### Abstract

We report the results of a study of superconducting proximity effects in clean ferromagnet/ferromagnet/superconductor (F _{1}F _{2}S) 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 _{1}F _{2}S systems are clearly different from those in F _{1}SF _{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.

Original language | English (US) |
---|---|

Article number | 014523 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 86 |

Issue number | 1 |

DOIs | |

State | Published - Jul 31 2012 |

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### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*86*(1), [014523]. https://doi.org/10.1103/PhysRevB.86.014523

**Proximity effects and triplet correlations in ferromagnet/ferromagnet/ superconductor nanostructures.** / Wu, Chien Te; Valls, Oriol T; Halterman, Klaus.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 86, no. 1, 014523. https://doi.org/10.1103/PhysRevB.86.014523

}

TY - JOUR

T1 - Proximity effects and triplet correlations in ferromagnet/ferromagnet/ superconductor nanostructures

AU - Wu, Chien Te

AU - Valls, Oriol T

AU - Halterman, Klaus

PY - 2012/7/31

Y1 - 2012/7/31

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevB.86.014523

DO - 10.1103/PhysRevB.86.014523

M3 - Article

VL - 86

JO - Physical Review B

JF - Physical Review B

SN - 2469-9950

IS - 1

M1 - 014523

ER -