Minigap in superconductor-ferromagnet junctions with inhomogeneous magnetization

We consider the minigap in a disordered ferromagnet (F) in contact with a superconductor (S) in the situation when the magnetization of the F layer is inhomogeneous in space and noncollinear. If the magnetization is strongly inhomogeneous, it effectively averages out, and the minigap survives up to the exchange field h_c∼(L/a)E_Th , where L is the thickness of the F layer, a is the scale on which the magnetization varies, and E_Th is the Thouless energy. Technically, we use the “triplet” version of the Usadel equations, including both singlet and triplet components of the Green’s functions. In many cases, the effect of disordered magnetization may be effectively included in the conventional Usadel equations as the spin-flip scattering term. In the case of low-dimensional magnetic inhomogeneities (we consider spiral magnetization as an example), however, the full set of “triplet” equations must be solved.