  Strong spin-orbit coupling in noncentrosymmetric materials and interfaces
results in remarkable physical phenomena, such as nontrivial spin textures,
which may exhibit Rashba, Dresselhaus, and other intricated configurations.
This provides a promising basis for nonvolatile spintronic devices and further
implications. Here, we simulate from first principles a two-dimensional
electron gas in ultrathin platinum and palladium layers grown on ferroelectric
PbTiO$_3$(001). The latter allows, in principle, to switch and control the
spin-to-charge conversion by the polarization reversal. We show how the band
structure and its Rashba splitting differ in the Pt and Pd overlayers and how
these electronic features change with increasing the overlayer thickness and
upon reversal of polarization. Besides, for both overlayers, we simulated their
current-voltage ($I-V$) characteristics, the resistance of which upon the
polarization reversal changes between 20% and several hundred percent. The
reported findings can be used to model directly the Rashba-Edelstein effect.
