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In magnetic superconductors vortices polarize spins nonuniformly andrepolarize them when moving. At a low spin relaxation rate and at low biascurrents vortices carrying magnetic polarization clouds become polaron-like andtheir velocities are determined by the effective drag coefficient which issignificantly bigger than the Bardeen-Stephen (BS) one. As current increases,vortices release polarization clouds and the velocity as well as the voltage inthe I-V characteristics jump to values corresponding to the BS drag coefficientat a critical current $J_c$. The nonuniform components of the magnetic fieldand magnetization drop as velocity increases resulting in weaker polarizationand {\it discontinuous} dynamic dissociation depinning transition.Experimentally the jump shows up as a depinning transition and thecorresponding current at the jump is the depinning current. As currentdecreases, on the way back, vortices are retrapped by polarization clouds atthe current $J_r<J_c$. As a result, polaronic effect suppresses dissipation andenhances critical current. Borocarbides (RE)Ni$_2$B$_2$C with a shortpenetration length and highly polarizable rare earth spins seem to be optimalsystems for a detailed study of vortex polaron formation by measuring I-Vcharacteristics. We propose also to use superconductor-magnet multilayerstructure to study polaronic mechanism of pinning with the goal to achieve highcritical currents. The magnetic layers should have large magneticsusceptibility to enhance the coupling between vortices and magnetization inmagnetic layers while the relaxation of the magnetization should be slow. ForNb and proper magnet multilayer structure, we estimate the critical currentdensity $J_c\sim 10^{9}\ \rm{A/m^2}$ at magnetic field $B\approx 1$ T.

Polaron-like vortices, dissociation transition and self induced pinning in magnetic superconductors