  Over the last two decades, non-trivial magnetic textures, especially the
magnetic skyrmion family, have been extensively explored out of fundamental
interest, and diverse possible applications. Given the possible technological
and scientific ramifications of skyrmion-texture on magnetic tunnel junction
(ST-MTJ), in this work, we present non-equilibrium Green's function (NEGF)
based description of ST-MTJs both for N\'eel and Bloch textures, to capture the
spin/charge current across different voltages, temperatures, and sizes. We
predict the emergence of a textured spin current from the uniform layer of the
ST-MTJs, along with a radially varying, asymmetrical voltage dependence of spin
torque. We delineate the voltage-induced rotation of the spin current texture,
coupled with the appearance of helicity in spin current, particularly in the
case of N\'eel skyrmions on MTJs. We describe the TMR roll-off in ST-MTJ with
lower cross-sectional area and higher temperature based on transmission spectra
analysis. We also introduce a computationally efficient coupled spatio-eigen
framework of NEGF to address the 3D-NEGF requirement of the ST-MTJs. With
analytical underpinning, we establish the generic nature of the spatio-eigen
framework of NEGF, alleviating the sine-qua-non of the 3D-NEGF for systems that
lack transnational invariance and simultaneous eigen-basis in the transverse
directions.
