In this thesis I present studies of some transport and spectroscopic properties for two di erent materials exhibiting large magnetoresistance. Both of these materials are oxides of transition metals, showing exotic magnetic and transport properties. Despite these similarities, they are very different in many other aspects. One of them is an oxide of Manganese, along with a rare-earth metal, and exhibits large magnetoresistance under certain conditions, when doped by an alkaline earth metal. They are known as doped rare-earth manganites. The other material, Sr2FeMoO6, exhibits large magnetoresistance in the parent compound, without any doping, but only in the polycrystalline state. The manganites, on the other hand, show magnetoresistance under appropriate conditions in both single crystal and in polycrystalline state. Moreover, manganites exhibit several Metal-Insulator Transitions (MIT) as a function of doping, temperature and magnetic field. Sr2FeMoO6, on the other hand, is usually always metallic. In the first chapter, a brief introduction is provided regarding different types of magnetoresistance (MR) phenomena observed in different materials, namely Anisotropic MR (AMR), Giant MR (GMR), Collosal MR (CMR), Tunneling MR (TMR), Powder MR (PMR) etc. Out of these, CMR and PMR are found in doped manganites, while Sr2FeMoO6 exhibits PMR only. Next, a brief overview of the structure, properties and theories for both of these materials is provided. For the case of doped manganites, a short introduction is given for a novel two-fluid hamiltonian (called l - b model) which was proposed recently by Ramakrishnan et. al.. This model reproduces several exotic transport and magnetic properties of manganites which were inexplicible by earlier theories. The model was solved within the Dynamical Mean Field Theory (DMFT) framework by Hassan et. al.. A brief description of this DMFT solution is given. Many of the DMFT results for this model have been used in the subsequent chapters. In the second chapter, the hysteresis behaviour of the magnetoresistance and the magnetization (M ) of powdered Sr2FeMoO6 is considered in detail. In a recent experi- ment by Sarma et. al., it was found that this material, when powdered exhibits an exotic variety of PMR. In ordinary PMR, the hysteresis behaviour of the MR is supposed to follow that of M, in the sense that the coercive fields should be identical in both cases. Also, the MR is supposed to be roughly proportional to the square of the magnetization. However, in the experiments by Sarma et. al. on cold-pressed Sr2FeMoO6 powder, it was observed that the M R did not appear to be determined purely by the magnetization. Rather, the coercive fields for the hysteresis of the MR was almost 6 times that of M . Moreover, the quantity M R/M2, instead of remaining constant with changing magnetic field, itself has a hysteresis loop. Apart from establishing the exotic nature of the PMR, the experiment also tries to determine whether the MR originates from intra-grain or inter-grain tunneling. In the second chapter we present a simple toy model to reproduce the experimental results, and provide theoretical explanations. A combination of Monte Carlo and transfer matrix methods are used to simulate the hysteresis behaviour of the M R as well as of M . We show that the observed data can be understood if it is as- sumed firstly that the MR arises predominantly from inter-grain rather than intra-grain tunneling, and that the inter-grain boundaries are themselves magnetic with a coercive field higher than that of the grains. In order to motivate the use of Monte Carlo method for studying hysteresis, a brief survey of main results obtained for some simple models using this technique is also provided. In the third chapter, we study the doping and temperature dependence of core-level photoemission spectra in doped rare-earth manganites. In some recent experiments on Strontium doped (LSMO) and Barium doped (LBMO) samples, it has been observed that the M n2p3/2 core-level spectra shows an intriguing spectral weight transfer over a range of several eV , as a function of doping (x) and temperature (T ), in the ferromagnetic metallic phase. Specifically, there appears a shoulder adjacent to the main peak on the side of lower binding energy, which increases in weight and intensity as the doping increases or the temperature decreases. In LSMO samples, another shoulder was noticed on the higher binding energy side also. Moreover, in data obtained from LBMO samples, the spectra at different temperatures was subtracted from the spectra at/above Tc, and then this difference spectrum was integrated. The integrated weight, when normalized by the weight at the lowest temperature, appears to follow the square of the measured magnetization almost exactly. In order to understand the experimental data, we extended the aforementioned l - b model to include a core-level, and the attractive interaction due to a core-hole on the local valence levels. The impurity problem arising in DMFT, consisting of a single impurity site coupled to a bath, was tailored for the photoemission problem, by including this extra core-level at the impurity site. The hybridization parameters for the bath were determined self-consistently from the DMFT, and then the single particle spectral function for the core-hole was determined. This spectral function is proportional to the photo emission intensity. We found that our calculations reproduced the observed spectral weight transfer as a function of x and T both in trends and in magnitude. The integrated difference spectra weight was found to follow the square of the DMFT magnetization, just as in the experiment. Linear discretization of the conduction bath was used for all the above-mentioned cases. In one particular case, a logarithmic discretization was also undertaken for comparison, and also to obtain the exponents of the edge singularities in the theoretical spectra. In the fourth chapter, the possibility of Anderson Localization in manganites is in- vestigated, using the l - b model. According to this model, a large fraction of the valence electrons are polaronically self-trapped even in the ferromagnetic metallic phase. Due to strong on-site Coulomb interaction, these polarons provide a strongly scattering background, which can localize the mobile-electron band states close to the band edges. Since the fraction of valence electrons which are truly mobile is small, hence the Fermi energy lies close to the lower band edge. Hence, there is a possibility of an Anderson Insulator phase where all charge carriers are localized. To investigate this, we studied the behaviour of the mobility edges as a function of doping. DMFT alone does not include the physics of localization. Hence, in order to obtain the mobility edges, we combined the DMFT results with the Self-consistent Theory of Localization (STL), using a simplified prescription called Potential Well Analogy (PWA) due to Economou et. al.. We found that there is indeed an Anderson Insulator phase in a certain region of doping, which would otherwise have been supposed to be metallic based on purely DMFT results. Finally, we have compared this result, obtained using effective field theories, with an actual real space simulation of the l - b model at T=0. In this case, the mobility edge trajectories were obtained by studying the Inverse Participation Ratio (IPR), as a function of band energy and doping. In the concluding chapter, the principal results presented in this thesis are summa- rized. The limitations of the approach or approximations used are discussed, and future possibilities for overcoming these limitations outlined.

In this work we study the interesting physics of the rare earths, and the microscopic state after ultrafast magnetization dynamics in iron. Moreover, this work covers the development, examination and application of several methods used in solid state physics. The first and the last part are related to strongly correlated electrons. The second part is related to the field of ultrafast magnetization dynamics. In the first part we apply density functional theory plus dynamical mean field theory within the Hubbard I approximation to describe the interesting physics of the rare-earth metals. These elements are characterized by the localized nature of the 4f electrons and the itinerant character of the other valence electrons. We calculate a wide range of properties of the rare-earth metals and find a good correspondence with experimental data. We argue that this theory can be the basis of future investigations addressing rare-earth based materials in general. In the second part of this thesis we develop a model, based on statistical arguments, to predict the microscopic state after ultrafast magnetization dynamics in iron. We predict that the microscopic state after ultrafast demagnetization is qualitatively different from the state after ultrafast increase of magnetization. This prediction is supported by previously published spectra obtained in magneto-optical experiments. Our model makes it possible to compare the measured data to results that are calculated from microscopic properties. We also investigate the relation between the magnetic asymmetry and the magnetization. In the last part of this work we examine several methods of analytic continuation that are used in many-body physics to obtain physical quantities on real energies from either imaginary time or Matsubara frequency data. In particular, we improve the Padé approximant method of analytic continuation. We compare the reliability and performance of this and other methods for both one and two-particle Green's functions. We also investigate the advantages of implementing a method of analytic continuation based on stochastic sampling on a graphics processing unit (GPU).