  Rashba-like spin-orbit interaction at oxide heterostructures emerges as a
much sought-after feature in the context of oxide spintronics and
spin-orbitronics. KTaO$_3$ (KTO) is one of the best substrates available for
the purpose, owing to its strong spin-orbit interaction and alternating $+1|-1$
charged layers along the (001) direction. Employing first-principles
calculations within density functional theory (DFT) and proposing a possible
electrostatic model for charge transfer to the surfaces of KTO slabs, we
comprehensively analyze Rashba-like spin-orbit interaction with the help of
three-dimensional band dispersion, isoenergetic contours, and projected spin
textures $-$ all directly obtained from our DFT results $-$ in a thin
insulating slab and a conducting thick slab of KTO. Our results reveal
reasonably strong linear Rashba interaction with no signature of Dresselhaus or
higher order Rashba interactions in the systems considered here. The rigorous
analysis presented here may be crucial for future developments in oxide
spintronics.
