Mesoscopic Josephson junctions with switchable current-phase relation

We propose and analyze a mesoscopic Josephson junction consisting of two ferromagnetic insulator-superconductors (FI-Ss) coupled through a normal metal (N) layer. The Josephson current of the junction is non-trivially affected by the spin-splitting field induced by the FIs in the two superconductors. In particular, it shows sizeable enhancement by increasing the amplitude of the exchange field ($h_{ex}$) and displays a switchable current-phase relation which depends on the relative orientation of $h_{ex}$ in the FIs. In a realistic EuS/Al-based setup this junction can be exploited as a high-resolution threshold sensor for the magnetic field as well as an on-demand tunable kinetic inductor.