Spin-orbit coupling assisted magnetoanisotropic Josephson effect in ferromagnetic graphene Josephson junctions

The spin-flipping effect can be induced by the Rashba spin-orbit coupling (RSOC), leading to triplet equal-spin pairs in a superconducting hybrid structure. Herein, by combining the Dirac-Bogoliubov-de Gennes equation and the Furusaki-Tsukada formalism at a finite temperature, we theoretically investigate the Josephson effect in graphene-based superconductor-ferromagnet-R-superconductor junctions, where R refers to a region with the RSOC. It is demonstrated that as a result of the RSOC, one 0-pi transition can be attained by tuning the orientation of the exchange field (h)over-right-arrow, which is determined by its magnitude h that could be periodically taken, and the periodical 0-pi transitions are also caused by manipulating h during a considerable scope of the orientation. More interestingly, although varying the RSOC strength lambda cannot give rise to the 0-pi transition in itself, not only is it a necessary condition for the 0-pi transition induced by modulating the orientation of it but (h)over-right-arrow also can produce the shift of the crossover point. Furthermore, two different kinds of anomalous Josephson current effect are exhibited by controlling the orientation of (h)over-right-arrow. Particularly, the out-of- and in-plane magnetoanisotropic Josephson currents always exist, varying monotonically with lambda while nonmonotonically with h. The characteristics may provide more insights into the proximity-induced RSOC and pave the way to a new class of tunable superconducting spintronic devices based on large-scale graphene.