  We study a two-dimensional electron gas exchanged-coupled to a system of
classical magnetic ions. For large Rashba spin-orbit coupling a single electron
can become self-trapped in a skyrmion spin texture self-induced in the magnetic
ions system. This new quasiparticle carries electrical and topological charge
as well as a large spin, and we named it as magnetic skyrmionic polaron. We
study the range of parameters; temperature, exchange coupling, Rashba coupling
and magnetic field, for which the magnetic skyrmionic polaron is the
fundamental state in the system. The dynamics of this quasiparticle is studied
using the collective coordinate approximation, and we obtain that in presence
of an electric field the new quasiparticle shows, because the chirality of the
skyrmion, a Hall effect. Finally we argue that the magnetic skyrmionic polarons
can be found in large Rashba spin-orbit coupling semiconductors as GeMnTe.
