B region in a Volume Defect-Dominating Superconductor

It has been generally accepted that the diamagnetic property of type II superconductor decreases after Hc1. On the other hand, we found that (Fe, Ti) particle-doped MgB2 specimens have a ∆H = ∆B region in the M-H curves, which is the region that the increase of a magnetic induction is as much as the increase of an applied magnetic field. Here we study whether this phenomenon was only confined to (Fe, Ti) particle-doped MgB2 superconductor, whether there is a theoretical basis, and why it does not appear in other superconductors. The cause of the ∆H = ∆B region was the pinning phenomenon of defects in the superconductor and it only occurs in volume defectdominating superconductors. Widths of the ∆H = ∆B region along the number of defects and Hc2 were calculated, and compared with the experimental results. We hypothesized that pinned fluxes have to be depinned from the defect and move into an inside of a superconductor regardless ∆Gdefect if the distance between fluxes pinned at the volume defect is equal to that of Hc2. The region means that the fluxes that have penetrated into the inside of a superconductor are pinned preferentially on the volume defects over the entire specimen before the general behavior. ∗Electronic address: yckim@pusan.ac. kr; Fax: +82-51-513-7664 1 ar X iv :1 80 5. 04 68 3v 2 [ ph ys ic s. ap pph ] 1 5 M ay 2 01 9 Although it is clear that superconductors have a flux pinning effect, the exact mechanism is not completely understood [1–4]. All superconductors have flux pinning effects because they have defects even if defects are few. Most of type II superconductors have shown that the diamagnetic property of the superconductor decreases gradually after Hc1 (not Hc1), which is defined as the field showing the maximum diamagnetic property. On the other hand, we observed a phenomenon in (Fe, Ti) particle-doped MgB2 specimens that do not show the general behavior after Hc1, which is the existence of a ∆H = ∆B region in the magnetization-applied field (M-H) curves. This is an unusual phenomenon that has not reported in other superconductors. The flux pinning phenomenon is caused mainly by defects in the superconductor. Generally, defects in the superconductor contain volume defects (such as general volume defects, precipitators, inclusions and columnar defects, etc.), planar ones (such as grain boundaries, twin boundaries and stacking faults plane, etc.), and line ones (such as dislocations). Although they all belong to a family of defects, a role difference for flux pinning is considerable. In the case of volume defects, pinned fluxes are difficult to escape from defects except when a force balance (Fpinning = Fpickout) is broken; hence, they are called strong pinning sites. On the other hand, weak pinning sites, such as planar defects and line defects, are entirely different from the strong pinning sites in the flux pinning mechanism. The grain boundaries (GBs), which have relatively lower pinning energy caused by planar characteristic, are connected to each other in the entire specimen as a planar defect. Therefore, fluxes pinned on the GB move easily along the GBs. In addition, because the total area as a defect is large, they have significant importance in the overall flux pinning effects. A superconductor dominated by planar defects in the flux pinning effect can be called a planar defect-dominating superconductor. High Tc superconductor (HTSC) bulks are associated in this category [6–9]. The depinning, which means the phenomenon that magnetic fluxes escape from the defect, will be considered by two ways. The one is pick-out depinning, which is the depinning that fluxes pinned on the volume defect are depinned together. The other is leak-out depinning, which is the depinning that fluxes pinned on the volume defect are depinned one by one. The former is the depinning by the force balance of fluxes pinned at the defect and the latter is depinning through grain boundaries connected on volume defect because grain boundaries does not only pin the fluxes but also leak out fluxes pinned at volume defects. Regarding dislocations, the penetration of fluxes through them is not too difficult as planar