Josephson junctions with chiral p-wave ferromagnetic superconductor reservoirs in presence of spin-orbit coupling interaction

Abstract

The spin transfer torque (STT), is studied in new cases of Josephson junctions containing triplet p-wave chiral ferromagnetic superconductor reservoirs (FS). To be more precise, FS$_1$|spin orbit coupling layer (SOC$_1$)|Normal metal (N)|SOC$_2$|FS$_2$ materials have been investigated. Specifically, FS$_1$|N|FS$_2$ structure with one layer of SOC at FS$_1$|N interface and also two layers of SOC at both FS$_1$|N and N|FS$_2$ interfaces are investigated. For the structures including two SOC layers, both symmetric and asymmetric cases with respectively equal and different potential strengths are studied. The ballistic Josephson junctions are studied solving the Bogoliubov-de-Gennes equation. In particular, the cases with short normal metal contacts with thickness much smaller than the superconducting coherence length, $\psi$, are studied. It is obtained for the case with only one SOC layer, while the absolute value of the out-of-plane STT remains almost unchanged, its direction reverses for lower values of $\alpha$, the angle between exchange fields of the two ferromagnetic superconductors. Also, the nanosystem in presence of two similar SOCs, exhibits lower out-of-plane STT. This is justified as the unit vector along the interface normal for the SOC$_1$ is in the opposite direction of the second SOC$_2$ layer. Hence, one can expect that these potentials fade the effect of each other. When the SOCs are not the same and have different values of potential strength, the out-of-plane STT reduces less which is attributed to slighter cancellation due to unequal potential strength. Moreover, the barrier strength is varied. It has been shown that the barrier strength increment changes the behavior of the STT. Particularly, it is found that it results in sign and value change of the STT. Further, the emergence of in-plane STTs in presence of SOC are confirmed and investigated for various systems.