Dissertations / Theses on the topic 'Quantum magnetisms'

À l'aube de la seconde révolution quantique, comprendre et exploiter les phénomènes résultant de l'interaction entre la non-localité intrinsèque de la mécanique quantique et les interactions purement non-locales est d'une importance cruciale pour le développement de nouvelles technologies quantiques. Dans cette thèse, nous nous concentrerons principalement sur les effets non-locaux introduits par la frustration topologique (FT), une forme de frustration faible qui a été introduite pour la première fois dans le contexte des chaînes de spins quantiques antiferromagnétiques en appliquant les conditions aux limites frustrées, réalisées comme une combinaison de conditions aux limites périodiques et d'un nombre impair de spins. Notre objectif est double. D'une part, nous améliorerons la compréhension théorique des phases topologiquement frustrées. Au-delà de ces implications théoriques, ce travail démontrera que les chaînes de spins FT présentent un potentiel technologique convaincant, les proposant comme des candidats compétitifs pour le développement de batteries quantiques robustes et efficaces
At the verge of the second quantum revolution, understanding and exploiting the phenomena resulting from the interplay between the intrinsic non-locality of quantum mechanics and purely non-local interactions is of crucial importance for the development of novel quantum technologies. In this thesis, we will mostly focus on the non-local effects introduced by topological frustration (TF), a form of weak frustration that was first introduced in the context of antiferromagnetic quantum spin chains by applying the so called frustrated boundary conditions, realized as a combination of periodic boundary conditions and odd number of spins. Our goal is double. From one side, we will further improve the theoretical understanding of topologically frustrated phases. Beyond these theoretical implications, this work will demonstrate that TF spin chains exhibit compelling technological potential, proposing them as competitive candidates for the development of robust and efficient quantum batteries

In the study of strongly interacting condensed-matter systems controlled microscopic theories hold a key position. Spin-wave theory, large-N expansion, and $epsilon$-expansion are some of the few successful cornerstones. In this doctoral thesis work, we have developed a novel large-$d$ expansion method, $d$ being the spatial dimension, to study model Hamiltonians hosting a quantum phase transition between a paramagnet and a magnetically ordered phase. A highlight of this technique is that it can consistently describe the entire phase diagram of the above mentioned models, including the quantum critical point. Note that most analytical techniques either efficiently describe only one of the phases or suffer from divergences near the critical point. The idea of large-$d$ formalism is that in this limit, non-local fluctuations become unimportant and that a suitable product state delivers exact expectation values for local observables, with corrections being suppressed in powers of $1/d$. It turns out that, due to momentum summation properties of the interaction structure factor, all diagrams are suppressed in powers of $1/d$ leading to an analytic expansion. We have demonstrated this method in two important systems namely, the coupled-dimer magnets and the transverse-field Ising model. Coupled-dimer magnets are Heisenberg spin systems with two spins, coupled by intra-dimer antiferromagnetic interaction, per crystallographic unit cell (dimer). In turn, spins from neighboring dimers interact via some inter-dimer interaction. A quantum paramagnet is realized for a dominant intra-dimer interaction, while a magnetically ordered phase exists for a dominant (or of the same order as intra-dimer interaction) inter-dimer interaction. These two phases are connected by a quantum phase transition, which is in the Heisenberg O(3) universality class. Microscopic analytical theories to study such systems have been restricted to either only one of the phases or involve uncontrolled approximations. Using a non-linear bond-operator theory for spins with S=$1/2$, we have calculated the $1/d$ expansion of static and dynamic observables for coupled dimers on a hypercubic lattice at zero temperature. Analyticity of the $1/d$ expansion, even at the critical point, is ensured by correctly identifying suitable observables using the mean-field critical exponents. This method yields gapless excitation modes in the continuous symmetry broken phase, as required by Goldstone\'s theorem. In appropriate limits, our results match with perturbation expansion in small ratio of inter-dimer and intra-dimer coupling, performed using continuous unitary transformations, as well as the spin-wave theory for spin-$1/2$ in arbitrary dimensions. We also discuss the Brueckner approach, which relies on small quasiparticle density, and derive the same $1/d$ expansion for the dispersion relation in the disordered phase. Another success of our work is in describing the amplitude (Higgs) mode in coupled-dimer magnets. Our novel method establishes the popular bond-operator theory as a controlled approach. In $d=2$, the results from our calculations are in qualitative agreement with the quantum Monte Carlo study of the square-lattice bilayer Heisenberg AF spin-$1/2$ model. In particular, our results are useful to identify the amplitude (Higgs) mode in the QMC data. The ideas of large-$d$ are also successfully applied to the transverse-field Ising model on a hypercubic lattice. Similar to bond operators, we have introduced auxiliary Bosonsic operators to set up our method in this case. We have also discussed briefly the bilayer Kitaev model, constructed by antiferromagnetically coupling two layers of the Kitaev model on a honeycomb lattice. In this case, we investigate the dimer quantum paramagnetic phase, realized in the strong inter-layer coupling limit. Using bond-operator theory, we calculate the mode dispersion in this phase, within the harmonic approximation. We also conjecture a zero-temperature phase diagram for this model.

This thesis presents an experimental and theoretical examination of five polymeric quantum magnets. The first of these is Cu(pyrazine)(glycinate)ClO4, an exchange-coupled spin-dimer system that undergoes a powerful and continuous magnetocaloric effect (MCE) in a rapidly changing magnetic field H. The evolution of the sample temperature T with H must be accounted for in order to reconcile an apparent discrepancy between the results of magnetometry measurements performed in quasistatic and pulsed magnetic fields, and the MCE is likely to be an important consideration for pulsed-field experiments performed on similar insulating materials. Heat capacity measurements of Cu(pyrazine)(glycinate)ClO4 are perturbed by zero-point fluctuations for T > 400 mK, and these data further suggest that this system exhibits possible two-dimensional universal behaviour. The results of single crystal x-ray diffraction measurements of a second material [H2F]2[NiF2(3-fluoropyridine)4]3[SbF6]2 at 100 K indicate that the Ni2+ ions of this complex are arranged on the vertices of a two-dimensional kagome lattice, wherein the spin S = 1 ions are bridged via charge-assisted Ni-F· · · H-F-H· · · F-Ni linkages. However, a density-functional theory study indicates that a positional disorder of the H2F+ moieties within these bridges suppresses the intraplane spin-exchange interactions. Powder muon spin-rotation measurements imply that the system is paramagnetic for T > 19 mK, while polycrystalline electron spin-resonance (ESR), magnetization M(H), and heat capacity experiments together indicate that the unixial and rhombohedral single-ion anisotropy of the Ni2+ ions are approximately D/kb = 8.3(4) K and E/kb = 1.2(3) K respectively. Lastly, neutron powder diffraction measurements of three isotructural compounds [M(HF2)(pyrazine)2]SbF6 (M = Cu2+, Ni2+ or Co2+) reveal that each system is tetragonal (P4/nmm) and that the spin-exchange interactions facilitated by the pyrazine (Jpyz) and bifluoride (Jfhf) ligands are antiferromagnetic. The Cu2+ congener is a quasi-two-dimensional Heisenberg S = 1/2 antiferromagnet, which displays an ordered moment of 0.6(1)μb per ion that is reduced from its paramagnetic value by quantum fluctuations. For the S = 1 Ni2+ complex, powder M(H) measurements suggest that D has an easy-plane character while inelastic neutron scattering experiments determine D/kb = 13.3(3) K, Jfhf/kb = 10.4(3) K and Jpyz/kb = 1.4(2) K. The S = 3/2 Co2+ system adopts an Ising-like antiferromagnetic ground state below 7.1(1) K, and its magnetic properties are parameterized with an effective spin-1/2 Hamiltonian for T < 50 K.

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.

This thesis presents the results of muon-spin relaxation (µ⁺SR) studies into magnetic materials, and demonstrates how these results can be exploited to quantify the materials’ low moments and reduced dimensionality. Dipole-field simulations, traditionally used to estimate likely muon sites within a crystal structure, are described. A novel Bayesian approach is introduced which allows bounds to be extracted on magnetic moment sizes and magnetic structures—previously very difficult using µ⁺SR—based on reasonable assumptions about positions in which muons are likely to stop. The simulations are introduced along with relevant theory, and MµCalc, a platform-independent program which I have developed for performing the calculations is described. The magnetic ground states of the isostructural double perovskites Ba₂NaOsO₆ and Ba₂LiOsO₆ are investigated with µ⁺SR. In Ba₂NaOsO₆ long-range magnetic order is detected via the onset of a spontaneous muon-spin precession signal below T_c = 7.2(2) K, while in Ba₂LiOsO₆ a static but spatially-disordered internal field is found below 8 K. Bayesian analysis is used to show that the magnetic ground state in Ba₂NaOsO₆ is most likely to be low-moment (˜ 0.2µ_B) ferromagnetism and not canted antiferromagnetism. Ba₂LiOsO₆ is antiferromagnetic and a spin-flop transition is found at 5.5 T. A reduced osmium moment is common to both compounds, probably arising from a combination of spin–orbit coupling and frustration. Results are also presented from µ⁺SR investigations concerning magnetic ordering in several families of layered, quasi–two-dimensional molecular antiferromagnets based on transition metal ions such as S = ½ Cu²⁺ bridged with organic ligands such as pyrazine. µ⁺SR allows us to identify ordering temperatures and study the critical behaviour close to T_N , which is difficult using conventional probes. Combining this with measurements of in-plane magnetic exchange J and predictions from quantum Monte Carlo simulations allows assessment of the degree of isolation of the 2D layers through estimates of the effective inter-layer exchange coupling and in-layer correlation lengths at T_N. Likely metal-ion moment sizes and muon stopping sites in these materials are identified, based on probabilistic analysis of dipole-fields and of muon–fluorine dipole–dipole coupling in fluorinated materials.

The interplay between electron correlation, local distortions and Spin Orbit Coupling is one of the most attractive phenomena in condensed matter Physics and have stimulated much attention in the last decade. In Osmates double perovskites the coupling between electronic, structural and orbital degrees of freedom leads to the formation of an unconventional magnetic phase, whose precise origin and characteristics are still not understood. In particular strong Spin Orbit Coupling effect is believed to occur and have a crucial role in enhancing multipolar exchange interactions in a fashion similar to the more studied 4f electron systems. In this thesis, by means of first principles calculations, we study the structural, electronic and magnetic proprieties of the Mott insulating Ba2NaOsO6 with Osmium in 5d1 electron configuration within the fully relativistic Density Functional Theory plus on site Hubbard U (DFT + U) scheme. We find that the system is subjected to local symmetry breaking and that the magnetic ground state is strongly dependent on the on site Coulomb interaction. Furthermore, by mapping the energy onto a Pseudospin Hamiltonian, we are capable to prove that quadrupolar and octupolar exchanges play a significant role. We repeated the study for Ba2CaOsO6 with Os in 5d2 electronic configuration as a preliminary step for understanding if phase transitions are possible when Ba2NaOsO6 is doped.

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 reports on recent results which pave the way for future experiments in the emerging field of quantum magnonics. Chapter 1 presents a brief outline of the field of magnonics, which provides the context in which quantum magnonics has begun to develop. Chapter 2 provides an introduction to the theory of spin waves, which is necessary to understand the experiments reported in the thesis. In Chapter 3, the experimental methods and materials used to carry out the investigations in the thesis are described. Chapter 4 describes the coupling of resonant magnon modes in a sphere of yttrium-iron garnet to photon modes in a coplanar-waveguide resonator. Strong coupling is achieved to multiple magnon modes, and a theoretical model is used to identify the magnon modes which couple most strongly to the photon mode. In Chapter 5, the behaviour of propagating magnon modes is investigated in a waveguide formed from a thin film of yttrium-iron garnet. Two different configurations are investigated supporting different types of propagating mode, namely backward-volume and surface spin waves. Simulations are performed which reproduce the main features of the data. Chapter 6 characterises the effect of the gadolinium-gallium garnet substrate on propagating spin waves. The magnitude of this effect is dependent on both the orientation and temperature of the sample. Finally, Chapter 7 provides a short summary of the results of the thesis, and speculates on how they may inform future work in the field.

Thesis advisor: Ziqiang Wang
The discovery of high-Tc superconductivity in cuprates, quantum Hall effect greatly challenge the single-electron understanding of condensed matter physics. In contrast to phonon-mediated BCS mechanism, the unconventional high-Tc superconductivity is widely believed to come from strongly electronic correlation. Strong electron-electron repulsion leads to the interplay among spin, charge, orbital and lattice degrees of freedom, resulting in high-temperature superconductivity, charge or spin density wave, Mott insulator, orbital order, nematicity etc. On the other hand, quantum Hall effect brings us the realization of the mathematical concept of topology in condensed matter. Topology has been widely explored in the topological insulator, topological superconductors, symmetry protected topological order etc. In this dissertation, we study theoretically the physics of electronic correlation and topology in various systems, including superconductivity in single layer CuO₂, electronic nematicity in FeSe, chiral spin density wave in honeycomb lattice and antiferromagnetic Chern insulator in 2D non-centrosymmetric systems
Thesis (PhD) — Boston College, 2018
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Physics

Quantum phase transitions (QPT) on the border of magnetism have provided a fertile hunting ground for the discovery of new states of matter, for example; the marginal Fermi Liquid and non Fermi Liquid states as well high T$_C$ cuprate and magnetically mediated superconductivity. In this thesis I present work on three materials in which it may be possible to tune the system through a magnetic QPT with the application of hydrostatic pressure. Although the details of the underlying physics are different in each of the materials, they are linked by the possibility of finding new states on the border of magnetism. Applying hydrostatic pressure, we have suppressed the ferromagnetic (FM) transition in metallic Fe$_2$P to very low temperature and to a potential QPT. Counter-intuitive broadening of the magnetic hysteresis leading up to the FM-AFM QPT may well be a crucial clue as to the nature of the model needed to understand this phase transition. A sharp increase in the quasi-particle scattering cross-section as well as the residual resistivity accompany a departure from the quadratic temperature dependence of the resistivity. This possible deviation from Fermi liquid behaviour is stable over a significant range of temperature. The unexplained upturn in the resistivity of CeGe that accompanies the AFM transition was studied under pressure. Pressure increased the residual resistivity as well as decreasing the relative size of the upturn, but had a moderate effect on the Neel temperature. The insensitivity of the N$\acute e$el temperature to pressure has been compared to its relative sensitivity to applied feld. The existence of the upturn and its evolution with pressure and applied feld can reasonably be argued to be due to the details of the electron band structure in the system. By applying pressure we have drastically reduced the resistivity of the insulating antiferromagnet NiPS$_3$. Concurrent work on FePS$_3$ has shown metallisation under pressure. It seems reasonable to speculate that NiPS$_3$ may also metallise at higher pressure. The energy gap is narrowed in both materials as pressure is increased. Magnetisation measurements have revealed a low temperature upturn indicating some possible ferromagnetic component or proximity to another magnetic state. A peak in the magnetisation is also seen at 45K in zero-feld cooled measurements. Both of these features point to a system with a complex magnetic ground state.

Molecular magnets are ideal systems to probe the realm that borders quantum and classical physics, as well as to study decoherence phenomena in nanoscale systems. The control of the quantum behavior of these materials and their structural characteristics requires synthesis of new complexes with desirable properties which will allow probing of the fundamental aspects of nanoscale physics and quantum information processing. Of particular interest among the magnetic molecular materials are single-molecule magnets (SMMs) and antiferromagnetic (AFM) molecular wheels in which the spin state of the molecule is known to behave quantum mechanically at low temperatures. In previous experiments the dynamics of the magnetic moment of the molecules is governed by incoherent quantum tunneling. Short decoherence times are mainly due to interactions between molecular magnets within the crystal and interactions of the electronic spin with the nuclear spin of neighboring ions within the molecule. This decoherence problem has imposed a limit to the understanding of the molecular spin dynamics and the sources of decoherence in condensed matter systems. Particularly, intermolecular dipolar interactions within the crystal, which shorten the coherence times in concentrated samples, have stymied progress in this direction. Several recent works have reported a direct measurement of the decoherence time in molecular magnets. This has been done by eliminating the dephasing created by dipolar interactions between neighboring molecules. This has been achieved by a) a dilution of the molecules in a liquid solution to decrease the dipolar interaction by separating the molecules, and b) by polarizing the spin bath by applying a high magnetic field at low temperatures. Unfortunately, both approaches restrict the experimental studies of quantum dynamics. For example, the dilution of molecular magnets in liquid solution causes a dispersion of the molecular spin orientation and anisotropy axes, while the large fields required to polarize the spin bath overcome the anisotropy of the molecular spin. In this thesis I have explored two methods to overcome dipolar interactions in molecular magnets: a) studying the dynamics of molecular magnets in single crystals where the separation between magnetic molecules is obtained by chemical doping or where the high crystalline quality allows observations intrinsic to the quantum mechanical nature of the tunneling of the spin, and b) studying the electronic transport through an individual magnetic molecule which has been carefully placed in a single-electron transistor device. I have used EPR microstrip resonators to measure Fe17Ga molecular wheels within single crystals of Fe18 AFM wheels, as well as demonstrating, for the first time in a Single Molecule Magnet, the complete suppression of a Quantum Tunneling of the Magnetization transition forbidden by molecular symmetry.
Ph.D.
Department of Physics
Sciences
Physics PhD

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.

This thesis describes an experimental study of the electronic properties of semiconductor heterostructure tunnel devices. InAs self-assembled quantum dots (QDs) are incorporated into the barrier layer of a GaAs/AlAs/GaAs tunnel diode. When a voltage, V, is applied across the device, we observe resonant features in the tunnel current, I, whenever an electron state in one of the qds comes into resonance with an occupied electron state in the emitter. We employ an electron state of a single qd as a spectroscopic probe of a two-dimensional electron system (2DES), from the Fermi energy to the subband edge [1]. For magnetic field B applied parallel to the current, we observe peaks in the I(V) characteristics corresponding to the formation of Landau levels in the 2DES. We obtain quantitative information about the energy dependence of the quasiparticle lifetime, Tqp, of the 2DES. We find that Tqp ~ 2.5 hbar=(Ef - E), in contrast with the expectation for a normal Fermi liquid, but in agreement with predictions for a Fermi liquid state of a disordered 2DES. Close to filling factor nu = 1 we observe directly the exchange enhancement of the g factor. This thesis also describes the design, realisation and measurement of a tunnel diode incorporating InAs QDs and a series of 4 planar electrostatic gates. By applying a bias to the gates, it is possible to selectively inject current into a particular QD. We use magneto-tunnelling spectroscopy to determine the energy levels of the ground and excited state of a single QD, and to map the spatial form of the wave functions of these states [2]. The effect of pressure on the resonant tunnelling of the QDs is also described. [1] P. C. Main et al., Phys. Rev. Lett. 84, 729 (2000) [2] R. J. A. Hill et al., Appl. Phys. Lett. 79, 3275 (2001)

The interplay between magnetism and structure has been studied in magnetic multilayers by electronic structure calculations based on density functional theory and analyzed in terms of models. The main ideas behind the Korringa-Kohn-Rostocker Green’s function method are described and the implementation of the coherent potential approximation is outlined.

A simple model for the bilinear magnetic interlayer coupling in metallic multilayers is derived that elucidates the main characteristics of the effect such as coupling period and origin of damping. An analysis of two exotic effects on the magnetic interlayer coupling, Fermi surface nesting and magnetic enhancement is also performed. The Fermi surface nesting in CuPd for the (110) direction is shown to induce a sharp peak in the magnetic interlayer coupling amplitude for a Fe/CuPd/Fe system when the Cu concentration is 60% in the CuPd alloy. The high magnetic susceptibility in Pd is shown to have strong influence on the magnetic interlayer coupling in a Fe/Pd/Fe (100) system where it changes the amplitude, phase and induces an offset.

The relation between surface structure and magnetic properties in metallic multilayers is investigated in terms of a theory that is based on a symbiosis between experiment and theory. By calculating the total magnetic moment of a sample for a large range of possible interface structures and comparing to experimental results for equivalent samples a parameter that describes the interface structure is determined. This parameter is then shown to be universal for the particular combination of elements in the structure both as regards the calculated total magnetic moment as well as the magnetic interlayer coupling and the critical temperatures.

In his programmatic article More Is Different (1972), Nobel laureate P. W. Anderson captured the fundamental interest in quantum matter in a nutshell. The central motive in this field is emergence. In the inaugural volume of the homonymous journal, J. Goldstein defined this as "the arising of novel and coherent structures, patterns and properties during the process of self-organization in complex systems". Famously, the idea that the "the whole is greater than the sum of its parts" goes back to Aristotle's metaphysics, and it has served as a stimulating concept in 19th century biology, economics and philosophy. The study of emergence in condensed matter physics is unique in that the underlying complex systems are sufficiently "simple" to be modelled from first principles. Notably, the emergent phenomena discovered in this field, such as high-temperature superconductivity, giant magnetoresistance, and strong permanent magnetism have had an enormous impact on technology, and thus, society. Historically, there has been a distinction between materials with localized, strongly interacting (or correlated) electrons - and non-interacting, itinerant electronic states. In the last decade, several new states of matter have been discovered, which emerge not from correlations, but from peculiar symmetries (or topology) of itinerant electronic states. The term quantum materials has therefore become popular to subsume these two strands of condensed matter physics: Electronic correlations and topology. In this thesis, I report investigations of four quantum materials which each illustrate present key interests in the field: The mechanism of high temperature superconductivity, the search for materials that combine both electronic correlations and non-trivial topology and novel emergent phenomena that arise from the synergy of electronic correlations and a strong coupling of spin- and orbital degrees of freedom. The common factor and potential key to understanding these materials is magnetism. My experimental work is focused on neutron and x-ray scattering techniques, which are able to determine both order and dynamics of magnetic states at the atomic scale. I illustrate the full scope of these methods with experimental studies at neutron and synchrotron radiation facilities. This includes both diffraction and spectroscopy, of either single- or polycrystalline samples. My in-depth analysis of each dataset is aided by structural, magnetic and charge transport experiments. Thus, I provide a quantitative characterization of magnetic fluctuations in an iron-based superconductor and in two Dirac materials, and determine the magnetic order in a Dirac semimetal candidate and a complex oxide. As a whole, these results demonstrate the elegant complementarity of modern scattering techniques. Although such methods have a venerable history, they are presently developing at a rapid pace. Several results of this thesis have only been enabled by very recent instrumental advances.

Quantum phenomena in high-Tc superconductors and dimerized quantum Heisenberg antiferromagnets are studied analytically in this thesis. The implications of the Fermi surface consisting of the disjoint pieces, observed in cuprate superconductors, are considered. It is demonstrated that in this case the g-wave superconducting pairing is closely related to d-wave pairing. The superconductivity in this system can be described in terms of two almost degenerate superconducting condensates. As a result a new spatial scale lg, much larger than the superconducting correlation length x, arises and a new collective excitation corresponding to the relative phase oscillation between condensates, the phason, should exist. The Josephson tunneling for such a two-component system has very special properties. It is shown that the presence of g-wave pairing does not contradict the existing SQUID experimental data on tunneling in the ab-plane. Possible ways to experimentally reveal the g-wave component and the phason in a single tunnel junction, as well as in SQUID experiments, are discussed. The dimerized quantum spin models studied in this thesis include double-layer and alternating chain Heisenberg antiferromagnets. To account for strong correlations between the S=1 elementary excitations (triplets) in the dimerized phase; the analytic Brueckner diagram approach based on a description of the excitations as triplets above a strong-coupling singlet ground state; has been applied. The quasiparticle spectrum is calculated by treating the excitations as a dilute Bose gas with infinite on-site repulsion. Analytical calculations of physical observables are in excellent agreement with numerical data.Results obtained for double layer antiferromagnet near the (zero temperature) quantum critical point coincide with those previously obtained within the nonlinear s model approach Additional singlet (S=0) and triplet (S=1) modes are found as two-particle bound states of the elementary triplets in the Heisenberg chain with frustration.

Doutoramento em Física
O modelo de Hubbard é um dos modelos mais simples para descrever o movimento e a interacção de electrões em sólidos. Tem sido largamente estudado pelas suas aplicações na descrição de condutores orgânicos e na procura de supercondutividade a cada vez mais altas temperaturas. O objectivo desta tese é contribuir para a melhor compreensão do comportamento do modelo de Hubbard a duas dimensões quando a geometria da rede é alterada, nomeadamente torcendo as condições de fronteira ou introduzindo frustração geométrica. Começa-se por fazer uma extensão do diagrama de fases magnéticas do modelo de Hubbard numa rede quadrada usando a aproximação de campo médio, introduzindo a possibilidade de modulação da densidade de spin, contrastando assim com estudos anteriores. Isto foi conseguido dividindo a rede quadrada em duas sub-redes, podendo as suas densidades de spin ser diferentes. Concluiu-se que, em algumas regiões do diagrama de fases, esta densidade de spin modulada permite ao sistema baixar a sua energia livre. Em segundo lugar, introduz-se uma variação da rede quadrada, a que chamamos rede helicoidal. Estas duas redes são equivalentes no limite termodinâmico, visto que apenas diferem nas condições de fronteira. É apresentado um Hamiltoniano efectivo que descreve as correcções de energia em primeira ordem devidas aos saltos transversais no limite de acoplamento forte (strong-coupling limit). Devido à introdução destes saltos, observa-se uma dinâmica de spins, mesmo no limite de interacção electrónica infinita (ou seja, sem as correcções de Heisenberg). É apresentada uma expressão analítica para a correcção energética no caso de uma lacuna e um spin invertido, bem como representações gráficas das correcções para vários spins invertidos, obtidas numericamente. Em terceiro lugar, apresenta-se uma unificação dos estados localizados de redes quadradas decoradas. Esta unificação é apresentada na forma de "regras de origami", que incluem dobrar e desdobrar estados localizados de Hamiltonianos sem interacções (tight-binding ). Mostra-se que os estados localizados das redes decoradas de Lieb, Mielke e Tasaki podem ser obtidos uns a partir dos outros aplicando estas regras. Seguidamente, dá-se ênfase às redes decoradas da classe de Lieb. Começa-se por estudar a evolução temporal dos seus estados localizados quando um campo magnético é aplicado lentamente e perpendicularmente ao plano da rede. Conclui-se que, em concordância com o teorema adiabático, o estado localizado mantém-se localizado desde que haja uma diferença energética finita entre a sua energia e o resto do espectro do Hamiltoniano. Além disto, mostra-se que a forma como o estado localizado evolui pode ser descrita por um Hamiltoniano mais simples, com apenas três níveis energéticos, cuja solução é análoga a um movimento de precessão clássico. Finalmente, introduz-se a interacção de Hubbard na rede de Lieb e, usando a aproximação de campo médio, obtém-se o diagrama de fases magnéticas desta rede, previamente inexistente na literatura. Conclui-se que, no caso de redes bipartidas com diferente número de átomos em cada sub-rede, a abordagem de campo médio tradicional não reproduz resultados correctos na situação de um electrão por sítio (half filling ). Posto isto, segue-se uma abordagem em campo médio mais complexa (Hartree-Fock generalizada), que permite que as sub-redes tenham diferentes magnetizações e densidades de carga. Com estas modificações, a nova abordagem de campo médio já reproduz correctamente os resultados exactos em half filling, dados pelo teorema de Lieb e pelo teorema da densidade uniforme.
The Hubbard model is one of the simplest models to describe the motion and interaction of electrons in solids. It has been widely studied due to its applications in the description of organic conductors and in the search for high-Tc superconductivity. The aim of this thesis is to contribute for the better understanding of the behavior of the two-dimensional Hubbard model when the geometry of the lattice is changed, namely by twisting the boundary conditions or introducing geometric frustration. We begin by extending the mean-field magnetic phase diagram of the Hubbard model in a square lattice, by adding the possibility of spin density modulation, in contrast with previous studies. This was done by considering a square lattice divided into two sublattices, which were allowed to have different spin densities. We found that, in some regions of the phase diagram, nonuniform spin density throughout the lattice leads to a lower free energy. Secondly, we introduce a variation of the square lattice, which we call the helicoidal lattice. This lattice and the square lattice are equivalent in the thermodynamic limit, as they differ only in the boundary conditions. We present an effective Hamiltonian that describes the first-order energy corrections due to transversal hoppings in the strong-coupling limit, and show that interesting spin dynamics arises, even without the Heisenberg correction, due to hole hoppings in the transversal direction. We present an analytic expression for the energy correction in the case of one hole and one inverted spin. The numerically-obtained corrections for higher number of inverted spins are also shown. Thirdly, we present a unifying picture for localized states of decorated square lattices. This unification is presented in the form of what we call the "origami rules", which include folding and unfolding localized states of tight-binding Hamiltonians. We show that localized states of decorated lattices of the Lieb, Mielke and Tasaki classes can be obtained from each other by applying these rules. We then focus on the decorated lattices of the Lieb class. We begin by studying the time evolution of its localized states when a magnetic field is slowly applied perpendicularly to the plane of the lattice. We find that, as stated by the adiabatic theorem, the localized eigenstate remains localized as long as there is an energy gap between its energy and the rest of the Hamiltonian spectrum. Furthermore, we show that the way that the localized state evolves can be described by a simple three-level toy Hamiltonian, whose solution is analogous to a classical precession motion. Lastly, we introduce the Hubbard interaction in the Lieb lattice and, using the mean-field approximation, obtain the magnetic phase diagram of this lattice, previously absent from the literature. We find that, in the case of bipartite lattices with a different number of atoms on each sublattice, the traditional mean-field approach fails to yield correct results at half-filling. Therefore, we follow a more complex (generalized Hartree-Fock) mean-field approach, which allows the sublattices to have different magnetizations and charge densities. Under these new considerations, the mean-field approach correctly reproduces the exact results at half-filling, given by Lieb’s theorem and the uniform density theorem.

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.

A major area of interest in condensed matter physics over the past decades has been the emergence of new states of matter from strongly correlated electron systems. A few limited examples would be the emergence of unconventional superconductivity in the high-T$_c$ superconductors and heavy-fermion systems, the appearance of the skyrmion magnetic vortex state in MnSi and magnetically mediated superconductivity in UGe$_2$. While detailed studies of many of the emergent phases have been made, there are still many gaps in understanding of the underlying states and mechanisms that allow them to form. This work aims to add to knowledge of the basic physics behind such states, and the changes within them as they are tuned to approach new phases. The cubic perovskite material SrTiO$_3$ has been studied for many decades and is well-documented to be an incipient ferroelectric, theorised to exist in the absence of any tuning in the proximity of a ferroelectric quantum critical point. This work presents the first high-precision dielectric measurements under hydrostatic pressure carried out on a quantum critical ferroelectric, leading to a full pressure-temperature phase diagram for SrTiO$_3$. The influence of quantum critical fluctuations is seen to diminish as the system is tuned away from the quantum critical point and a novel low temperature phase is shown to be emergent from it. The Néel Temperature of the two-dimensional antiferromagnet FePS$_3$ was found to increase linearly with applied hydrostatic pressure. Evidence of an insulator-metal transition is also presented, and an unexplained upturn in the resistivity at low temperatures in the metallic phase.

pintronics is a rapidly developing field in solid state physics based on the quantum property of spin angular momentum. It has the potential to offer a new generation of electronic devices exploiting spin properties instead of, or in addition to, charge. Such quantum-based devices are expected to demonstrate significant advantages over traditional charge based electronics with a promise of faster data processing speeds and lower power consumption. One of the most widely studied spintronic materials is the dilute magnetic semiconductor gallium manganese arsenide ((Ga,Mn)As). This continues to be a valuable test ground for spintronics applications due to its close relation to the traditional, and well-characterised, semiconductor GaAs, and its relatively high Curie temperature despite values remaining some way off the much sought-after room temperature. The two primary focuses of this thesis are phase-coherent transport and critical phenomena, both of which whilst well understood in metals have seen limited work in (Ga,Mn)As. Critical behaviour in particular has not been extensively studied despite continued disputes over theoretical models and resistance peak positions relative to Curie temperature. Studies of both these areas are presented within this thesis split over four main chapters. The first of these chapters acts as a general introduction to spintronics, and includes both a brief history of the subject, and a theoretical overview focused on the structure and properties of (Ga,Mn)As. This introductory chapter also includes an in-depth review of nanofabrication including typical processing techniques and their applications to the study of spintronics in Nottingham. The second chapter presents a comprehensive study of critical phenomena within (Ga,Mn)As, showing how the behaviour of magnetic properties close to Tc are strongly correlated between samples. Both magnetisation and susceptibility are found to demonstrate behaviour very close to that predicted by the Heisenberg model; a result in strong agreement with theoretical work. The study of critical behaviour is carried over into the third chapter with transport measurements showing that resistance data can be directly used to accurately measure sample Curie temperature by finding the peak in the derivative deltaR/deltaT. This potentially offers an alternate approach to calculating Tc that is faster and cgeaper than the more conventional magnetometry or Arrott plot methods. Analysis is also carried out on the resistance peak which is expected to follow the critical behaviour of the specific heat. The final experimental chapter focuses on the development of nanoring fabrication processes in (Ga,Mn)As including the difficulties associated with fabricating nanoscale structures, the testing performed to achieve high quality, reproducible structures, and the final adopted recipe. This chapter then details early test measurements on these devices including an initial study on the first structures within a dilution refrigerator, and prelimenary work on a second improved batch at 4He temperatures. This work will act as a foundation for the future aim of conducting a full phase-coherence phenomena study in highly optimised (Ga,Mn)As samples grown in Nottingham.

This thesis describes a theoretical and numerical study of quantum transport and optical effects through an array of self-assembled InAs quantum dots grown in the intrinsic region of a GaAs p-i-n junction. We present a numerical simulation of this system and compare the generated transport and elecroluminescence results to recent experimental data. The simulation first calculates the quantum tunnelling, excitonic recombination, and relaxation rates within the dots, and then uses a stochastic model to simulate carriers entering and leaving the array. We highlight a number of features within the simulation, which shed light on similar features seen in experimental data. In particular, we demonstrate the importance of including the effects of the Coulomb interactions between the carriers, as this is shown be necessary for the simulated and experimental results to match closely. We also investigate a model of Auger processes which is shown to produce up-conversion luminescence, and study the effect of varying the location of the array within the intrinsic region. Additionally we present a master equation approach, which we use to describe a correlated tunnelling regime, in which the Coulomb interaction between an electron and a hole forces them to tunnel alternately onto a single dot before recombination. We produce current and photon noise predictions for both tunnelling and recombination limited regimes. We also investigate this phenomena for a pair of interacting dots, and find a number of two dot configurations which are able to produce current and electroluminescence. We present current and photo-current rate predictions for each case, and associated current and photon noise results.

Molecular materials have raised much interest in the last decades in the quest for new multifunctional devices. Among the multiple properties that those materials may present, one of the most typical is magnetism, which arises from the presence of unpaired electrons in the molecules that constitute the three-dimensional crystal. Magnetism has a macroscopic observable, the magnetic susceptibility (Ji), which is usually rationalized in terms of a set of JAB magnetic interactions between pairs of molecules. However, any experimental technique allows for such direct correspondence and, thus, the experimental interpretation of the magnetic properties usually requires further analysis from the point of view of computational chemistry. Consequently, the present PhD thesis is a contribution to the computational modeling of molecule-based magnetic materials. Specifically, we describe how the tools of computational chemistry may be used in order to study those materials from different perspectives. With this aim in mind, we have applied computational chemistry techniques to rationalize the magnetic properties of several systems of interest, ranging from metal-organic compounds, based on Cu(II), to pure organic radicals based on the DTA and Benzotriazinyl building blocks, and including compounds based on the metal-radical synthetic approach, and also spin crossover materials based on Fe(II). Along the thesis we have demonstrated that computational chemistry is a helpful discipline, capable to aid in the interpretation of experimental results and in the prediction of interesting properties, especially when working in close collaboration with experimentalists. In particular, the First Principles Bottom-Up (FPBU) procedure, extensively developed in our group, is a useful tool to rationalize the magnetic properties of any molecular magnetic material. To this purpose, the magnetic topology (i.e. the network of JAB within the crystal) is the key element. Regarding the magnetic topology, we have also demonstrated that it can be more intricate and complex than expected, and that it cannot be directly inferred from the coordination pattern of the molecule-based material. Therefore, the experimental assignation of the magnetic topology, by means of a fitting procedure, must be taken with caution. About the JAB values, we have proved that they depend on temperature, and that this dependence may be especially important when working with organic radicals. On this class of materials, we have analyzed how the JAB values evolve with time, and seen that this evolution may involve huge fluctuations of their magnitude as a consequence of the thermal motion at finite temperatures. Interestingly, we demonstrate herein that, when the JAB values depend non-linearly with the thermal vibrations of a material, the standard static perspective of magnetism is not valid to fully understand their magnetic properties, and that it is then required to adopt a dynamic perspective. Regarding the computational modeling of JAB values, we have seen that the combination of UB3LYP and the Broken-Symmetry approach yields JAB values, when transformed into the macroscopic observables, are in good agreement with experiment. In fact, we have demonstrated that, in order to predict the strength of a given JAB value, small distortions in the crystal structure can induce large variations, which may be much more important than the intrinsic error associated with the theoretical method employed. We have also observed that the counterions and diamagnetic ligands may have an important effect in defining the magnetic properties of a system. Overall, we have demonstrated that the magnetic topology and, thus, the macroscopic magnetic properties of a given material, cannot be understood without the proper knowledge of their crystal structure.
Els materials moleculars han despertat molt d'interès en les últimes dècades degut a la seva possible aplicació en nous dispositius multifuncionals. Entre les diferents propietats que aquests materials poden presentar, una de les més típiques és el magnetisme, el qual sorgeix de la presència d’electrons desaparellats en les molècules que constitueixen el cristall tridimensional. El magnetisme té un observable macroscòpic, la susceptibilitat magnètica (Ji), que sol ser racionalitzada en termes microscòpics mitjançant el conjunt d'interaccions magnètiques JAB entre determinats parells de molècules. No obstant això, cap tècnica experimental permet aquesta correspondència directa i, per tant, la interpretació experimental de les propietats magnètiques sol requerir d’un posterior anàlisi des del punt de vista de la química computacional. La present tesi doctoral pretén doncs contribuir en el camp del magnetisme molecular i, més concretament, en com es poden utilitzar les eines de la química computacional per a modelitzar materials magnètics moleculars des de diferents perspectives. Amb aquest objectiu en ment, s’han racionalitzat les propietats magnètiques de diversos sistemes d'interès, que van des de compostos metal•lorgànics basats en ions de Cu(II) o de Co(II), radicals orgànics purs, compostos basats en l’estratègia sintètica de “metall-radical”, i finalment també materials de spin crossover basats en Fe(II). Al llarg de la tesi s'ha demostrat que la química computacional és una disciplina útil, capaç d'ajudar a la interpretació dels resultats experimentals i en la predicció de propietats interessants, especialment quan es treballa en estreta col•laboració amb els experimentadors. En particular, el procediment de primers principis Bottom-Up (FPBU, per les seves sigles en anglès), desenvolupat àmpliament en el nostre grup, és una eina útil per racionalitzar les propietats magnètiques de qualsevol material magnètic molecular. Per a aquest propòsit, la topologia magnètica (és a dir, la xarxa de JAB dins del cristall) és l'element clau. A més, hem analitzat diversos factors que afecten aquesta topologia magnètica, com els contraions, els radicals diamagnètics o l’efecte de la temperatura, mitjançant el la seva manifestació en les vibracions del cristall i en la contracció (expansió) que pateix al refredar-se (escalfar-se).

This thesis describes an experimental investigation of the resonant injection of carriers into self-assembled indium arsenide (InAs) quantum dots incorporated in the intrinsic region of gallium arsenide (GaAs) p-i-n resonant tunneling diodes, and of the resulting electroluminescence spectrum associated with carrier recombination in the quantum dots, wetting layer and GaAs matrix. A series of devices of different designs have been measured and it is shown that bipolar resonant injection, i.e. resonant injection of both electrons andholes, into the zero-dimensional states provided by the InAs quantum dots is possible. It is shown that bias-tunable tunneling of carriers into the dots provides a means of controlling injection and light emission from a small number of individual dots within a large ensemble. Magnetotunneling spectroscopy is used to investigate the possibility that fluctuations in the potential profile of the GaAs emitter layer play a significant role in the carrier dynamics of such devices. We also show that the extent of carrier energy relaxation prior to recombination can be controlled by tailoring the morphology of the quantum dot layer. Additionally, a study into the phenomenon of low-temperature up-conversion electroluminescence (UCEL) is presented. Injection of carriers into the quantum dot states at an applied bias well below the GaAs flat-band condition results in near-band-edge GaAs electroluminescence, i.e., emission of photons with energies much larger than that supplied by the applied bias and the thermal energy. The origin of this UCEL is discussed and is attributed to carrier excitation resulting from (non-radiative) Auger recombination of electron-hole pairs in the quantum dot ground states.

An investigation of the electronic structure of some transition metal clusters comprising anti-ferromagnetically coupled, heterometallic arrays of eight metal ions that are wheel-shaped, is reported. The compounds were synthesized and provided by Dr. Grigore Timco of The University of Manchester and are formulated by their metal content as Cr7M, where M = a divalent 3d metal. Two families of wheels are the subject of this research, defined ‘green’ and ‘purple’ from their physical appearance. Within each family, the compounds are all isostructural. From simulation using a single Hamiltonian for Cr7M-purple compounds, where M = Zn, Mn, or Ni, it is shown that with only two exchange parameters, one JCr-Cr and one JCr-M, data from bulk magnetization, neutron scattering, Electron Paramagnetic Resonance (EPR) spectroscopy at multiple frequencies and specific heat measurements can be modelled and that there is transferability of parameters. Preliminary attempts to measure electron spin relaxation times for two of the purple wheels have shown values of T1 and T2 that are comparable with those of the more extensively studied green wheels and hence further studies in this area are warranted. Variable temperature Q- and W-band EPR spectra for a series of nine heterodimers comprising one green and one purple wheel, M=Zn, Mn or Ni in each case, are reported. For Cr7Zn-purple there is no magnetic exchange detected, whereas weak and quantifiable exchange is required to interpret the spectra from the other six dimers. EPR studies of three trimers of the form purple-green-purple are reported and the presence of magnetic exchange is identified by comparison with the spectra of the component single and double wheel compounds, although this is not quantified because of the numerical size of the simulations that are required. The process of comparing simulated to experimental spectra is a complex problem and one which is central to the work reported in this thesis. The problem of fitting has been investigated and two novel solutions, one based upon pixel mapping and the other based on wavelet transformation are proposed.

In this dissertation, we examine quantum ferromagnets and determine various effects of the magnetic Goldstone modes or "magnons'' in these systems. Firstly, we calculate the magnon contribution to the transport relaxation rate of conduction electrons in metallic ferromagnets and find that at asymptotically low temperatures, the contribution behaves as T^2 exp(-T_0/T) and not as T^2 predicted previously. To perform these calculations, we derive and use a very general effective theory for metallic ferromagnets. This activation barrier-like behavior is due to the fact that spin waves only couple electrons from different Stoner subbands that arise from the splitting of the conduction band in presence of a nonzero magnetization. The T^2 behavior is found to be valid only in a pre-asymptotic temperature window. The temperature scale T_0 is the energy of the least energetic ferromagnon that couples electrons of different spins. Second, we discuss magnon-induced long-range correlation functions in quantum magnets. In the ordered phases of both classical ferromagnets and antiferromagnets, the long-range correlations induced by the magnons lead to a singular wavenumber dependence of the longitudinal order-parameter susceptibility in spatial dimensions 2