  We study the effects of the Rashba spin-orbit coupling on the polaron
formation, using a suitable generalization of the Momentum Average
approximation. Contrary to previous investigations of this problem, we find
that the spin-orbit interaction decreases the effective electron-phonon
coupling. It is thus possible to lower the effective mass of the polaron by
increasing the spin-orbit coupling. We also show that when the spin-orbit
coupling is large as compared to the phonon energy, the polaron retains only
one of the spin polarized bands in its coherent spectrum. This has major
implications for the propagation of spin-polarized currents in such materials,
and thus for spintronic applications.
