Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization

We calculate the dc Josephson current I-J 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 h(tau)<<1, the expression for the Josephson critical current I-c is reduced to that which can be obtained from the Usadel equation (h is the exchange energy, and tau is the momentum relaxation time). In the opposite limit h tau>>1 the superconducting condensate oscillates with period upsilon (F)/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 I-j in the case when the F layer presents a nonhomogeneous (spiral) magnetic structure with the period 2 pi /Q. It is shown that for not too low temperatures, the pi 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 xi (T)= rootD/2 piT. 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 I-c depends on the relative orientation of the effective exchange field h of the bilayers. In the case of an antiparallel orientation, I-c 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.