Neste trabalho estudamos modelos teóricos que descrevem sistemas eletrônicos fortemente correlacionados, em especial o modelo t-J, e suas aplicações a compostos de óxidos de cobre, notadamente os compostos que apresentam supercondutividade de alta temperatura crítica e o composto Sr2CuO2Cl2. No primeiro capítulo do trabalho, fazemos uma exposição de três modelos que envolvem o tratamento das interações elétron-elétron, que são os modelos de Hubbard de uma banda, o modelo de Heisenberg e o modelo t-J. Na dedução deste último fazemos uma expansão canônica do hamiltoniano de Hubbard, no limite de acoplamento forte, levando-nos a obter um novo hamiltoniano que pode ser utilizado para descrever um sistema antiferromagnético bidimensional na presen- ça de lacunas, que é exatamente o que caracteriza os compostos supercondutores de alta temperatura crítica na sua fase de baixa dopagem.Após termos obtido o hamiltoniano que descreve o modelo t-J, aplicamos à este uma descrição de polarons de spin, numa representação de holons, que são férmions sem spin, e spinons, que são bósons que carregam somente os graus de liberdade de spin. Utilizando uma função de Green para descrever a propagação do polaron pela rede, obtemos uma equação para a sua autoenergia somando uma série de diagramas de Feynman, sendo que para este cálculo utilizamos a aproxima ção de Born autoconsistente[1]. Do ponto de vista numérico demonstramos que a equação integral de Dyson resultante do tratamento anterior não requer um procedimento iterativo para sua solução, e com isto conseguimos trabalhar com sistemas com grande número de partículas. Os resultados mostram, como um aspecto novo, que o tempo de vida média do holon tem um valor bastante grande no ponto (π,0 ) da rede recíproca, perto da singularidade de Van Hove mencionada na literatura[2]. Este aspecto, e suas implicações, é amplamente discutido neste capítulo. No capítulo 3 estudamos o modelo estendido t-t'-J, com tunelamento à segundos vizinhos e a incorporação dos termos de três sítios[3]. Fazemos a mesma formulação do capítulo anterior, e discutimos as aplicações dos nossos resultados ao óxido mencionado anteriormente. Finalmente, no último capítulo apresentamos uma aplicação original do modelo t-J à uma rede retangular, levemente distorcida, e demonstramos que os resultados do capítulo 3 são reproduzidos sem necessidade de introduzir termos de tunelamento adicionais no hamiltoniano. Esta aplicação pode se tornar relevante para o estudo das fases de tiras encontradas recentemente nesses materiais de óxidos de cobre.

L'objectif principal de ma thèse porte sur les composés à base d'europium, une des terres rares qui est magnétique et qui forme des semiconducteurs magnétiques. Le but premier était de mesurer les corrélations magnétiques dans l'EuB6 à l'aide de la technique diffraction de neutrons à petits angles SANS (small angle neutron scattering en anglais), plus précisément de mesurer la longueur de corrélation des polarons magnétiques. La raison de sonder les polarons magnétiques dans l'EuB6 est que leur présence pourrait expliquer la grande magnétorésistance proche de la transition Curie associée avec l'ordre ferromagnétique. Ceci est une tâche particulièrement difficile puisque l'europium est un très grand absorbeur de neutrons, affectant donc la durée d'acquisition. De longs temps d'exposition étaient nécessaires pour obtenir un bruit de fond adéquat. Suite à l'analyse des données, nous avons pu conclure que les polarons magnétiques sont définitivement présents. De plus, leur présence augmente de façon non négligeable les fluctuations magnétiques. Par contre, la présence de ces fluctuations magnétiques rend la tâche de mesurer la longueur de corrélation plus difficile. La plus grande découverte de mon doctorat a été la phase nématique dans le EuB6 grâce à des mesures de magnétorésistance en fonction de l'angle. Ceci se manifestait avec une brisure de symétrie du cristal seulement dans les propriétés électroniques. Ces données m'ont permis de mieux comprendre le rôle que jouent les polarons magnétiques dans ce système. En dopant le système au calcium, nous avons confirmé la présence d'une transition vers un ordre de verre de spins à partir d'une concentration de 30% de calcium. Ce composé semble posséder la même phase nématique que le EuB6. Toutefois, cette phase est bien plus concentrée autour de la transition à cause du manque de fluctuations magnétiques au-dessus de celle-ci. / The main objective of my thesis is about Europium, a magnetic rare earth, based compounds which produces magnetic semiconductors. The primary goal was to measure magnetic correlations in the EuB6 using SANS (small angle neutron scattering) technique, more precisely, to measure the correlation length of magnetic polarons. The raison for studying magnetic polarons in EuB6 is that their presence can explain the large magnetoresistance near the Curie transition associated to a ferromagnetic order. This is a particularly difficult task since Europium (Eu2+) is a very strong neutron absorber, thus affecting the acquisition time. Long exposure times were necessary to obtain adequate background. After the analysis of the data, we have finally been able to conclude that magnetic polarons are definitely present. In addition, their presence increases significantly magnetic fluctuations. On the other hand, the presence of these magnetic fluctuations makes the task of measuring the correlation length more difficult. The biggest discovery of my Ph.D. was the nematic phase in the EuB6 using angle-based magneto-resistance measurements. The nematic phase is caracterized by a breaking of symmetry only in the electronic properties. These data have allowed me to better understand the role played by magnetic polarons in this system. By doping the system with calcium, we confirmed the presence of a transition to a spin glass order from a concentration of 30% calcium. This compound seems to have the same nematic phase as its parent compound. However, this phase is much more concentrated around the spin glass transition because of lack of magnetic fluctuations above it.

Organic π-conjugated solids are promising candidates for new optoelectronic materials. The large body of evidence points at their advantageous properties such as high charge-carrier mobility, large nonlinear polarizability, mechanical flexibility, simple and low cost fabrication and superior luminescence. They can be used as nonlinear optical (NLO) materials with large two-photon absorption (2PA) and as electronic components capable of generating nonlinear neutral (excitonic) and charged (polaronic) excitations. In this work, we investigate the appropriate theoretical methods used for the (a) prediction of 2PA properties for rational design of organic materials with improved NLO properties, and (b) understanding of the essential electronic excitations controlling the energy-transfer and charge-transport properties in organic optoelectronics. Accurate prediction of these electro-optical properties is helpful for structureactivity relationships useful for technological innovations. In Chapter 1 we emphasize on the potential use of the organic materials for these two applications. The 2PA process is advantageous over one-photon absorption for deep-tissue fluorescence microscopy, photodynamic therapy, microfabrication and optical data storage owing to the three-dimensional spatial selectivity and improved penetration depth in the absorbing or scattering media. The design of the NLO materials with large 2PA cross-sections may reduce the optical damage due to the use of the high intensity laser beams for excitation. The organic molecules also possess self-localized excited states which can decay radiatively or nonradiatively to form excitonic states. This suggests the use of these materials in the electroluminescent devices such as light-emitting diodes and photovoltaic cells through the processes of exciton formation or dissociation, respectively. It is therefore necessary to understand ultrafast relaxation processes required in understanding the interplay between the iv efficient radiative transfer between the excited states and exciton dissociation into polarons for improving the efficiency of these devices. In Chapter 2, we provide the detailed description of the various theoretical methods applied for the prediction as well as the interpretation of the optical properties of a special class of substituted PPV [poly (p-phenylene vinylene)] oligomers. In Chapter 3, we report the accuracy of different second and third order time dependent density functional theory (TD-DFT) formalisms in prediction of the 2PA spectra compared to the experimental measurements for donor-acceptor PPV derivatives. We recommend a posteriori Tamm-Dancoff approximation method for both qualitative and quantitative analysis of 2PA properties. Whereas, Agren's quadratic response methods lack the double excitations and are not suitable for the qualitative analysis of the state-specific contributions distorting the overall quality of the 2PA predictions. We trace the reasons to the artifactual excited states above the ionization threshold. We also study the effect of the basis set, geometrical constraints and the orbital exchange fraction on the 2PA excitation energies and cross-sections. Higher exchange (BMK and M05-2X) and range-separated (CAM-B3LYP) hybrid functionals are found to yield inaccurate predictions both quantitatively and qualitatively. The failure of the exchangecorrelation (XC) functionals with correct asymptotic is traced to the inaccurate transition dipoles between the valence states, where functionals with low HF exchange succeed. In Chapter 4, we test the performance of different semiempirical wavefunction theory methods for the prediction of 2PA properties compared to the DFT results for the same set of molecules. The spectroscopic parameterized (ZINDO/S) method is relatively better than the general purpose parameterized (PM6) method but the accuracy is trailing behind the DFT methods. The poor performances of PM6 and ZINDO/S methods are attributed to the incorrect description of excited-to-excited state transition and 2PA energies, respectively. The different v semiempirical parameterizations can at best be used for quantitative analysis of the 2PA properties. The ZINDO/S method combined with different orders of multi-reference configuration interactions provide an improved description of 2PA properties. However, the results are observed to be highly dependent on the specific choice for the active space, order of excitation and reference configurations. In Chapter 5, we present a linear response TD-DFT study to benchmark the ability of existing functional models to describe the extent of self-trapped neutral and charged excitations in PPV and its derivative MEH-PPV considered in their trans-isomeric forms. The electronic excitations in question include the lowest singlet (S1) and triplet (T1 † ) excitons, positive (P+ ) and negative (P- ) polarons and the lowest triplet (T1) states. Use of the long-range-corrected DFT functional, such as LC-wPBE, is found to be crucial in order to predict the physically correct spatial localization of all the electronic excitations in agreement with experiment. The inclusion of polarizable dielectric environment play an important role for the charged states. The particlehole symmetry is preserved for both the polymers in trans geometries. These studies indicate two distinct origins leading to self-localization of electronic excitations. Firstly, distortion of molecular geometry may create a spatially localized potential energy well where the state wavefunction self-traps. Secondly, even in the absence of geometric and vibrational dynamics, the excitation may become spatially confined due to energy stabilization caused by polarization effects from surrounding dielectric medium. In Chapter 6, we aim to separate these two fundamental sources of spatial localization. We observe the electronic localization of P + and Pis determined by the polarization effects of the surrounding media and the character of the DFT functional. In contrast, the self-trapping of the electronic wavefunctions of S1 and T1(T1 † ) mostly follows their lattice distortions. Geometry vi relaxation plays an important role in the localization of the S1 and T1 † excitons owing to the nonvariational construction of the excited state wavefunction. While, mean-field calculated P + , Pand T1 states are always spatially localized even in ground state S0 geometry. Polaron P+ and Pformation is signified by the presence of the localized states for the hole or the electron deep inside the HOMO-LUMO gap of the oligomer as a result of the orbital stabilization at the LCwPBE level. The broadening of the HOMO-LUMO band gap for the T1 exciton compared to the charged states is associated with the inverted bond length alternation observed at this level. The molecular orbital energetics are investigated to identify the relationships between state localization and the corresponding orbital structure. In Chapter 7, we investigate the effect of various conformational defects of trans and cis nature on the energetics and localization of the charged P + and Pexcitations in PPV and MEHPPV. We observe that the extent of self-trapping for P+ and Ppolarons is highly sensitive on molecular and structural conformations, and distribution of atomic charges within the polymers. The particle-hole symmetry is broken with the introduction of trans defects and inclusion of the polarizable environment in consistent with experiment. The differences in the behavior of PPV and MEH-PPV is rationalized based on their orbital energetics and atomic charge distributions. We show these isomeric defects influence the behavior and drift mobilities of the charge carriers in substituted PPVs.

In this work the transient non-instantaneous polarization, i.e., laser-pulse injected small polarons and self-trapped excitons, is studied in the perovskite-like ferroelectric lithium niobate. The investigations span a time scale from femtoseconds to several hours. It is shown that the established small polaron picture is not able to describe transient absorption and photoluminescence of lithium niobate consistently. Several strong indications are presented demonstrating that the photoluminescence cannot be caused by geminate small polaron annihilation. Instead, the idea of radiatively decaying self-trapped excitons at the origin of the blue-green photoluminescence is revived. Excitons pinned on defect sites are proposed to lead to the already observed long-lived transient absorption in the blue spectral range in Mg- and Fe-doped crystals. Excitons pinned on iron-defects are studied in more detail. Their spectral fingerprint and absorption cross section is determined. Furthermore, it is shown that the occurrence of these pinned STEs can be tailored by chemical treatment of the samples and the experimental parameters such as the pump pulse intensity and photon energy. Based on the new experimental results and reviewing data published in literature, an atomistic picture of hopping and pinning of self-trapped excitons in lithium niobate is proposed. The question is addressed whether small polarons and self-trapped excitons in lithium niobate are coupled species in the sense that oppositely-charged polarons may merge into self-trapped excitons or STEs break into small polaron pairs. Decay kinetics of transient absorption and luminescence assigned to free small polarons and STEs indicate that this is not the case. For a more complete picture the ultrafast time scale is investigated as well. The formation times of small polarons and STEs are determined, which both lie in the range of 200 fs. No indications are found on the (sub)picosecond time scale indicating a coupling of both quasi-particle species either. In order to gain access to the formation of self-trapped excitons a custom-built femtosecond broadband fluorescence upconversion spectrometer is installed. Based on an already existing scheme, it is adapted to the inspection of weakly luminescent solid samples by changing to an all reflective geometry for luminescence collection. To avoid the necessity for an experimentally determined photometric correction of the used setup, an already established calculation method is extended considering the finite spectral bandwidth of the gate pulses. The findings presented here are important not only as fundamental research, but also regarding the technical application of lithium niobate and other similar nonlinear optical crystals. The simultaneous occurrence of both small polarons and self-trapped excitons is a rather rarely described phenomenon. Usually, the optical response of wide band gap oxide dielectrics is associated with only one of these quasi-particle species. This work may therefore be a stimulus to review the existing microscopic models for transient phenomena in other oxide dielectrics, which may help to improve their application in nonlinear optical and electro-optical devices. In this context the ultrafast transient photoluminescence spectroscopy established here for weakly luminescing solid samples may again provide valuable insight. With respect to lithium niobate, the results do not only resolve inconsistencies between the microscopic pictures described in literature, but also provide information regarding the extends to which the propagation of ultrashort laser pulses may be affected by (pinned-)STE absorption. It is shown that tailoring of the long-lived absorption center in the blue spectral range is possible, which may be used to avoid optical damage when high repetition rates are applied. It is important to emphasize that the microscopic model proposed in this work is mainly based on experimental indications. It is the task of further detailed theoretical investigations, e.g., via time-dependent density functional theory, to test whether the proposed model is justified. From an experimental perspective the important question remains whether (pinned-)STEs contribute to a photorefractive effect. In the experimentally easily accessible spectral range no absorption feature of mobile STEs is observed. As a complementary experimental technique, ultrafast holographic spectroscopy may reveal an excitonic contribution to photorefraction and provide further insight to STE transport and pinning phenomena.

Quasi-particles formed in lithium niobate after pulse exposure were investigated by transient absorption and photoluminescence spectroscopy as well as numerical simulations. This includes the formation process, the transport through the crystal, interim pinning on defects during the relaxation process, and the final recombination with deep centers. It was shown that the charge-transport through the crystal can be described by a hopping transport including different types of hops between regular or defective lattice sites, i.e., the transport includes a mixture of free and bound small polarons. Furthermore, the different types of hops connected with varying activation energies and their distribution are responsible for an altered temporal decay curve when changing the crystal composition or temperature. Additionally, it was shown that the hitherto accepted recombination model is insufficient to describe all transient absorption and luminescence effects in lithium niobate under certain experimental conditions, i.e., long-living absorption dynamics in the blue/UV spectral range do not follow the typical polaron dynamics and cannot be described under the assumption of charge compensation. However, similar decay characteristics between self-trapped excitons known from photoluminescence spectroscopy and the unexpected behavior of the transient absorption were found leading to a revised model. This includes, besides the known polaron relaxation and recombination branch, a significant role of self-trapped excitons and their pinning on defects (pinned STEs). Since the consideration of further absorption centers in the relaxation path after pulse exposure might result in misinterpretations of previously determined polaron absorption cross-sections and shapes, the necessity to perform a review became apparent. Therefore, a supercontinuum pump-probe experiment was designed and all measurements applied under the same experimental conditions (temperature, polarization) so that one can extract the absorption amplitudes of the single quasi-particles in a spectral range of 0.7-3.0eV. The detailed knowledge might be used to deconvolve the absorption spectra and transform them to number densities of the involved centers which enables one to obtain an easier insight into recombination and decay dynamics of small polarons and self-trapped excitons. As the hopping transport of quasi-particles and the concept of pinned STEs might be fundamental processes, a thorough understanding opens up the possibility of their exploitation in various materials. In particular, results presented herein are not only limited to lithium niobate and its applications; an extension to a wide range of further strongly polar crystals in both their microscopic processes and their use in industry can be considered.

In this work the electronic and magnetic structure of the crystals Sr2FeMoO6, Fe0.5Cu0.5Cr2S4, LuFe2O4 and the molecules FeStar, Mo72Fe30, W72Fe30 are investigated by means of X-ray spectroscopic techniques. These advanced materials exhibit very interesting properties like magnetoresistance or multiferroic behaviour. In case of the molecules they also could be used as spin model systems. A long standing issue concerning the investigation of these materials are contradicting results found for the magnetic and electronic state of the iron (Fe) ions present in these compounds. Therefore this work focuses on the Fe state of these materials in order to elucidate reasons for these problems. Thereby the experimental results are compared to multiplet simulations.

In der vorliegenden Arbeit werden die nichtlinearen optischen Eigenschaften der Materialien Lithiumniobat und Di-Zinn-Hexathiohypodiphosphat aufgrund der Suszeptibilität 3. Ordnung und kleiner Polaronen untersucht. Zudem wird gezeigt, dass die Interferenz verschiedenfarbiger Laserpulse die Aufzeichnung von statischen und dynamischen holographischen Gittern ermöglicht. Ein Teil dieser Arbeit ist in den im Anhang angegebenen 6 Publikationen bereits veröffentlicht. Lithiumniobat wird mit einer Erweiterung des Z-Scan Experiments untersucht, welches die Pulslängenabhängige Messung der nichtlinearen Absorption und der nichtlinearen Brechungsindexänderung ermöglicht. Dabei konnte festgestellt werden, dass bei sehr kurzen Pulslängen von 70 fs ein Effekt der Polaronen auf die nichtlineare Absorption vernachlässigbar ist und die Zwei-Photonen-Absorption die nichtlineare Absorption dominiert. Mit größerer Pulslänge gibt es allerdings Abweichungen zwischen der Theorie der Zwei-Photonen-Absorption und den Messergebnissen. Mit der Entwicklung eines Polaronen-Anregungs-Modells, welches eine polaronische Absorption aufgrund wiederholtem optisch induziertem Hopping annimmt, konnte dieser Effekt konsistent erklärt werden. Die Messungen der nichtlinearen Brechungsindexänderung lassen darauf schließen, dass sowohl freie Ladungsträger als auch kleine Polaronen neben der Suszeptibilität 3. Ordnung einen Einfluss auf die Brechungsindexänderung haben, da eine nichtlineare Abhängigkeit von der Intensität auch bei Pulslängen von 70 fs festgestellt werden konnte. Analog dazu konnte in Di-Zinn-Hexathiohypodiphosphat ein großer Zwei-Photonen-Absorptionskoeffizient festgestellt werden, welcher für Photonenenergien nahe der Bandkante Werte zeigt, die größer sind als theoretischen Überlegungen zeigen. Eine transiente Absorption nach optischer Anregung, gemessen durch ein Anreg-Abtast-Experiment, sowie Literatur legen nahe, dass in Di-Zinn-Hexathiohypodiphosphat gebundene Lochpolaronen durch optische Anregung entstehen können. Durch den hohen Zwei-Photonen-Absorptionskoeffizienten konnte das Aufzeichnen eines kontrastreichen, dynamischen Amplitudengitters mittels Femtosekundenpulsen gezeigt und nachgewiesen werden. Die Kürze der Femtosekundenpulse ermöglicht aber nicht nur das Aufzeichnen eines Zwei-Photonen-Absorptionsgitters aufgrund der hohen Intensitäten, sondern erlaubt zudem die Beobachtung von Interferenz zwischen verschiedenfarbigen Pulsen. In der Zeitspanne der Pulslänge beträgt die Bewegung der Interferenzstreifen, welche in der Größenordnung der Lichtgeschwindigkeit liegt, nur ein Bruchteil der Streifendistanz, sodass das Interferenzmuster eingefroren und beobachtbar erscheint. Somit lassen sich statische Hologramme in holographischen Filmen, wie auch dynamische Hologramme aufzeichnen. Über ein dynamisches holographisches Gitter mittels Zwei-Photonen-Absorption konnte so eine Frequenzkonversion durch Dopplerverschiebung in Lithiumniobat gezeigt werden.