps de relaxation relativement longs et ne dépendent pas du ZFS. Ceci garantit la possibilité d'obtenir un signal RPE permettant une étude détaillée des composés. Pour les complexes de Cu(II), les temps de relaxation relativement longs (T₂ = 1 µs et T₁ (7.5K) = 1.8 ms) trouvés dans l'unité monomérique restent inchangés dans le complexe binucléaire. Nous avons essayé de préparer plusieurs complexes binucléaires de Cu(II) avec différentes distances Cu-Cu. Nous avons également mesuré le temps de cohérence des spins nucléaires d'un proton et d'un azote couplés par une interaction superhyperfine au spin électronique du Cu(II) et avons trouvé une valeur T₂ de plus de 500 µs pour le proton. Nous avons ainsi montré la capacité d'une seule molécule magnétique à porter plusieurs ressources pour réaliser les portes quantiques nécessaires à l'informatique quantique
The exponential growth in information processing and the demand for solving new challenges have led to the development of new paradigms, such as quantum information, which uses quantum computers based on quantum bits (qubits). Magnetic molecules, are attractive candidates to encode spin qubits. Among the challenges in the molecular magnet as qubit research we found obtaining long phase memory relaxation times and coupling qubit among them. A spin qubit is a system of two non-degenerated quantum levels that can be put into superposition long enough to allow measurements to be made. This can be achieved with molecules having an unpaired electron (such as an organic radical) with a ½ spin or by designing molecules with an integer spin (S=1 for Ni(II) complexes) to lift degeneracy without a magnetic field (ZFS). The transition between these levels, known as the clock transition (CT), is protected from magnetic fluctuations, lengthening the T₂ relaxation time. In these projects we studied various nickel compounds and tried to predict the sign of the axial anisotropy from their structure. We measured the EPR spectra of these compounds to access the ZFS parameters and rationalised the results by calculation. The modulation of the coordination sphere by steric, electronic and packing effects of Ni(II) complexes has resulted in compounds with accessible clock transitions. The pulsed EPR study of these complexes has pointed out a strategy to increase the T₁ and demonstrated the robustness of a CT against. magnetic fluctuactions. We also switch our focus on the study of complexes with an S = 1/2 spin value, which have relatively long relaxation times and are not dependent on ZFS. This guarantees the possibility of obtaining an EPR signal so that a detailed study could be carried out. For Cu(II) complexes, the relatively long relaxation times (T₂ = 1µs and T₁ (7.5K) = 1.8 ms) found in the monomeric unit remain unchanged in the binuclear complex. We tried to prepare several binuclear Cu(II) complexes with different Cu-Cu distances. We also measured the coherence time of the nuclear spins of a proton and a nitrogen coupled via superhyperfine interaction to the Cu(II) electronic spin and found a T₂ value of more than 500 µs, demonstrating the ability of a single magnetic molecule to bear several ressources to perform quantum gates that are required for quantum computation

This thesis presents neutron and x-ray scattering measurements on quasi-two-dimensional honeycomb antiferromagnets A2IrO₃ (A=Na, Li) and the solid-solution intermediate material (Na_1-xLi_x)₂IrO₃. The aim is to study the magnetic order and excitations of 5d Ir⁴⁺ ions in a honeycomb lattice, where unusual magnetic properties have been theoretically predicted to be stabilised by the combinations of strong spin-orbit coupling and honeycomb lattice geometry with 90 degree Ir-O-Ir bonding. By using an optimised setup to minimise the strong neutron absorption by Ir nuclei, inelastic neutron scattering measurements on powder sample of Na₂IrO₃ observed dispersive excitations below 5meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zigzag magnetic order. The onset of long-range magnetic order was confirmed by the observation of oscillations in zero-field muon-spin rotation experiments. Higher-resolution inelastic neutron data found features consistent with a spin gap of 1.8meV and the data was parameterised by including Ising-type exchange anisotropy. Combining single-crystal diffraction and density functional calculations, a revised crystal structure model with significant departures from the ideal 90 degree Ir-O-Ir bonds required for dominant Kitaev exchange was proposed. Various "idealised'' crystal structures were constructed to emphasize the departures between the actual structure and structures with cubic IrO₆ octahedra. The magnetic excitations from the isostructural Li₂IrO₃ revealed strongly dispersive magnetic excitations, qualitatively different from Na₂IrO₃. Elastic neutron diffraction detected a magnetic Bragg peak with a wavevector consistent with spiral orders. To explain the observed neutron data, the spiral H2 phase in the Heisenberg J₁-J₂-J₃ model was proposed, and a full calculation was performed with strong in-plane anisotropic interaction. A further measurement for improving the lower-energy excitation found no clear evidence for a spin gap down to E=0.7meV. Lastly, the crystal structure of (Na_1-xLi_x)₂IrO₃ was investigated with single-crystal x-ray diffraction, revealing a site-mixing of Ir and Na ions in the honeycomb lattice and insensitivity of the refinement to the Li positions. Ab initio calculations suggested that up to x=0.25 Li ions replaced Na in the honeycomb centre and phase separation occurred beyond that, which is consistent with the evolution of observed lattice parameters.

A Kitaev quantum spin liquid is a phase of matter predicted to host excitations that can be used to preform fault-tolerant quantum computation. Though the theoretical prediction of such a state is on firm footing, its realisation in real materials has proven to be elusive. Recent developments have suggested honeycomb materials consisting of 3d transition metal ions as possible candidates. The focus of this thesis is the magnetic properties of one such material, K2Ni2–xCoxTeO6. It is part of a family of layered two dimensional materials consisting of honeycomb structured transition metal layers sandwiched between layers of alkali ions. A characterisation of the magnetic properties of K2Ni2–xCoxTeO6 has been carried out with the techniques of muon spin rotation/relaxation/resonance and bulk magnetisation as a function of the chemical composition. Further investigations of the detailed atomic structure and spin order using neutron scattering was also initiated. The results of such characterisations are presented and discussed in this thesis.
En Kitaev kvantspinvätska är en fas av materia som har förespåtts kunna husera exciterade tillstånd som kan användas for att konstruera en kvantdator. Även om de teoretiska rönen är väl underbyggda, har ett förverkligande av en sådan fas i verkliga material varit svår att åstadkomma. Nya rön har pekat ut bikakematerial bestående av 3d övergångsmetaller som potentiella kandidater. Därav fokuserar denna avhandling på ett sådant material, K2Ni2–xCoxTeO6. Det är en del av en familj av liknande material bestående av tvådimensionella lager av bikakeformade övergångsmetaller mellan lager av alkaliska joner. En karaktärisering av de magnetiska egenskaperna av K2Ni2–xCoxTeO6 har utförts genom att analysera data från myon spin rotation/dämpning/resonans samt magnetiserings mätningar som funktion av materialets kemiska samansättning. Ytterligare mätningar av den atomära strukturen och spinordning påbörjades också med hjälp av neutronspridningstekniker. I denna avhandling presenteras och diskuteras resultaten av dessa karaktäriseringar.

Dans cette thèse nous étudions expérimentalement les propriétés magnétiques de condensats de sodium de spin 1 à l'équilibre. Dans ce système les atomes peuvent occuper chacun des trois états Zeeman caractérisés par la projection de leur spin sur l'axe de quantification m=+1,0,-1. Nous mesurons l'état de spin à N particules du système en fonction du champ magnétique appliqué et et de la magnétisation (différence entre les populations des états m=+1 et m=-1) du nuage atomique. Nos mesures sont en très bon accord avec la prédiction de la théorie de champ moyen, et nous identifions deux phases magnétiques résultant de la compétition entre les interactions de spin antiferromagnétiques et l'effet du champ magnétique. Nous décrivons ces deux phases en terme d'un ordre nématique de spin caractérisant la symétrie de l'état de spin à N particules. Dans une seconde partie nous nous concentrons sur les propriétés du condensat à très faible magnétisation et soumis à un faible champ magnétique. Dans ces conditions, la symétrie du système se manifeste à travers de très grandes fluctuations de spin. Ce phénomène n'est pas explicable par une théorie de champs moyen naïve, et nous développons une approche statistique plus élaborée pour décrire l'état de spin du condensat. Nous mesurons les fluctuations de spin et nous sommes capables de déduire de leur analyse la température caractérisant le degré de liberté de spin du condensat. Nous trouvons que cette température diffère de celle décrivant les atomes thermiques entourant le condensat. Nous interprétons cette différence comme une conséquence du faible couplage entre ces deux systèmes
In this thesis we study experimentally the magnetic properties of spin-1 Bose-Einstein condensate of Sodium at equilibrium. In this system the atoms can occupy any of the three Zeeman states characterized by their spin projection on the quantization axis m=+1,0,-1. We measure the many-body spin state of the system as a function of the applied magnetic field and of the magnetization (difference between the populations of the spin states m=+1 and m=-1) of the atomic sample. We find that our measurements reproduce very well the mean-field prediction, and we identify two magnetic phases expressing the competition between the antiferromagnetic inter-particle interactions and the effect of the magnetic field. We describe these phases in terms of a spin nematic order characterizing the symmetry of the many-body spin state. In a second part we focus on the properties of condensates of very low magnetization under a weak magnetic field. In these conditions, the symmetry of the system manifests itself in huge spin fluctuations. This phenomenon is not explainable by a naive mean-field theory and we develop a more elaborate statistical approach to describe the spin state of the condensate. We measure the spin fluctuations and are able from their analysis to infer the temperature characterizing the spin degree of freedom of the condensate. We find that this temperature differs from the temperature of the thermal fraction surrounding the condensate. We interpret this difference as a consequence of the weak coupling between these two systems

Molecular Nanomagnets have been proposed as plausible candidates in a variety of futuristic applications. Thorough understanding of the magnetic properties of these systems is therefore necessary to develop devices that include such units. The aim of this thesis is to synthesise and structurally and magnetically characterise a range of systems that could be used as elementary units in three proposed applications such as: data storage devices, magnetic refrigerants and qubits for quantum computing. A series of mixed 3d/4f metal complexes were synthesised through solvothermal reactions and characterised by X-ray single crystal diffraction and SQUID magnetometry. Through indirect methods it was possible to obtain high magnetic entropy change for some systems. It was also possible to obtain some insight into the magnetic interactions within the systems through modelling the magnetic data. The role of the 4f-4f and 3d-4f interactions in two sets of molecules is also described. The first study is in an asymmetric dysprosium dimer, where through a range of experimental techniques and advanced theoretical methods, such ab-initio calculations we are able to explain the role of the intramolecular interactions and their effect on the SMM properties of this system. Similarly, insight into the role of the 3d-4f interactions is achieved through the observation of the magnetic behaviour of a family of 27 tetranuclear systems, though SQUID data and ab-initio calculations. Finally, chemical functionalization of a well-proposed qubits, namely {Cr7Ni} and subsequent reaction with a redox active metal ion, CoII/III, two {Cr7Ni} systems are linked. The magnitude of the exchange interaction between the {Cr7Ni}-CoII-{Cr7Ni} was determined through Electron Paramagnetic Resonance. Furthermore, by chemical oxidation/reduction of the cobalt between paramagnetic and diamagneticstates, i.e. CoII and CoIII respectively, we demonstrate that the interaction can be switched ON/OFF. This characteristic makes of these systems candidates to function as a SWAP gate.

The on-surface reactions of 10-bromo-10'-(2,6-dimethylphenyl)-9,9'-bianthracene on Au(111) surface have been investigated by a combination of bond-resolved scanning tunneling microscopy, scanning tunneling spectroscopy, and tightbinding and mean-field Hubbard calculations. The reactions afford the synthesis of two open-shell nanographenes (1a and 1b) exhibiting different scenarios of all-carbon magnetism. 1a, an allbenzenoid nanographene with previously unreported triangulenelike termini, contains a high proportion of zigzag edges, which endows it with an exceedingly low frontier gap of 110 meV and edge-localized states. The dominant reaction product (1b) is a non-benzenoid nanographene consisting of a single pentagonal ring in a benzenoid framework. The presence of this nonbenzenoid topological defect, which alters the bond connectivity in the hexagonal lattice, results in a non-Kekulé nanographene with a spin S = ½, which is detected as a Kondo resonance. Our work provides evidence of all-carbon magnetism, and motivates the use of topological defects as structural elements toward engineering agnetism in carbon-based nanomaterials for spintronics.

Strongly correlated metals are known to give rise to a variety of exotic states. In particular, if a system is tuned towards a quantum critical point, new ordered phases may arise. Sr₃Ru₂O₇ is a quasi-two dimensional metal in which field-tuned quantum criticality has been observed. In very pure single crystals of this material, a phase with unusual transport properties forms in the vicinity of its quantum critical point. Upon the application of a small in-plane field, electrical resistivity becomes anisotropic, a phenomenon which has led to the naming of this phase as an `electron nematic'. The subject of this thesis is a study of the electrical transport in high purity crystals of Sr₃Ru₂O₇. We modified an adiabatic demagnetisation refrigerator to create the conditions by which the entire temperature-field phase diagram can be explored. In particular, this allowed us to access the crossover between the low-temperature Fermi liquid and the quantum critical region. We also installed a triple axis `vector magnet' with which the applied magnetic field vector can be continuously rotated within the anisotropic phase. We conclude that the low- and high-field Fermi liquid properties have a complex dependence on magnetic field and temperature, but that a simple multiple band model can account for some of these effects, and reconcile the measured specific heat, dHvA quasiparticle masses and transport co-efficients. At high temperatures, we observe similarities between the apparent resistive scattering rate at critical tuning and those observed in other quantum critical systems and in elemental metals. Finally, the anisotropic phase measurements confirm previous reports and demonstrate behaviour consistent with an Ising-nematic, with the anisotropy aligned along either of the principal crystal axes. Our observations are consistent with the presence of a large number of domains within the anisotropic phase, and conclude that scattering from domain walls is likely to contribute strongly to the large measured anisotropy.