Abstract
We study the Josephson effect in graphene-based ballistic superconductor-ferromagnet-superconductor (SFS) junctions. We find an oscillatory Josephson coupling ${I}_{c}{R}_{N}$ of F graphene whose amplitude is nonvanishing for a half-metallic graphene, increases for the exchange fields $h$ above the Fermi energy ${E}_{F}$ and shows only a slow damping at strong exchange fields $h⪢{E}_{F}$. We interpret this long-range Josephson coupling as the result of the exchange mediated Andreev-Klein process at FS interfaces which enhances the induced antiparallel-spin superconducting correlations in F graphene by increasing $h$ above ${E}_{F}$. We further demonstrate the existence of regular temperature-induced transitions between 0 and $\ensuremath{\pi}$ couplings in the plane of $T$ and $h$ where the phase boundaries have distinct shapes at the two regimes of $h$ below and above ${E}_{F}$.
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