Small polarons in spin-orbit coupled osmates

Small polarons (SP) have been thoroughly investigated in 3d transition metal oxides and they have been found to play a crucial role in physical phenomena such as charge transport, colossal magnetoresistance and surface reactivity. However, our knowledge about these quasi-particles in 5d systems remains very limited, since the more delocalised nature of the 5d orbitals reduces the strength of the Electronic Correlation (EC), making SP formation in these compounds rather unexpected. Nevertheless, the Spin-Orbit coupled Dirac-Mott insulator Ba2NaOsO6 (BNOO) represents a good candidate for enabling polaron formation in a relativistic background, due to the relatively large EC (U ∼ 3 eV) and Jahn-Teller activity. Moreover, anomalous peaks in Nuclear Magnetic Resonance (NMR) spectroscopy experiments suggest the presence of thermally activated SP dynamics when BNOO is doped with Ca atoms. We investigate SP formation in BNOO both from an electronic and structural point of view by means of fully relativistic first principles calculations. Our numerical simulations predict a stable SP ground state and agree on the value of 810 K for the dynamical process peak found by NMR experiments.

Analytical and numerical study of polarons

The aim of this thesis is to introduce the polaron concept and to perform a DFT numerical calculation of a small polaron in the rutile phase of TiO2. In the first chapters, we present an analytical study of small and large polarons, based on the Holstein and Fröhlich Hamiltonians. The necessary mathematical formalism and physics fundamentals are briefly reviewed in the first chapter. In the second part of the thesis, Density Functional Theory (DFT) is introduced together with the DFT+U correction and its implementation in the Vienna Ab-Initio Simulation Package (VASP). The calculation of a small polaron in rutile is then described and discussed at a qualitative level. The polaronic solution is compared with the one of a delocalized electron. The calculation showed how the polaron creates a new energy level 0.70 eV below the conduction band. The energy level is visible both in the band structure diagram and in the density of states diagram. The electron is localized on a titanium atom, distorting the surrounding lattice. In particular, the four oxygen atoms closer to the titanium atom are displaced by 0.085 Å outwards, whereas the two further oxygen atoms by 0.023 Å. The results are compatible, at a qualitative level, with the literature. Further developments of this work may try to improve the precision of the results and to quantitatively compare them with the literature.