  Sn-Pb solders are superconducting materials whose Sn and Pb are perfectly
phase-separated. Recently, anomalous magnetic-flux trapping in a Sn45-Pb55
solder has been revealed where the magnetic fluxes are selectively trapped in
the Sn regions due to the supercurrents in the surrounding Pb regions. Here, we
report on the observation of the anomalous critical field (Hc)-temperature (T)
phase diagram of superconductivity in the Sn45-Pb55 solder. Although the Hc(T)
for the Pb regions decreases with increasing field as in normal type-I
superconductors and is consistent with the conventional trend with Hc(0) ~ 800
Oe, the Hc(T) for the Sn regions exhibits anomalous behaviors. The most
noticeable trend was observed in the field-cooled (under 1500 Oe) solder. The
Hc-T phase diagram for the Sn regions largely varies when the applied external
field is reversed, and Tc increases with increasing field amplitude when H < 0
Oe is applied. On the basis of the flux trapping and the observed anomalous
Hc-T phase diagrams, we propose that the field-robust superconductivity in the
Sn regions is related to the ferromagnetically-aligned magnetic fluxes (or
formation of vortices) in the Sn regions of the Sn45-Pb55 solder.
