Temperature-dependent matching in a flux-line lattice interacting with a triangular array of pinning centers without long-range order

A triangular array of nanoscaled artificial pinning centers (APCs) for magnetic flux lines is prepared into a Nb thin film. The APCs are formed by deposition of Nb onto a Si substrate covered with nanopillars with diameters of 20 nm and lattice constant a=122 nm. The production of pillars is based on arrays of gold nanoparticles used as etching masks during reactively ion etching a Si substrate. In this way, the pattern of the original nanoparticle array is transferred onto the substrate. The Au nanoparticles in turn were prepared using the self-organization of inverse micelles formed by diblock copolymers, whose core is loaded with a gold precursor. The resulting lattice of APCs formed by the Si pillars perforating the Nb film mirrors the order of the micellar array which has triangular, short-range order, but loses its directional order for distances larger than about 4-8 lattice constants. Similar to the Little-Parks experiments with external magnetic fields perpendicular to the superconducting film, the resulting T-c(B) curves show Delta T-c deviations. Those vanish for B larger than the first matching field B-1 indicating that no more than one single flux quantum can be captured at each APC, even at low temperatures. Moreover, integer and fractional matching effects in the critical current are observed within a wide temperature range. Two critical currents can be distinguished indicating different types of pinning mechanisms: Strong pinning at APCs and weaker pinning at interstitial sites accompanied by strong caging effects. A unique feature of such prepared samples is the surprising temperature dependence of the matching field for which a value of B-1 is observed close to T-c, which, however, is shifted towards smaller values at lower temperatures. This effect is traced back to a temperature dependent averaging over differently ordered domains within the array of APCs.