Advanced nanoscopic studies in magneto-electric manganites and high T$_c$ superconductors

Technological advances in materials synthesis and the development of new experimental techniques have created a wealth of information with remarkable implications for understanding the macroscopic properties of systems with strongly correlated electronic properties. These advances allowed the observation of a wide range of exotic phenomena such as high T$_c$ superconductivity, colossal magneto-resistance or, more recently, multiferroic behavior, which are known to be strongly dependent on the nanoscale phenomenology. In fact, several experimental and theoretical studies demonstrated that strongly correlated electron systems are not homogeneous at a local scale due to simultaneously active spin, charge, lattice and/or orbital interactions. Consequently, these systems show nanoscale chemical and electronic disorder, which lead to a rich variety of macroscopic properties. It is under this scope that the nuclear hyperfine techniques are introduced, being particularly useful to infer the local lattice structure, electric and magnetic correlations in the strongly correlated electron systems by reducing the observation scale to the atomic environment. In particular the perturbed angular correlations technique when combined with powerful first principle simulation techniques of the observables of the electric field gradient provide unique ways to characterize nanoscopic phenomena which would not be unveiled in other ways. The first theme of this thesis is related to the study of the hyperfine interactions in a series of hexagonal and orthorhombic rare-earth manganites (RMnO$_3$, R= Nd, Sm, Eu, Gd, Tb, Ho, Y, Er, Lu). The electric field gradients at the probe sites ($^{111}$Cd) have been measured and compared with the results obtained with first principle calculations via the augmented plane wave method of the charge densities in the compounds. All studied compounds present two distinct local environments, which only one can be directly attributed to the regular rare-earth crystallographic sites. The existence of a second local environment, which cannot be assigned to the regular rare-earth or manganese sites, suggests for the presence of distortions in the rare-earth local environment. The lattice sites and collective ordering of oxygen atoms, in the second and third member of Hg-based superconductors family (HgBa$_{2}$Ca$_{n-1}$Cu$_n$O$_{2n+2+δ}$, n= 2 and 3), have been studied in the scope of the second theme of this thesis. The electric field gradients at the Hg nuclei have been measured as function of oxygen doping concentration on the Hg planes, above and below T$_C$. In iii comparison with the results obtained for oxygen and fluorine doping in the first member (Hg-1201), the analysis show that, at a local scale, there is non uniform oxygen distribution. A series of first principle electric field gradient calculations allowed to infer that at low concentrations, regions without oxygen coexist with regions where O$_{2δ}$ dumbbell molecules are located at the centre of the Hg mesh. At high concentrations, O$_{2δ}$ dumbbell molecules coexist with single O$_δ$ atoms occupying the centre of the Hg mesh. The existence of O$_{2δ} $molecular dumbbells in competition with single O$_δ$ atoms in the Hg planes may provide additional understanding for justifying the systematic differences reported between the measured atomic dopant concentration and the number of holes created in the copper planes of these compounds. One shall note that to achieve this work several methods for synthesizing high purity samples have been applied and developed.