Flux pinning mechanisms and a vortex phase diagram of tin-based inverse opals

Three-dimensional periodic tin structures were synthesized by filling pores in silicon opals with a sphere diameter of 194 nm (Sn190) and 310 nm (Sn300). The samples were examined by the ultra-small-angle x-ray diffraction method, energy dispersive x-ray microanalysis and scanning electron microscopy. It was found that the inverse opal structure consists of tin nanoparticles inscribed in octahedral and tetrahedral pores with diameters of 128 nm and 70 nm for the sample Sn300, and 80 nm and 42 nm for the sample Sn190. The study of the magnetic properties of the samples by SQUID magnetometry showed that magnetization reversal curves exhibit hysteretic behavior. The mechanisms of magnetic flux pinning in the samples depend on the size of the tin nanoparticles. Tin nanoparticles in Sn300 behave like a classical type-I superconductor. The hysteretic behavior of the magnetization reversal curves at low magnetic fields is due to the formation of a network of superconducting contours in Sn300. These superconducting contours effectively trap the magnetic flux. The octahedral tin nanoparticles in Sn190 remain type-I superconductors, but smaller tetrahedral particles behave like type-II superconductors. Type-I and II superconducting particles in Sn190 lead to the coexistence of different mechanisms of flux pinning. These are flux trapping by superconducting contours at low magnetic fields and flux pinning by tetrahedral particles due to the surface barrier at high magnetic fields.