Magnetic orderings and electronic structure of complex oxides from advanced Hubbard functionals

Transition metal oxides represent a class of materials displaying very unusual electronic, structural and magnetic properties. They are extremely interesting, both from a technological and fundamental point of view. The most important characteristic of them is the presence of localised electrons - originating from d-orbitals of the transition metal atoms - which makes their theoretical understanding very challenging. In our research, we address the problem of correctly simulate them at the microscopic level, by means of first-principles studies. To do this, we employ DFT calculations augmented with Hubbard corrections. In the first part we applied existing methods (DFT + U and DFT + U + V) to study an interesting class of magnetic insulating oxides: the rare-earth nickelates RNiO3, with R = Pr, Y. We have shown that in order to predict all the well-estabilished experimental features characterizing the low-temperature insulating phase of these materials (namely antiferromagnetism, insulating behaviour, structural distortions and multiferroicity) it is necessary to include inter-site interactions between the transition metals (nickel) and the ligands (oxygen). In the second part of the thesis, we generalized the current state-of-the-art methods of DFT + Hubbard functionals with novel methodological developments. These latter consist in the extension of DFT + U in order to deal with noncollinear magnetism and spin-orbit coupling within the ultrasoft pseudopotential approach. We have also further extended the new noncollinear, relativistic DFT + U method to include inter-site Hubbard interactions (DFT + U + V), and generalized it to one of the most advanced pseudopotential scheme currently present in literature: the projector augmented-wave method. Finally, we present a preliminary work consisting in the incorporation of the newly-developed noncollinear, relativistic DFT + Hubbard functionals for the ab initio computation of spin fluctuation spectra.