### Abstract

We present a study of various aspects of proximity effects in F/S (ferromagnet/superconductor) bilayers, where F has a spiral magnetic texture such as that found in holmium, erbium, and other materials, and S is a conventional s-wave superconductor. We numerically solve the Bogoliubov-de Gennes (BdG) equations self-consistently and use the solutions to compute physical quantities relevant to the proximity effects in these bilayers. We obtain the relation between the superconducting transition temperature T _{c} and the thicknesses d_{F} of the magnetic layer by solving the linearized BdG equations. We find that the T_{c}(d_{F}) curves include multiple oscillations. Moreover, the system may be reentrant not only with d_{F}, as is the case when the magnet is uniform, but also with temperature T: the superconductivity disappears in certain ranges of d _{F} or T. The T reentrance reported here occurs when d_{F} is larger than the spatial period of the conical exchange field. We compute the condensation free energies and entropies from the full BdG equations and find the results are in agreement with T_{c} values obtained by linearization. The inhomogeneous nature of the magnet makes it possible for all odd triplet pairing components to be induced. We have investigated their properties and found that, as compared to the singlet amplitude, both the m=0 and ±1 triplet components exhibit long-range penetration. For nanoscale bilayers, the proximity lengths for both layers are also obtained. These lengths oscillate with d_{F} and they are found to be long range on both sides. These results are shown to be consistent with recent experiments. We also calculate the reverse proximity effect described by the three-dimensional local magnetization, and the local density of states, which reveals important energy-resolved signatures associated with the proximity effects.

Original language | English |
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Article number | 184517 |

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

Volume | 86 |

Issue number | 18 |

DOIs | |

State | Published - 30 Nov 2012 |

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## Cite this

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

*86*(18), [184517]. https://doi.org/10.1103/PhysRevB.86.184517