Super-Hard Superconductivity

We present the magnetic response of Type-II superconductivity in the extreme pinning limit, where screening currents within an order of magnitude of the Ginzburg-Landau depairing critical current density develop upon the application of a magnetic field. We show that this ``super-hard'' limit is well approximated in highly disordered, cold drawn, Nb wire whose magnetization response is characterized by a cascade of Meissner-like phases, each terminated by a catastrophic collapse of the magnetization. Direct magneto-optic measurements of the flux penetration depth in the virgin magnetization branch are in excellent agreement with the exponential model in which $J_c(B)=J_{co}\exp(-B/B_o)$, where $J_{co}\sim5\rm{x}10^6$ A/cm$^2$ for Nb. The implications for the fundamental limiting hardness of a superconductor will be discussed.