Spin Josephson diode effect induced by higher-harmonic spin Josephson currents in a diffusive Josephson junction.

We theoretically investigate the spin Josephson diode effect (SJDE) in a diffusive Josephson junction with a Rashba metal layer under a ferromagnetic exchange field. Within the quasiclassical Green's function framework, we derive analytical expressions for the first- and second-harmonic spin Josephson currents. The interplay between Rashba spin-orbit interaction and the exchange field breaks inversion and time-reversal symmetries, generating additional cosine terms in the spin current-phase relations and a finitephase shift. This phase shift induces an intrinsic asymmetry between forward and backward spin currents, leading to the SJDE without an external magnetic field. Numerical results show that the efficiency decreases with increasing metal thickness due to suppression of the second-harmonic component, while its dependence on spin-orbit interaction strength reflects competing effects between phase shift enhancement and harmonic suppression. These findings demonstrate that the interplay between harmonic components provides a mechanism for nonreciprocal spin transport without requiring suppression of spin-singlet correlations.