The emerging field of spintronics relies on the manipulation of electron spin in order to use it in spin-based electronics. Such a paradigm change has to tackle several challenges including finding materials with sufficiently long spin lifetimes and materials which are efficient in generating pure spin currents. This thesis predicts that two types of material families could be a solution to the aforementioned challenges: complex oxides and bismuth based materials. We derived a general approach for constructing an effective spin-orbit Hamiltonian which is applicable to all nonmagnetic materials. This formalism is useful for calculating spin-dependent properties near an arbitrary point in momentum space. We also verified this formalism through comparisons with other approaches for III-V semiconductors, and its general applicability is illustrated by deriving the spin-orbit interaction and predicting spin lifetimes for strained SrTiO3 and a two-dimensional electron gas in SrTiO3 (such as at the LaAIO3/SrTiO3 interface). Our results suggest robust spin coherence and spin transport properties in SrTiO3 related materials even at room temperature. In the second part of the study we calculated intrinsic spin Hall conductivities for bismuth-antimony Bi1-xSbx semimetals with strong spin-orbit couplings, from the Kubo formula and using Berry curvatures evaluated throughout the Brillouin zone from a tight-binding Hamiltonian. Nearly crossing bands with strong spin-orbit interaction generate giant spin Hall conductivities in these materials, ranging from 474 ((ћ/e)Ω-1cm-1) for bismuth to 96((ћ/e)Ω-1cm-1) for antimony; the value for bismuth is more than twice that of platinum. The large spin Hall conductivities persist for alloy compositions corresponding to a three-dimensional topological insulator state, such as Bi0.83Sb0.17. The spin Hall conductivity could be changed by a factor of 5 for doped Bi, or for Bi0.83Sb0.17, by changing the chemical potential by 0.5 eV, suggesting the potential for doping or voltage tuned spin Hall current. We have also calculated intrinsic spin Hall conductivities of Bi2Se3 and Bi2Te3 topological insulators from an effective tight-binding Hamiltonian including two nearest-neighbor interactions. We showed that both materials exhibit giant spin Hall conductivities calculated from the Kubo formula in linear response theory and the clean static limit. We conclude that bismuth-antimony alloys and bismuth chalcogenides are primary candidates for efficiently generating spin currents through the spin Hall effect.

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