Super-hard Superconductivity
We present a study of 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 and V wires 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~5x10^6 A/cm^2 for Nb. The implications for the fundamental limiting hardness of a superconductor are discussed.