Vortex formation in pure-Sn islands in field-cooled Sn-Pb solders

Formation of vortices is a typical phenomenon in type-II superconductors under a magnetic field (H). In contrast, type-I superconductors do not host the vortices because of their Meissner state, and the vortices have rarely observed in the intermediate states of type-I superconductors and Pb at extremely low temperature (T) under H. Here, we show the thermodynamic evidences of vortex formation in pure-Sn islands in the field-cooled Sn-Pb solders, where Sn and Pb are well phase-separated. Noticeably, the vortex states appear even after demagnetization (H = 0 Oe). We analyze specific heat data of the Sn10-Pb90, Sn20-Pb80, Sn70-Pb30, and Sn90-Pb10 solder samples after field cooling at H greater than the critical filed, and the measurements are performed at various H. Although the Pb regions exhibit conventional H-T phase diagrams for all the samples, the Sn regions of the most samples exhibit the robustness of superconductivity to H, which is similar to the anomalous H-T trend recently observed in Sn45-Pb55. We show that the specific heat jump at the superconducting transition of the Sn regions is clearly enhanced with decreasing the Sn amount, and the increase in the jump magnitude correlates with the amount of the magnetic fields trapped after field cooling but not with the Sn amount. Furthermore, the jump magnitude is several times larger than the value expected from a conventional superconducting transition (electron entropy change). The large specific heat jump and the enhancement of the jump magnitude by the increase in trapped magnetic field indicate that the Sn regions exhibit bulk vortex states with an obvious entropy change (emergence of new degree of freedom) when the solders are initially field-cooled.