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

摘要

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 (hat 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.