  We study the effect of an applied magnetic field on sub-10nm wide MoGe and Nb
superconducting wires. We find that magnetic fields can enhance the critical
supercurrent at low temperatures, and does so more strongly for narrower wires.
We conjecture that magnetic moments are present, but their pair-breaking
effect, active at lower magnetic fields, is suppressed by higher fields. The
corresponding microscopic theory, which we have developed, quantitatively
explains all experimental observations, and suggests that magnetic moments have
formed on the wire surfaces.
