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

Abstract

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 Tc as a function of the angle α between the exchange fields in F1 and F2. We find that the results for Tc(α) in F1F2S systems are clearly different from those in F1SF2 systems, where Tc monotonically increases with α and is highest for antiparallel magnetizations. Here, Tc(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 Tc. 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 Tc. The local magnetization vector, which exhibits reverse proximity effects, is also investigated.

Source-reported materials — not catalogue approval

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