Perspectives from Ab-initio and Tight-binding: Applications to Transition Metal Compounds and Superlattices

The experimental and theoretical study of transition metal compounds have occupied condensed matter physicists for the best part of the last century. The rich variety of physical behaviour exhibited by these compounds owes its origin to the subtle balance of the energy scales at play for the $d$ orbitals. In this thesis, we study three different systems comprised of transition metal atoms from the third, the fourth, and the fifth group of the periodic table using a combination of \emph{ab-initio} density functional theory (DFT) computations and effective tight-binding models for the electronic properties. We first consider the electronic properties of artificially fabricated perovskite superlattices of the form [(\ce{SrIrO3})$_m$ / \ce{SrTiO3}] with integer $m$ denoting the number of layers of \ce{SrIrO3}. After discussing the results of experiments undertaken by our collaborators, we present the results of our DFT calculations and build tight-binding models for the $m=1$ and $m=2$ superlattices. The active ingredient is found to be the \ce{Ir} 5$d$ orbitals with significant spin-orbit coupling. We then study the energies of magnetic ground states within DFT and compare and contrast our results with those obtained for the bulk Ruddlesden-Popper iridates. Together with experimental measurements, our results suggest that these superlattices are an exciting venue to probe the magnetism and metal-insulator transitions that occur from the intricate balance of the spin-orbit coupling and electron interactions, as has been reported for their bulk counterparts. Next, we consider $\alpha$-\ce{RuCl3}, a honeycomb lattice compound. We first show using DFT calculations in conjunction with experiments performed by our collaborators, how spin-orbit coupling in the 4$d$ orbitals of \ce{Ru} is essential to understand the insulating state realized in this compound. Then, in the latter half of the chapter, we study the magnetic ground states of a two-dimensional analogue of $\alpha$-\ce{RuCl3} in weak and strong-coupling regimes obtained from a tight-binding model for the 4$d$ orbitals. We further compare these results with energies obtained from DFT calculations. We obtain a zig-zag magnetic ground state for this compound, in all the three approaches. Within DFT, we find that correlations enhance the spin-orbit coupling in this compound and that the anisotropic Kitaev interactions between the spins are dominant in a strong-coupling model. Then, we move on to study the electronic band structures of the higher manganese silicides, which are good thermoelectric materials. Using results from DFT calculations on \ce{Mn4Si7} and structural arguments, we construct an effective tight-binding model for the first three members of this series - \ce{Mn4Si7}, \ce{Mn11Si19}, and \ce{Mn15Si26}.Ph.D