Proximity effects and triplet correlations in ferromagnet/ferromagnet/superconductor nanostructures

We report the results of a study of superconducting proximity effects in clean ferromagnet/ferromagnet/ superconductor (F1F2S) heterostructures, where the pairing state in S is a conventional singlet s-wave. We numerically find the self-consistent solutions of the Bogoliubov-de Gennes (BdG) equations and use these solutions to calculate the relevant physical quantities. By linearizing the BdG equations, we obtain the superconducting transition temperatures T-c as a function of the angle alpha between the exchange fields in F-1 and F-2. We find that the results for T-c (alpha) in F1F2S systems are clearly different from those in F1SF2 systems, where T-c monotonically increases with alpha and is highest for antiparallel magnetizations. Here, T-c(alpha) is in general a nonmonotonic function, and often has a minimum near alpha approximate to 80 degrees. For certain values of the exchange field and layer thicknesses, the system exhibits reentrant superconductivity with alpha: it transitions from superconducting to normal, and then returns to a superconducting state again with increasing alpha. This phenomenon is substantiated by a calculation of the condensation energy. We compute, in addition to the ordinary singlet pair amplitude, the induced odd triplet pairing amplitudes. The results indicate a connection between equal-spin triplet pairing and the singlet pairing state that characterizes T-c. We find also that the induced triplet amplitudes can be very long ranged in both the S and F sides and characterize their range. We discuss the average density of states for both the magnetic and the S regions, and its relation to the pairing amplitudes and T-c. The local magnetization vector, which exhibits reverse proximity effects, is also investigated.