The Rashba effect is one of the most striking manifestations of spin-orbit coupling in solids, and provides a cornerstone for the burgeoning field of semiconductor spintronics. It is typically assumed to manifest as a momentum-dependent splitting of a single initially spin-degenerate band into two branches with opposite spin polarisation. Here, combining polarisation-dependent and resonant angle-resolved photoemission measurements with density-functional theory calculations, we show that the two spin-split branches of the model giant Rashba system BiTeI additionally develop disparate orbital textures, each of which is coupled to a distinct spin configuration. This necessitates a re-interpretation of spin splitting in Rashba-like systems, and opens new possibilities for controlling spin polarisation through the orbital sector.
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