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.
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