Magnetic flux pinning in proton-irradiated thick Nb samples

Abstract

Very pure annealed Nb samples having a resistivity ratio, Γ≡ρ296/ρ4.2, in the range 1300–1700 were irradiated with 3–8-MeV protons to fluences of 6.8×1016 and 3.4×1016 protons/cm2. Local magnetic induction profiles, when the samples were in the superconducting mixed state, were obtained using the ac technique of Rollins, Küpfer, and Gey. Electron micrographs of the irradiated samples show that the damage caused by proton irradiation was inthe form of dislocation loops. The volume pinning force Fv, calculated for the dislocation loops using flux pinning models and theories for b=0.7 and T=4.2 K, is compared with the experimentally obtained Fv. The Fv calculated from direct summation law is an order of magnitude higher than the experimental result and the Fv calculated from models, which use Labusch quadratic summation law, is two to three orders of magnitude smaller than the experimental value. Our experimental pinning force per dislocation loop is in agreement with a master curve obtained by Kramer as an empirical solution to the summation problem. Experimentally obtained Fv, for temperatures lying betweeen 2 and 7 K obey a scaling law. If the temperature dependence is written as Fv∝Hnc, then we found n to be slightly dependent on depth x from the sample surface. At x=20 μm, n=3.2±0.2; while at x=84 μm, n=2.7±0.2. The experimental scaling law is compared with the scaling laws obtained from the Labusch model for point pinning centers and Kramer’s model for line pinning centers. Irradiated samples were observed to have a region at the surface with no apparent pinning. This observation is discussed in terms of two different effects: (i) reversible motion of flux lines and (ii) a threshold for flux pinning.