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

Abstract

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