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We propose to use superconductor-magnet multi-layer structure to achieve highcritical current density by invoking polaronic mechanism of pinning. Themagnetic layers should have large magnetic susceptibility to enhance thecoupling between vortices and magnetization in magnetic layers. The relaxationof the magnetization should be slow. When the velocity of vortices is low, theyare dressed by nonuniform magnetization and move as polarons. In this case, theviscosity of vortices proportional to the magnetic relaxation time is enhancedsignificantly. As velocity increases, the polarons dissociate and the viscositydrops to the usual Bardeen-Stephen one, resulting in a jump in the I-V curve.Experimentally the jump shows up as a depinning transition and thecorresponding current at the jump is the depinning current. For Nb and propermagnet multi-layer structure, we estimate the critical current density $J_c\sim10^{9}\ \rm{A/m^2}$ at magnetic field $B\approx 1$ T.

physical review. b, condensed matter and materials physics

Enhancement of critical current density in superconducting/magnetic  multi-layers with slow magnetic relaxation dynamics and large magnetic  susceptibility