Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization

We calculate the dc Josephson current IJ for two types of superconductor-ferromagnet (S/F) Josephson junctions. The junction of the first type is a S/F/S junction. On the basis of the Eilenberger equation, the Josephson current is calculated for an arbitrary impurity concentration. If hτ1, the expression for the Josephson critical current Ic is reduced to that which can be obtained from the Usadel equation $(h$ is the exchange energy, and {τ} is the momentum relaxation time). In the opposite limit hτ1 the superconducting condensate oscillates with period vF/h and penetrates into the F region over distances of the order of the mean free path l. For this kind of junctions we also calculate IJ in the case when the F layer presents a nonhomogeneous (spiral) magnetic structure with the period 2π/Q. It is shown that for not too low temperatures, the {π} state which occurs in the case of a homogeneous magnetization $(Q=0)$ may disappear even at small values of Q. In this nonhomogeneous case, the superconducting condensate has a nonzero triplet component and can penetrate into the F layer over a long distance of the order of ξT=√D/2πT. The junction of the second type consists of two S/F bilayers separated by a thin insulating film. It is shown that the critical Josephson current Ic depends on the relative orientation of the effective exchange field h of the bilayers. In the case of an antiparallel orientation, Ic increases with increasing h. We establish also that in the F film deposited on a superconductor, the Meissner current created by the internal magnetic field may be both diamagnetic or paramagnetic.