Apresentamos dois modelos para o elétron na eletrodinâmica clássica que incorporam alguns efeitos da eletrodinâmica quântica. No primeiro modelo, o elétron é tratado como uma partícula extensa como conseqüência das oscilações de alta-freqüência (Zitterbewegung) que sua carga elétrica realiza. Mostramos que este modelo prevê corretamente a magnitude do spin do elétron e lhe atribui o mesmo fator giromagnético previsto pela equação de Dirac sem correções radiativas. Neste modelo, a auto-energia do elétron diverge logaritmicamente como resultado da distribuição extensa de sua carga elétrica. No segundo modelo, a criação de pares virtuais em torno do elétron é levada em conta por uma generalização da lagrangeana do campo eletromagnético que respeita as simetrias da eletrodinâmica clássica. Esta generalização altera a interação entre o elétron e o campo eletromagnético em pequenas distâncias e permite que a auto-força de uma partícula puntiforme seja determinada de modo consistente. Mostramos que as soluções da equação de movimento resultante não apresentam auto-aceleração nem pré-aceleração, sendo consistentes com a causalidade. / We present two models for the electron in classical electrodynamics, which include some effects from quantum electrodynamics. In the first model, the electron is treated as an extended particle owing to the high-frequency oscillations (Zitterbewegung) of its electrical charge. We show that this model predicts correctly the magnitude of the electron spin and it gives the electron the same gyromagnetic factor as predicted by Dirac equation without radiative corrections. In this model, the electron self-energy has a logarithmic divergence due to the extended distribution of its electric charge. In the second model, virtual pair creation around the electron is taken into account by a generalization of the lagrangian for the electromagnetic field that preserves the symmetries of classical electrodynamics. This generalization changes the interaction of the electron with the electromagnetic field at small distances and allows us to evaluate the self-force of a point particle in a consistent way. We show that the solutions of the derived equation of motion do not exhibit self-acceleration nor pre-acceleration, being consistent with causality.

Orientador: Pascoal José Giglio Pagliuso / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T11:57:27Z (GMT). No. of bitstreams: 1 Souza_JeanCarlo_M.pdf: 4438731 bytes, checksum: aaba7a375b2b45b638619e944111c41b (MD5) Previous issue date: 2017 / Resumo: A ideia de topologia na Física da Matéria da Condensada, apesar de ter surgido com o efeito Hall quântico inteiro, só voltou a ser explorada recentemente na busca de novas fases da matéria depois do surgimento dos Isolantes Topológicos (ITs) 2D. Após a previsão teórica, e a descoberta experimental, foi proposto que esta nova fase poderia ser generalizada para sistemas 3D, em que o volume do material seria isolante com estados metálicos de superfície que possuiriam canais de spin polarizados. Apesar de diversos experimentos e o surgimento de outras fases topológicas da matéria subsequentes, ainda há dúvidas sobre a natureza dos ITs 3D. Os efeitos topológicos mais claros ainda não foram observados de forma inequívoca e reprodutível experimentalmente e ainda seria de extrema valia encontrar técnicas experimentais que possam complementar os mais discutidos experimentos de ARPES. Nesta dissertação foram estudadas duas famílias distintas de materiais propostas como possíveis ITs 3D: os binários Bi2Se3 e Sb2Te3 e o half-Heusler YPdBi. Utilizando a técnica de auto-fluxo e a fusão estequiométrica, os sistemas foram sintetizados dopados com os terras-rara Gd3+, Nd3+ e Er3+ para realizar estudos de ressonância de spin eletrônico (RSE) e do papel dos efeitos de campo cristalino (CEF) - no caso do half-Heusler. Para o ternário YPdBi foram feitos dois estudos. Na família dos half-Heuslers, a ordem topológica surge da relação entre o acoplamento spin-órbita e a hibridização, que está ligada com a mudança do parâmetro de rede, então os efeitos de CEF poderiam estar refletindo a transição entre a trivialidade e a não-trivialidade. A partir das medidas de susceptibilidade magnética em função da temperatura das amostras dopadas com Nd3+ e Er3+ combinadas com os estudos de RSE, foi possível extrair os parâmetros de campo cristalino (CFP) de quarta e sexta ordem. Comparando esses dados com resultados anteriores para o material, supostamente, não-trivial YPtBi, observou-se uma mudança sistemática no sinal dos CFP. Resultados prévios para as amostras de YPtBi dopadas com Nd3+ mostram uma evolução não usual para uma forma de linha difusiva com a potência de micro-onda. Neste trabalho também foi realizado um estudo da forma de linha em função da potência. Apenas a ressonância do Nd3+ para os monocristais de 10% de Nd em YPdBi mostrou uma forma de linha difusiva que evolui com a potência da micro-onda. No caso dos binários Bi2Se3 e Sb2Te3, o objetivo era otimizar a rampa de tratamento térmico para obter monocristais melhores que poderiam permitir a observação de um espectro totalmente resolvido do Gd3+. Após mudanças no crescimento dos monocristais, o espectro totalmente resolvido foi obtido para as amostras de Bi2Se3. No caso do Sb2Te3 apenas uma linha central com a estrutura fina colapsada foi observada. Acompanhando o deslocamento g e a evolução da largura de linha dH da RSE do Gd3+ com a temperatura, o comportamento negativo do deslocamento g para toda a faixa de temperatura indica que elétrons do tipo p são os grandes responsáveis pela formação da superfície de Fermi residual destes sistemas. Um aumento no coeficiente angular de dH em função da temperatura, a taxa Korringa b, foi observado em baixas temperaturas, logo diferentes concentrações de Gd3+ foram utilizadas para estudar este comportamento. Novamente observou-se um comportamento anômalo em baixas temperaturas, o que poderia estar relacionado com a evolução dos CFP com a temperatura. Todos esses resultados foram discutidos levando-se em conta a possibilidade de existência de topologia não-trivial na estrutura eletrônica desses materiais, com foco particular na relação da interação spin-órbita e os efeitos de campo cristalino com a manifestação da topologia não trivial nesses sistemas / Abstract: The idea of topological systems in Condensed Matter Physics, although already explored in the Quantum Hall Effect, has recently become a topic of intense scientific investigation. In particular, great efforts have been dedicated to the search for new quantum phases since the proposal of the Topological Insulators (TIs) in 2D. After the theoretical prediction and the experimental discovery of the TIs in the 2D case, the existence of the Quantum Hall Spin Effect in 3D, 3D TIs, was proposed, where an insulator bulk and metallic surface states with spin polarized channels could be experimentally realized. Although many experiments have been performed, and some groups claimed the direct observation of such new topological phases, there is still a lot of controversy about the nature of the 3D TIs and about the actual microscopic origin of the metallic states on the surface of the studied materials. Other signatures of the topological phases have not been unambiguously and repeatedly measured yet and there is an obvious lack of a supplementary lab technique to be compared to the most used technique to probe these states, which is ARPES. In this work we have studied two different classes of 3D TIs: the binaries Bi2Se3 and Sb2Te3 and the half-Heusler YPdBi. We have been able to grow single crystals of these materials pure and rare-earth doped with Gd3+, Nd3+ and Er3+ using the self-flux technique and the stoichiometric melting. The aim was to use these crystals to study Electron Spin Resonance (ESR) as a potential probe to investigate the existence of the metallic surface states and to explore the possible of the crystalline electrical field (CEF) effects on the formation of the non-trivial electronic structure of these materials. Regarding the YPdBi, our ESR and magnetization studies have revealed that, in the half-Heusler family, the topological order emerges from the interplay between spin-orbit coupling and the hybridization, which is connected with the changes on the lattice parameter. Thus, the CEF effects could reflect the transition from trivial to nontrivial topology. From the magnetic susceptibility data as a function of temperature from the Nd3+ and Er3+ doped samples combined with the ESR studies, it was possible to extract the fourth and sixth order crystal field parameters (CFP). Comparing our data with the previous results from YPtBi, which is a putative non-trivial material, a systematic change in the sign of the CFP was observed. Previous results with the YPtBi Nd-doped samples show an unusual evolution of the Nd3+ ESR line to a diusive-like line shape as a function of the microwave power. In this work we have performed a similar study of the Nd3+ ESR line shape as a function of the microwave power. Only for the single crystal of 10% Nd in YPdBi resonance shows a diffusive-like line shape that evolves with the microwave power. In the case of the binaries Bi2Se3 e Sb2Te3, the aim of this work was to optimize the heat treatment used in previous works of our group to obtain better single crystals that could allow the observation of the full resolved spectra from Gd3+. After many changes in the single crystal growth method, we were able to observe fully resolved Gd3+ ESR spectra in the Bi2Se3 samples. Regarding the Sb2Te3 single crystals, only a single Gd3+ Dysonian ESR line was observed. Following the Gd3+ ESR dg and dH as a function of temperature, the observed negative behavior of dg, in the whole temperature range studied, indicates that p-type electrons are the main source for the formation of the small the Fermi surface of these materials. An increase of the angular coefficient of dH as a function of temperature, the Korringa rate b, at low temperatures was observed and different concentrations of Gd3+ were required to investigate this anomaly. Again this anomalous behavior at low temperatures was observed for the all Gd-doped samples, which could be related to an evolution of CFP with temperature. We discuss our results taking into account the existence of non-trivial topological states in our samples and the role of spin-orbit and CEF effects might have in the formation of such states / Mestrado / Física / Mestre em Física / 132653/2015-0 / CNPQ / CAPES / FAPESP

Since the last few decades frustrated spin systems have attracted much interest. These studies are motivated by the rich variety of their unusual magnetic properties and potential applications. In this thesis, excitation spectra of the weakly coupled dimer system Ba3Cr2O8, the spin-1/2 chain material with distorted diamond structure Cu3(CO3)2(OH)2 (natural mineral azurite), and the quasi-twodimensional antiferromagnet with triangle spin structure Cs2CuBr4 have been studied by means of high-field electron spin resonance. Two pairs of gapped modes corresponding to transitions from a spin-singlet ground state to the first excited triplet state with zero-field energy gaps, of 19.1 and 27 K were observed in Ba3Cr2O8. The observation of ground-state excitations clearly indicates the presence of a non-secular term allowing these transitions. Our findings are of crucial importance for the interpretation of the field-induced transitions in this material (with critical fields Hc1 = 12.5 T and Hc2 = 23.6 T) in terms of the magnon Bose-Einstein condensation. The natural mineral azurite, Cu3(CO3)2(OH)2, has been studied in magnetic fields up to 50 T, revealing several modes not observed previously. Based on the obtained data, all three critical fields were identified. A substantial zero-field energy gap, Δ = 9.6 K, has been observed in Cs2CuBr4 above the ordering temperature. It is argued that contrary to the case for the isostructural Cs2CuCl4, the size of the gap can not be explained solely by the uniform Dzyaloshinskii-Moriya interaction, but it is rather the result of the geometrical frustration stabilizing the spin-disordered state in Cs2CuBr4 in the close vicinity of the quantum phase transition between a spiral magnetically ordered state and a 2D quantum spin liquid.

The idea of miniaturizing devices down to the nanoscale where quantum ffeffects become relevant demands a detailed understanding of the interplay between classical and quantum properties. Therefore, characterization of newly produced nanoscale materials is a very important part of the research in this fifield. Studying structural and magnetic properties of nano- and molecular magnets and the interplay between these properties reveals new interesting effects and suggests ways to control and optimize the respective material. The main task of this thesis is investigating the magnetic properties of molecular magnetic clusters and magnetic nanoparticles recently synthesized by several collaborating groups. This thesis contains two main parts focusing on each of these two topics. In the first part the fundamental studies on novel metal-organic molecular complexes is presented. Several newly synthesized magnetic complexes were investigated by means of different experimental techniques, in particular, by electron spin resonance spectroscopy. Chapter 1 in this part provides the theoretical background which is necessary for the interpretation of the effects observed in single molecular magnetic clusters. Chapter 2 introduces the experimental techniques applied in the studies. Chapter 3 contains the experimental results and their discussion. Firstly, the magnetic properties of two Ni-based complexes are presented. The complexes possess different ligand structures and arrangements of the Ni-ions in the metal cores. This difffference dramatically affffects the magnetic properties of the molecules such as the ground state and the magnetic anisotropy. Secondly, a detailed study of the Mn2Ni3 single molecular magnet is described. The complex has a bistable magnetic ground state with a high spin value of S = 7 and shows slow relaxation and quantum tunnelling of the magnetization. The third section concentrates on a Mn(III)-based single chain magnet showing ferromagnetic ordering of the Mn-spins and a strong magnetic anisotropy which leads to a hysteretic behavior of the magnetization. The last section describes a detailed study of the static and dynamic magnetic properties of three Mn-dimer molecular complexes by means of static magnetization, continuous wave and pulse electron spin resonance measurements. The results indicate a systematic dependence of the magnetic properties on the nearest ligands surrounding of the Mn ions. The second part of the thesis addresses magnetic properties of nano-scaled magnets such as carbon nanotubes fifilled with magnetic materials and carbon-coated magnetic nanoparticles. These studies are eventually aiming at the possible application of these particles as agents for magnetic hyperthermia. In this respect, their behavior in static and alternating magnetic fifields is investigated and discussed. Moreover, two possible hyperthermia applications of the studied magnetic nanoparticles are presented, which are the combination of a hyperthermia agents with an anticancer drug and the possibility to spatially localize the hyperthermia effffect by applying specially designed static magnetic fifields.

Die Elektronenspinresonanz (ESR) untersucht die im quasistatischen Magnetfeld resonante Absorption eines an die Probe angelegten Mikrowellenmagnetfeldes. Es wurde das System Yb1-w A1-w (Rh1-x Cox)2 (Si1-y Gey) 2 mit A=La, bzw. Lu, sowie das System YbIr2Si2 mittels ESR untersucht. Unter Kondo-Wechselwirkung vieler Leitungselektronen mit einem lokalen 4f-Moment des Kondo-Ions bildet sich ein nicht-magnetisches Grundzustands-Singlett, was zur Abschirmung des magnetischen Moments führt. YbRh2Si2 ist das erste Schwere-Fermionen-System mit Kondo-Ionen, das ohne Dotierung zusätzlicher ESR-Sonden ein ESR-Signal unterhalb der Kondo-Temperatur aufweist. Es zeigt sich, dass das ESR-Signal nicht mittels gängiger ESR-Theorien konsistent beschrieben werden kann. Die Messungen, die im Rahmen dieser Arbeit angestellt wurden, flossen in die Entwicklung von weiterführenden Theorien (z.B. [1], [2]) ein. Die Temperaturabhängigkeit des ESR-g-Faktors konnte damit erfolgreich beschrieben werden, womit erstmals der Nachweis einer Kondo-Wechselwirkung in Kondo-Gitter-Systemen mittels ESR gelang. Ferner konnte die Bedeutung von ferromagnetischen Fluktuationen für eine kleine, beobachtbare Linienbreite beschrieben werden. Der ESR-Methode ist somit die Kondo-Spindynamik direkt zugänglich. Dieser Zugang ist neu und einzigartig, denn andere Methoden (NMR, inelastische Neutronenstreuung) charakterisieren die Kondo-Spindynamik auf indirekte Weise. [1] P. Wölfle und E. Abrahams. Phenomenology of esr in heavy-fermion systems: Fermi-liquid und nicht-fermi-liquid regimes Phys. Rev. B, 80(23): 235112, 2009. [2] B. I. Kochelaev, S. I. Belov, A. M. Skvortsova, A. S. Kutusov, J. Sichelschmidt, J. Wykhoff, C. Geibel und F. Steglich. Why could electron spin resonance be observed in a heavy fermion kondo lattice? Eur. Phys. J. B, 72(4): 485, 2009.

Abstract This thesis reports simulations of direct observables in electron and nuclear spin relaxation experiments in an example paramagnetic system, as well as polarization transfer occurring in a spin-exchange optical pumping (SEOP) experiment. Studies of paramagnetic relaxation are important, e.g., in the development of agents used for enhanced contrast in magnetic resonance imaging. SEOP is used to produce hyperpolarized noble gases, which are then used to, e.g., enhance sensitivity in structural studies of matter with nuclear magnetic resonance. Presently the theory, available software and hardware for such computational modeling have reached a state in which quantitative reproduction of the experimentally observed magnetization decay is possible from first principles. The present multiscale computations are carried out from first principles combining molecular dynamics simulations of atomistic motion and quantum-chemical electronic structure calculations of the spin interaction parameters that enter the effective spin Hamiltonian. A time series of the spin Hamiltonian is then explicitly used to propagate spin dynamics in the system, and dynamical time constants of the magnetization are obtained through ensemble averaging. The complete decay of electron spin magnetization could be followed directly within the duration of the simulation, whereas the nuclear spin relaxation rates were extracted using Kubo’s theory regarding generalized cumulant expansion and stochastic processes. The extracted electron and nuclear spin relaxation rates for the chosen prototypic system, the aqueous solution of Ni²⁺, are in quantitative and semi-quantitative agreement, respectively, with the available experimental results. The simulations of polarization transfer corroborate the empirical observations on the importance of van der Waals complexes and binary collisions in the spin-exchange process. Long van der Waals complexes represent the overwhelmingly most significant kind of individual events, but the short binary collisions can also give a relatively important contribution due to their vast abundance. This thesis represents a first study in which first principles-calculated trajectories of individual events could be followed. The simulations reported in this thesis were run without any empirical parametrization and thus represent a significant step in first-principles computational modeling of magnetization dynamics.

Orientador: Prof. Dr. Wendel Andrade Alves / Tese (doutorado) - Universidade Federal do ABC. Programa de Pós-Graduação em Ciência e Tecnologia/Química, 2016. / Nanotubos de titanato tem atraído muita atenção devido a suas propriedades únicas, que permitem sua aplicação em catálise, fotocatálise, e no desenvolvimento de dispositivos de conversão de energia. No entanto, esses materiais são capazes de absorver somente radiação UV, o que torna necessária sua sensibilização frente à radiação visível que pode ser feito através da dopagem ou sensibilização com corantes. Neste trabalho, nanotubos de titanato foram preparados através da síntese hidrotérmica alcalina e dopados usando um método de troca iônica seguida por uma etapa de calcinação a 200 ºC e 400 ºC, resultando em duas séries de catalisadores: nanotubos de titanato dopados com nitrogênio (NTiNTs) e nanotubos de dióxido de titânio dopados com nitrogênio (NTiO2NTs), respectivamente. A caracterização destes materiais revelou que a temperatura de calcinação afeta a intensidade de cor, área superficial, energia band gap e natureza da espécie de nitrogênio dopante. Os catalisadores NTiO2NTs reúnem as propriedades que os qualificam como melhores fotocatalisadores, sendo capazes de degradar de 1,8% (m/m, massa de corante degradado por 100g de catalisador) a 2,9%, enquanto os NTiNTs foram capazes de degradar somente de 0,17%mg mg-1 a 0,60%. Os catalisadores NTiNTs e NTiO2NTs também foram sensibilizados com ftalocianina de cobre(II) tetracarboxilada. Observou-se que a sensibilização não afeta a forma nem a estrutura cristalina dos nanotubos, no entanto, ela promove alterações nas propriedades superficiais levando a interações diferenciadas entre os tubos. Esses materiais foram aplicados na degradação de rodamina B através de mecanismos de fotocatálise e catálise mediada por H2O2. Observou-se que os catalisadores sensibilizados apresentam eficiência fotocatalítica cerca de 50% menor do que os materiais não sensibilizados. No caso da catálise mediada por H2O2 a sensibilização aumenta a atividade catalítica, podendo atingir 100% de eficiência. Por fim, foram desenvolvidos novos eletrodos multi-hierárquicos baseados em filmes de nanobastões de óxido de zinco (ZnONR) decorados com nanotubos de titanato, utilizando glicina como uma ponte para promover o aumento da interação entre as estruturas. Estes eletrodos foram aplicados como fotoanodos no desproporcionamento fotoeletroquímica da água, gerando O2 e H2. Os resultados mostraram que a heterojunção dos dois óxidos metálicos leva a um aumento da eficiência fotoeletroquímica. Desse modo, os eletrodos multihierárquicos são capazes de produzir correntes de geração de O2 de 0,90 mA cm-2 (a 1,23 V vs ERHE), enquanto os eletrodos de ZnONR puros produzem 0,45 mA cm-2. O potencial de evolução de O2 também diminui de 0,8 V (vs ERHE) para eletrodos de TiNTs para 0 V no caso dos eletrodos multi-hierárquicos. / Titanate nanotubes have attracted much attention due do their unique properties which allow their application in catalysis, photocatalysis and energy conversion devices development. However, this material is able to absorb only UV radiation making necessary its sensibilization toward visible radiation that can be done through doping or dye sensibilization. In this work, titanate nanotubes were prepared through alkaline hydrothermal synthesis and doped using an ion exchange methodology followed by a calcination step at 200 ºC and 400ºC, resulting in two series of catalysts: nitrogen doped titanate nanotubes (NTiNTs) and nitrogen doped titanium dioxide nanotubes (NTiO2NTs), respectively. The characterization of these materials revealed that the calcination temperature affects color intensity, surface area, band gap energy and nature of doping nitrogen species. The NTiO2NTs catalysts gather the properties that qualify them as better photocatalysts, being capable of degrading from 1,8% (m/m, degraded dye mass by 100 g of catalyst) to 2,9%, whereas the NTiNTs are capable of degrading only 0,17% to 0,60%. The catalysts NTiNTs and NTiO2NTs were also sensitized with tetracarboxylate cooper(II) phthalocyanine. It has been observed that the sensibilization does not affect the morphology or crystalline structure of the nanotubes; however, it promotes changes on the surface properties leading to differentiated interactions between the tubes. These materials were applied on rhodamine B degradation through mechanisms of photocatalysis and catalysis mediated by H2O2. It was observed that the sensibilized catalysts exhibit photocatalytic efficiency of about 50% lower than nonsenbilized materials. In the case of catalysis mediated by H2O2 the sensibilization increases catalytic activity, which can reach 100% of efficiency. Finally, new multihierarchical electrodes were developed, based on zinc oxide nanorods (ZnONR) films decorated with titanate nanotubes, using glycine as a bridge to promote the increasing of the interaction between the structures. These electrodes were applied as photoanodes for photoelectrochemical water splitting, producing O2 e H2. The results show that the heterojunction of the two metal oxides leads to an increasing of the photoelectrochemical efficiency. Thus, the multi-hierarchical electrodes are capable of producing O2 evolution currents of 0.90 mA cm-2 (at 1.23 V vs ERHE), whereas the pure ZnONR electrodes produce 0.45 mA cm-2. The O2 evolution potential also decreases from 0.8 V (vs ERHE) for TiNTs electrodes to 0V for the multi-hierarchical electrodes.

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