Phase-Slip Lines in Wide Superconducting Strips: Charge and Spin Relaxation Lengths

Penetration of spin-polarized charges from a nearby ferromagnetic metallic layer into 100-μm-wide superconducting films of Pb and Mo–Re alloy with similar critical parameters but quite different spin-orbit coupling strengths is studied. It is shown that the diffusion of magnetic properties into a nearby superconductor can be employed as an electrically tunable source of phase-slip events manifesting itself by a staircase response in current-voltage characteristics of the superconductor with discrete metastable resistivity states. Unlike for normal metals, the spin injection into an adjoining quasi-two-dimensional superconducting strip creates not only spin but also charge imbalance in the quasiparticle population which are not necessarily relaxing over the same time scale. Interplay of the two intrinsic length scales sets the width of a phase-slip line in superconducting strips under the injection which may change from nano- to micro-scales. Its experimental determination can be used for estimating the longest relaxation length in a superconductor. Our observations show that spin-orbit coupling in superconductors may lead to novel non-trivial effects linking spin and charge degrees of freedom.