  Diodes are key elements for electronics, optics, and detection. The search
for a material combination providing the best performances for the required
application is continuously ongoing. Here, we present a superconducting
spintronic tunnel diode based on the strong spin filtering and splitting
generated by an EuS thin film between a superconducting Al and a normal metal
Cu layer. The Cu/EuS/Al tunnel junction achieves a large rectification (up to
$\sim40$\%) already for a small voltage bias ($\sim 200$ $\mu$V) thanks to the
small energy scale of the system: the Al superconducting gap. With the help of
an analytical theoretical model we can link the maximum rectification to the
spin polarization of the barrier and describe the quasi-ideal Schottky-diode
behavior of the junction. This cryogenic spintronic rectifier is promising for
the application in highly-sensitive radiation detection for which two different
configurations are evaluated. In addition, the superconducting diode may pave
the way for future low-dissipation and fast superconducting electronics.
