Transition metal oxides (TMO), especially MF₂O₄ spinels (where M is a transition metal ion), play a significant role in technology and find a variety of applications. Among spinels, cobalt ferrite, CoFe₂O₄, shows potential applications especially as a photo- and electrochemical catalyst for water splitting and also in heterostructures owing its unique properties such as high chemical stability, low cost and desirable optical properties. Motivated by these findings, the first part of this thesis provided an in-depth analysis of electronic and optical properties of fully and partially inverse (Co_1-xFe_x)^Tet(Co_xFe_2-x)^OctO₄ (x = 0.0, 0.5, 1.0) spinel from first principles calculations including many-body effects (G₀W₀+BSE).  Various exchange-correlation functionals were used to conduct a systematic analysis of the ground state and optical properties. It was found that the electronic properties of CoFe₂O₄, such as the band gap were improved with the single-shot G₀W₀ method.  The starting exchange-correlation functionals strongly influenced the onset of the optical spectrum within the independent particle (IP) and G₀W₀ methods. However, inclusion of the excitonic effects significantly reduced these deviations. The good agreement with experiment found for the optical spectra computed using the BSE emphasizes the importance of the inclusion of electron-hole interaction.

In the next part of this thesis, building on a previous study on CoFe₂O₄(001) Co-rich surface, here we presented another step towards understanding of the oxygen evolution reaction (OER) of CoFe₂O₄ as a function of surface termination and orientation by employing DFT+U calculations. Due to the cation ordering in bulk CoFe₂O₄, this inverse spinel contains alternating layers of octahedral Co and Fe in the (001) direction and mixed Co and Fe layers along the (100) orientation. The OER activity of CoFe₂O₄(001) Fe-rich and (100) surfaces was explored in the gas and liquid phase by including the implicit solvation effect for the latter.  In the gas phase, Co at octahedral site at the A terminations with the lowest overpotential of η = 0.20 V at (100) surface was identified as the possible active site for the OER. However, in the liquid phase, Fe at the octahedral site at the B termination of (001) Fe-rich surface (η = 0.37 V) is more active than other sites indicating the necessity of the further studies of the Fe on the OER performance of spinels.

In the last part, based on DFT+U calculations, in collaboration with experiment, the structural, electronic and magnetic properties of bulk CoFe₂O₄ (ferrimagnet), Co₃O₄ (antiferromagnet) and Co₂FeO₄ (ferrimagnet) as well as the heterostructures of Co₃O₄/CoFe₂O₄ with (001) and (111) orientation and for the latter case interfaces along the (111) and (1̄1̄2) direction were modeled. The spinel Co₂FeO₄ is found to separate into a Fe-rich and a Co-rich phase due to the miscibility gap in the phase diagram of spinels at low temperature (400 ^◦ C).
Here, we studied the phase separation observed in Co₂FeO₄ into a Fe-rich and a Co-rich phase which leads to a smaller lattice constant in the Fe-rich part and also experimentally observed exchange bias effect for the sample. Analysis of the spin densities, magnetic moments of ions as well as the layer and element-resolved density of states of the Co₃O₄/CoFe₂O₄ heterostructure indicates a significant exchange splitting in both the majority and minority spin channels at the interface Co₃O₄ layer compared to the bulk which is likely the origin of the exchange bias, observed in magnetometry experiment.