The Andreev reflection amplitude at a clean interface between a half-metallic ferromagnet (H) and a superconductor (S) for which the half metal's magnetization has a gradient perpendicular to the interface is proportional to the excitation energy ɛ and vanishes at ɛ=0 [Béri et al., Phys. Rev. B 79, 024517 (2009)]. Here we show that the presence of impurities at or in the immediate vicinity of the HS interface leads to a finite Andreev reflection amplitude at ɛ=0. This impurity-assisted Andreev reflection dominates the low- bias conductance of an HS junction and the Josephson current of an SHS junction in the long-junction limit.
