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

We propose to use superconductor-magnet multi-layer structure to achieve high critical current density by invoking polaronic mechanism of pinning. The magnetic layers should have large magnetic susceptibility to enhance the coupling between vortices and magnetization in magnetic layers. The relaxation of the magnetization should be slow. When the velocity of vortices is low, they are dressed by nonuniform magnetization and move as polarons. In this case, the viscosity of vortices proportional to the magnetic relaxation time is enhanced significantly. As velocity increases, the polarons dissociate and the viscosity drops 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 the corresponding current at the jump is the depinning current. For Nb and proper magnet multi-layer structure, we estimate the critical current density $J_c\sim 10^{9}\ \rm{A/m^2}$ at magnetic field $B\approx 1$ T.