  Spin-charge interconversion is a very active direction in spintronics. Yet,
the complex behaviour of some of the most promising systems such as SrTiO$_3$
(STO) interfaces is not fully understood. Here, on the basis of a 6-band
$\boldsymbol{k.p}$ method combined with spin-resolved scattering theory, we
give a theoretical demonstration of transverse spin-charge interconversion
physics in STO Rashba interfaces. Calculations involve injection of spin
current from a ferromagnetic contact by resonant tunneling into the native
Rashba-split resonant levels of the STO triangular quantum well. We compute an
asymmetric tunneling electronic transmission yielding a transverse charge
current flowing in plane, with a dependence with gate voltage in a very good
agreement with existing experimental data.
