Effect of columnar grain boundaries on flux pinning in MgB ₂ films

Columnar grain boundaries are widely known to be a very effective source for flux pinning in MgB ₂ films. In this study, we have investigated the pinning effect of a columnar grain boundary at various temperatures of 5, 10, 20, 30, and 35 K in columnar structured MgB ₂ films with an average grain size of ∼300 nm. The average vortex-vortex spacing (a ₀) is estimated at a specific magnetic field, B _peak, where the B _peak is the magnetic field when the flux pinning force density (F _p) reaches a maximum. The values of a ₀2, which largely affect the vortex-vortex interaction, are much closer to the coherence length of MgB ₂, than to the penetration depth, which indicates that the vortices can be strongly pinned to the columnar grain boundaries. Furthermore, we found that the columnar grain boundaries acted as strong pinning sources over a wide temperature region, although their effectiveness began to lessen slowly at temperatures above ∼20 K, which was determined on the basis of the flux-line lattice-shearing mechanism.