Triplet proximity effect in superconducting heterostructures with a half-metallic layer

We present the Usadel theory describing the superconducting proximity effect in heterostructures with a half-metallic layer. It is shown that the full spin polarization inside the half-metals gives rise to an additional component of the Green's function which results in the giant triplet spin-valve effect in superconductor (S)-ferromagnet (F)-half-metal (HM) trilayers and provides a natural explanation for the phi(0)-junction formation in the S/F/HM/F/S systems. In addition, we consider the exactly solvable model of the S/F/HM trilayers of atomic thickness and demonstrate that it reproduces the main features of the spin-valve effect found within the Usadel approach. Our results are shown to be in qualitative agreement with the recent experimental data on the spin-valve effect in MoGe/Ni/Cu/CrO2 hybrids [Singh et al., Phys. Rev. X 5, 021019 (2015)].