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The effect of spin-orbit coupling had once been thought to be a minor perturbation to the low energy band structure that could be ignored. Instead, a surge in recent theoretical and experimental efforts have shown spin-orbit interactions to have significant consequences. The main objective of this thesis is to investigate the role of the orbital sector and crystal symmetries in governing the spin texture in materials that have strong spin- orbit interactions. This can be accessed through a combination of spin- and angle-resolved photoemission spectroscopy (ARPES and spin-ARPES), both of which are powerful techniques for probing the one-electron band structure plus interactions, and supported by density functional theory calculations (DFT). We focus first on a globally inversion asymmetric material, the layered semiconductor BiTeI, which hosts a giant spin-splitting of its bulk bands. We show that these spin-split bands develop a previously undiscovered, momentum-space ordering of the atomic orbitals. We demonstrate this orbital texture to be atomic element specific by exploiting resonant enhancements in ARPES. These orbital textures drive a hierarchy of spin textures that are then tied to the constituent atomic layers. This opens routes to controlling the spin-splitting through manipulation of the atomic orbitals. This is contrasted against a material where inversion symmetry is globally upheld but locally broken within each monolayer of a two layer unit cell. Through our ARPES and spin-ARPES measurements of 2H-NbSe2, we discover the first experimental evidence for a strong out-of-plane spin polarisation that persists up to the Fermi surface in this globally inversion sym- metric material. This is found to be intrinsically linked to the orbital character and dimensionality of the underlying bands. So far, previous theories underpinning this (and related) materials' collective phases assume a spin- degenerate Fermi sea. We therefore expect this spin-polarisation to play a role in determining the underlying mechanism for the charge density wave phase and superconductivity. Through these studies, this thesis then develops the importance of global versus local inversion symmetry breaking and uncovers how this is intricately tied to the underlying atomic orbital configuration.

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