Possible origin of double-peak behavior of the pinning-force density in thick MgB₂ films with columnar structures

We have investigated the flux pinning force in MgB₂ thick films with columnar structures. Three types of thick films with different grain sizes were prepared on c-cut Al₂O₃ substrates by using the hybrid physical-chemical vapor deposition method at 520, 540 and 560 °C. For all of the samples, the pinning force densities showed an unusual double-peak behavior with two types of irreversible fields, H* , separating the peaks. This double-peak behavior of the pinning forces did not obey any flux pinning scaling laws, but could be well scaled by using separate pinning forces with the reduced irreversible fields b_H = H/H_irr and b_L = H/H*. These results suggest that these double-peak features are associated with two different pinning mechanisms, such as point defects in intragrains and planar defects between columnar grains. The latter pinning sources were observed to be stronger pinning centers compared to the former ones.