Switching effects in superconductor/ferromagnet/superconductor graphene junctions

The Josephson effect in the superconductor/ferromagnet/superconductor (SFS) graphene Josephson junction is studied using the Dirac Bogoliubov-de Gennes (DBdG) formalism. It is shown that the SFS graphene junction drives 0–π transition with the increasing of p=h₀L/v_Fħ, which captures the effects of both the exchange field and the length of the junction; the spin-down current is dominant. The 0 state is stable for p < p_c (critical value p_c ≈ 0.80) and the π state is stable for p > p_c, where the free energy minima are at φ_g=0 and φ_g=π, respectively. The coexistence of the 0 and π states appears in the vicinity of p_c.