Controlling charge and spin transport in an Ising-superconductor Josephson junction

An in-plane magnetic field applied to an Ising superconductor converts spin-singlet Cooper pairs to spin-triplet ones. In this work, we study a Josephson junction formed by two Ising superconductors that are proximitized by ferromagnetic layers. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a $\pi$-state can be realized. Furthermore, the charge and spin current-phase relations display a $\phi_0$-junction behavior for a strongly spin-polarized ferromagnetic barrier.