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.
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