Charge and Spin Supercurrents in Magnetic Josephson Junctions with Spin Filters and Domain Walls

TL;DR

This paper theoretically investigates how domain walls affect the Josephson current in magnetic superconducting junctions with spin filters, revealing effects like current suppression, diode behavior, and DW positioning forces.

Contribution

It introduces a model analyzing the impact of domain walls on Josephson and spin currents in magnetic Josephson junctions with spin filters, including effects of multiple DWs and skyrmion-like configurations.

Findings

Domain walls reduce the critical Josephson current for equal spin polarization.

Spontaneous currents arise with different chiralities of triplet pairs, causing a diode effect.

The critical current peaks when the DW is at the F layer center.

Abstract

We analyze theoretically the influence of domain walls (DWs) on the DC Josephson current in magnetic superconducting S$_{m}$/Fl/F/Fl/S$_{m}$ junctions. The Josephson junction consists of two "magnetic" superconductors S$_{m}$ (superconducting film covered by a thin ferromagnetic layer), spin filters Fl and a ferromagnetic layer F with or without DW (DWs). The spin filters Fl allow electrons to pass with one specific spin orientation, such that the Josephson coupling is governed by a fully polarized long-range triplet component. In the absence of DW(s), the Josephson and spin currents are nonzero when the right and left filters, Fl$_{r,l}$, pass electrons with equal spin orientation and differ only by a temperature-independent factor. They become zero when the \textbf{spins} of the triplet Cooper pairs passing through the Fl$_{r,l}$ have opposite directions. Furthermore, for the different chiralities of the injected triplet Cooper pairs the spontaneous currents arise in the junction yielding a diode effect. Once a DW is introduced, it reduces the critical Josephson current $I_{c}$ in the case of equal spin polarization and makes it finite in the case of opposite spin orientation. The critical current $I_{c}$ is maximal when the DW is in the center of the F film. A deviation of the DW from the center generates a force that pushes the DW to the center of the F film. In addition, we consider the case of an arbitrary number $N$ of DW's, with the case $N=2$ corresponding to a model system for a magnetic skyrmion.