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 (F ₁F ₂S) 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 α between the exchange fields in F ₁ and F ₂. We find that the results for T _c(α) in F ₁F ₂S systems are clearly different from those in F ₁SF ₂ systems, where T _c monotonically increases with α and is highest for antiparallel magnetizations. Here, T _c(α) is in general a nonmonotonic function, and often has a minimum near α 80 ^-. For certain values of the exchange field and layer thicknesses, the system exhibits reentrant superconductivity with α: it transitions from superconducting to normal, and then returns to a superconducting state again with increasing α. 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.