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.

From the time of the unexpected discovery of the insulating nature of NiO by Verwey half a century ago, Oxide materials have continued to occupy the centre stage of condensed matter physics. The recent discovery of high temperature superconductivity in doped cuprates has given a new impetus to the study of the strongly correlated electron systems. Besides, the occurrence of Colossal Magneto-Resistance (CMR) in doped rare earth manganite has also created renewed interest in these rather old systems. Understanding of the rich and complex phase diagram of these materials and their sensitivity to small perturbations e.g. external magnetic field of a few Tesla, temperature, change in isotope etc. are of great theoretical interest and also these materials have many potential technological applications. A common feature of all these oxide materials is that the transition metal ions have partially filled d-shells. Unlike s and p-electrons which gives rise to hybridized Bloch states, the d-electrons retain their atomic nature in a solid. This gives rise to strong Coulomb interaction among d-electrons which may be comparable or more than its kinetic energy. The strong correlation effects are evident from the experimental fact that the undoped parent compounds are insulators rather than metals as suggested by band theory, which favours a metallic state for systems with one electron per unit cell since this gives rise to partially filled bands (and hence a metallic state). These insulators termed Mott insulators, arise solely due to strong electron-electron correlations as compared to the band insulators which arise due to complete filling of one electron bands thereby giving rise to a gap (band gap)in the excitation spectra. The delicate competition between the kinetic energy and the Coulomb energy for d-electrons is broadly responsible for the wide variety of phenomena like Mott metal-insulator transition (MIT), magnetic transitions, charge ordering, orbital ordering, ferro/antiferroelectricity, and most interestingly the observation of high Tc superconductivity in doped cuprates. In this thesis we will restrict our interest to one such class of oxide materials, namely the doped rare earth manganites. In Chapter 1 we give a brief overview of the structure and basic interactions present in the doped manganites. Also, in the same Chapter we give a brief introduction to the phenomenology of manganites, particularly its phase diagram in the doping and temperature plane and various experimental features, e.g. the wide variety of phase transitions and phenomena particularly the observation of CMR, charge ordering and incipient meso-scale phase separations etc.. Then we briefly introduce a recently proposed microscopic model which is believed to be a minimal model which, for the first time, includes the three most important interactions present in the manganites namely the following -1)coupling of the orbitally degenerate eg electrons to local lattice distortions of Jahn-Teller type which gives rise to two species of electrons. The one denoted by by ℓ is associated with Jahn-Teller effects and hence is localized whereas the other denoted by b is an extended state and propagates through the lattice. 2) The strong Hund’s couplingof ℓ and b electrons to the t2g core spin and 3) the strong Coulomb correlation between the two species of electrons. Additionally, the model includes a new doping dependent ferromagnetic exchange between the t2g core spins which can arise from “virtual double exchange” mechanism which will be discussed in great detail in Chapter 1 . Finally, we give a brief account on Dynamical Mean Field Theory (DMFT) and Numerical Renormalization Group (NRG) as an impurity solver for the single impurity problem arising under single site DMFT approximation. In Chapter 2 we study the effect of inter-site ℓ - b hybridization on the ‘ℓ - b’ model. The single impurity problem arising under DMFT approximation has close connection with the Vigman-Finkelshtein (VF)model. Then we briefly introduce the VF model and bring out its close connection with the impurity problem. We consider both the particle-hole symmetric as well as the U → ∞ particle-hole asymmetric cases. We derive various spectral functions at T = 0K and discuss the nature of fixed points under various circumstances. We explicitly show that for the particle-hole symmetric case the Hamiltonian flows from X-ray edge singularity fixed point to Free Electron fixed point under Renormalization Group transformation. This is evident from the spectral properties of the model. We write down the effective Hamiltonian at the free electron fixed point. For the particle-hole asymmetric case the model flows from X-ray edge singularity fixed point to Free Electron/Strong Coupling fixed point with additional potential scattering terms. We write down the effective Hamiltonian at this fixed point and derive various leading order deviations. We found all of them to be irrelevant in nature also most interestingly the quasi-particles describing the under lying Fermi liquid state are found to be asymptotically non-interacting. We also calculate the Fermi liquid parameter, z, by analyzing the energy level structure of a non-interacting Hamiltonian with effective renormalized parameter. Also, we consider the case of ‘self consistent bath hybridization’ without ℓ - b hybridization for Bethe lattice with infinite coordination. Low energy qualitative features are found to be same but some of the high energy features get qualitatively modified. In Chapter 3 we discuss the transport properties of doped manganites in the insulating phases and also the Hall effect in the metallic phase. In the first part of this chapter we calculate the resistivity based on the ‘ℓ - b’model and try to fit it to the semiconducting form: ρ(T )= ρ0(T /T0)−nexp[Δ(T )/kBT ] and extract the “transport gap”, Δ(T ). This gap can be characterized in terms of the “spectral gap” which can be defined for the ℓ - b model. It is found that the transport gap in the paramagnetic phase can be characterized in terms of the near constant “spectral gap” in this phase whereas the same in the ferromagnetic phase can be characterized in terms of the zero temperature spectral gap. In the last part of this chapter we calculate the Hall resistivity (ρxy) of these materials in the metallic phase. Ρxy is found to be negative and linear in applied field -quite consistent with the experimental findings but this fails to explain the positive linear Hall resistivity at low temperatures and its crossover as a function of field and temperature. We then present a reasonable explanation for this discrepancy and support it by calculating the Hall density of states for a two band “toy model” involving inter species hybridization. In Chapter 4 we calculate the optical conductivity, σ(ω), in ℓ - b model. σ(ω) arises from two independent processes. One of the processes involves ‘b’ electrons only and termed as ‘b - b channel’ and this gives rise to a Drude peak in the low frequency region. another process termed as the ‘ℓ - b channel’ involves hopping of an ℓ-electron to a neighbouring empty site and transforms into a ‘b’like state. This process gives rise to a broad mid-infrared peak. The total conductivity is the sum of contributions from these two incoherent channels. Calculated σ(ω) for metallic systems shows lot of similarities with experimental observations particularly the temperature evolution of the mid-infrared peak and the spectral weight transfer between the two peaks. But for the insulating systems the calculated optical conductivity showed trends similar to more recent experimental observations on some insulating systems (x =0.125) but contradicts with earlier experimental observations on some other insulating system (x =0.1). Finally, in the concluding chapter, we summarize results from all the chapters and also sketch some possible future directions of investigations.