Proximity Effects in Conical-Ferromagnet/Superconductor bilayers

TL;DR

This paper investigates the proximity effects in ferromagnet/superconductor bilayers with spiral magnetic textures, revealing multiple oscillations in transition temperature, reentrant superconductivity phenomena, and long-range triplet pairing, supported by numerical solutions of BdG equations.

Contribution

It introduces a comprehensive numerical analysis of proximity effects in F/S bilayers with spiral magnetism, including T_c oscillations, reentrant behavior, and triplet pairing, advancing understanding of complex magnetic-superconducting interactions.

Findings

Multiple oscillations in T_c as a function of magnetic layer thickness.

Observation of temperature and thickness reentrant superconductivity.

Long-range penetration of triplet pairing components.

Abstract

We study 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 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 with temperature $T$: the superconductivity disappears in certain ranges of $d_F$ or $T$. The $T$ reentrance 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 $m=\pm 1$ 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 DOS, which reveals important energy resolved signatures associated with the proximity effects.