Spin-polarized Josephson current in SFS junctions with inhomogeneous magnetization

TL;DR

This paper numerically investigates how inhomogeneous magnetization textures in SFS junctions affect spin and charge transport, revealing unique behaviors of spin current and its relation to the 0-$$ transition.

Contribution

It introduces a detailed numerical analysis of spin and charge transport in SFS junctions with non-uniform magnetization, including domain walls and conical ferromagnetism, highlighting the impact on 0-$$ transitions and spin current symmetry.

Findings

Spin current can be non-zero even when charge current vanishes.

Spin current exhibits discontinuous jumps at 0-$$ transition points.

The symmetry of the spin current differs from the charge current with respect to phase reversal.

Abstract

SHORTENED ABSTRACT: We study numerically the properties of spin- and charge-transport in a nanoscale diffusive superconductor$\mid$ferromagnet$\mid$superconductor junction when the magnetization texture is non-uniform. Specifically, we incorporate the presence of a Bloch/Neel domain walls and conical ferromagnetism, including spin-active interfaces. The superconducting leads are assumed to be of s-wave type. We investigate how the 0-$\pi$ transition is influenced by the inhomogeneous magnetization texture and focus on the particular case where the charge-current vanishes while the spin-current is non-zero. In the case of a Bloch/Neel domain-wall, the spin-current can be seen only for one component of the spin polarization, whereas in the case of conical ferromagnetism the spin-current has the three components. We explain all of these results in terms of the interplay between the triplet anomalous Green's function induced in the ferromagnetic region and the local direction of the magnetization vector in the ferromagnet. Interestingly, we find that the spin-current exhibits discontinuous jumps at the 0--$\pi$ transition points of the critical charge-current. We explain this result in terms of the different symmetry obeyed by the current-phase relation when comparing the charge- and spin-current. Specifically, we find that whereas the charge-current obeys the well-known relation $I_c(\phi) = -I_c(2\pi-\phi)$, the spin-current satisfies $I_s(\phi) = I_s(2\pi-\phi)$, where $\phi$ is the superconducting phase difference.