Thermally induced flux motion and the elementary pinning force in Nb thin films

The thermally induced flux motion and the elemental pinning force $f_p$ for Nb thin films (1000–5000 Å) were measured for applied magnetic fields ranging from 0.3 to 7.5 G and temperatures from 4.22 to 5.72 K. The magnitude of $f_p$(H,d,T) ranged from ${10}^{\mathrm{-}12}$ to ${10}^{\mathrm{-}11}$ N/m. This is approximately 6 orders of magnitude smaller than Lorentz-force depinning measurements made on thin-film Nb for the low-field regime (∼7 G) of isolated or weakly interacting flux lines. Some of these results are similar to the work of Huebner et al., who also found a large discrepancy in pinning-force values derived from Lorentz-force and thermal-force measurements for the high-field regime (flux-line lattice). Our results suggest that a transport current flows between the trapped flux lines such that the Lorentz force is minimized. This channeling produces a current density around a pinned flux line that is greatly reduced below the measured current divided by the cross-sectional area. This is believed to lead to a discrepancy in the value of the pinning force measured by thermal gradients with those obtained in transport current measurements. The ΔΦ versus ΔT data, for small ΔT values, implied a spectrum of pinning-force values where the flux lines that were depinned had substantially weaker pinning forces than the vast majority of the flux lines that remained pinned. Using statistical arguments, the qualitative features of the $f_p$(H,d) and ΔΦ(H,d) data are explained. The data exhibited a magnetic-field threshold, below which there is no flux motion for the temperature range studied. This threshold field increased with increasing thickness.