Spin-resolved Josephson diode effect through strongly spin-polarized conical magnets

We present a theoretical study of the spin-resolved Josephson diode effect in junctions comprising strongly spin-polarized conical magnets (FM) coupled to singlet superconductors (SC). The system is treated by making use of the Gor$^\prime$kov and quasiclassical Green$^\prime$s function methods. Modeling the SC/FM interfaces as spin-dependent $\delta$-potentials, we apply our model to an SC/FM/SC junction and account for the Josephson current-phase relation (CPR). The nontrivial coupling between the spin bands in the conical magnet gives rise to a strong Josephson diode effect with an efficiency greater than 40%. The effect essentially depends on the quantum spin-geometric phase that enters the Josephson CPR in a very similar manner to the superconducting phase difference. The former is generated non-locally by the intrinsically noncoplanar spin arrangement of the conical magnet, which breaks the time-reversal and inversion symmetries. Strong spin polarization and a helical pitch of the conical magnet comparable to the superconducting coherence length are essential for the effect. We perform a harmonic analysis of the Josephson CPR and interpret the effect in terms of coherent transfer of multiple equal-spin triplet Cooper pairs across the conical magnet.