Quantum magnetism in relativistic osmates from first principles

The interplay between electron correlation, local distortions and Spin Orbit Coupling is one of the most attractive phenomena in condensed matter Physics and have stimulated much attention in the last decade. In Osmates double perovskites the coupling between electronic, structural and orbital degrees of freedom leads to the formation of an unconventional magnetic phase, whose precise origin and characteristics are still not understood. In particular strong Spin Orbit Coupling effect is believed to occur and have a crucial role in enhancing multipolar exchange interactions in a fashion similar to the more studied 4f electron systems. In this thesis, by means of first principles calculations, we study the structural, electronic and magnetic proprieties of the Mott insulating Ba2NaOsO6 with Osmium in 5d1 electron configuration within the fully relativistic Density Functional Theory plus on site Hubbard U (DFT + U) scheme. We find that the system is subjected to local symmetry breaking and that the magnetic ground state is strongly dependent on the on site Coulomb interaction. Furthermore, by mapping the energy onto a Pseudospin Hamiltonian, we are capable to prove that quadrupolar and octupolar exchanges play a significant role. We repeated the study for Ba2CaOsO6 with Os in 5d2 electronic configuration as a preliminary step for understanding if phase transitions are possible when Ba2NaOsO6 is doped.