  We present a theoretical analysis of dynamic spin injection due to
spin-dependent tunneling between a quantum well (QW) and a bound state split in
spin projection due to an exchange interaction or external magnetic field. We
focus on the impact of Coulomb correlations at the bound state on spin
polarization and sheet density kinetics of the charge carriers in the QW. The
theoretical approach is based on kinetic equations for the electron occupation
numbers taking into account high order correlation functions for the bound
state electrons. It is shown that the on-site Coulomb repulsion leads to an
enhanced dynamic spin polarization of the electrons in the QW and a delay in
the carriers tunneling into the bound state. The interplay of these two effects
leads to non-trivial dependence of the spin polarization degree, which can be
probed experimentally using time-resolved photoluminescence experiments. It is
demonstrated that the influence of the Coulomb interactions can be controlled
by adjusting the relaxation rates. These findings open a new way of studying
the Hubbard-like electron interactions experimentally.
