Spin-dependent Cooper Pair Phase and Pure Spin Supercurrents in Strongly Polarized Ferromagnets

We study heterostructures of singlet superconductors (SC) and strongly spin-polarized ferromagnets (sFM) and show that a relative phase arises between the superconducting proximity amplitudes in the two ferromagnetic spin bands. We find a tunable pure spin supercurrent in a sFM contacted with only one SC electrode. We show that Josephson junctions are most effective for a spin polarization $P\sim 0.3$, and that critical currents for positive and negative bias differ for a high transmission Josephson junction, due to a relative phase between single and double pair transmission.