The proximity effect at superconductor-ferromagnet interfaces produces damped oscillatory behavior of the Cooper pair wave function within the ferromagnetic medium. This is analogous to the inhomogeneous superconductivity, predicted long ago by Fulde and Ferrell (P. Fulde and R. A. Ferrell, 1964, ``Superconductivity in a strong spin-exchange field,'' Phys. Rev. 135, A550--A563), and by Larkin and Ovchinnikov (A. I. Larkin and Y. N. Ovchinnikov, 1964, ``Inhomogeneous state of superconductors,'' Zh. Eksp. Teor. Fiz. 47, 1136--1146 [Sov. Phys. JETP 20, 762--769 (1965)]), and sought by condensed-matter experimentalists ever since. This article offers a qualitative analysis of the proximity effect in the presence of an exchange field and then provides a description of the properties of superconductor-ferromagnet heterostructures. Special attention is paid to the striking nonmonotonic dependence of the critical temperature of multilayers and bilayers on the ferromagnetic layer thickness as well as to the conditions under which ``$\ensuremath{\pi}$'' Josephson junctions are realized. Recent progress in the preparation of high-quality hybrid systems has permitted the observation of many interesting experimental effects, which are also discussed. Finally, the author analyzes the phenomenon of domain-wall superconductivity and the influence of superconductivity on the magnetic structure in superconductor-ferromagnet bilayers.

Proximity effects in superconductor-ferromagnet heterostructures

Materials with flat electronic bands often exhibit exotic quantum phenomena owing to strong correlations. An isolated low-energy flat band can be induced in bilayer graphene by simply rotating the layers by 1.1°, resulting in the appearance of gate-tunable superconducting and correlated insulating phases. In this study, we demonstrate that in addition to the twist angle, the interlayer coupling can be varied to precisely tune these phases. We induce superconductivity at a twist angle larger than 1.1°—in which correlated phases are otherwise absent—by varying the interlayer spacing with hydrostatic pressure. Our low-disorder devices reveal details about the superconducting phase diagram and its relationship to the nearby insulator. Our results demonstrate twisted bilayer graphene to be a distinctively tunable platform for exploring correlated states.

https://science.sciencemag.org/content/sci/early/2019/01/23/science.aav1910.full.pdf

Tuning superconductivity in twisted bilayer graphene.

This review considers unusual effects in superconductor-ferromagnet structures, in particular, the triplet component of the condensate generated in those systems. This component is odd in frequency and even in momentum, which makes it insensitive to nonmagnetic impurities. If the exchange field is not homogeneous in the system, the triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. Some other effects considered here and caused by the proximity effect are enhancement of the Josephson current due to the presence of the ferromagnet, induction of a magnetic moment in superconductors resulting in a screening of the magnetic moment, and formation of periodic magnetic structures due to the influence of the superconductor. Finally, theoretical predictions are compared with existing experiments.

https://arxiv.org/pdf/cond-mat/0506047.pdf

Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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The current-phase relation in Josephson junctions

Traditional studies that combine spintronics and superconductivity have mainly focused on the injection of spin-polarized quasiparticles into superconducting materials However, a complete synergy between superconducting and magnetic orders turns out to be possible through the creation of spin-triplet Cooper pairs, which are generated at carefully engineered superconductor interfaces with ferromagnetic materials Currently, there is intense activity focused on identifying materials combinations that merge superconductivity and spintronics to enhance device functionality and performance The results look promising: it has been shown, for example, that superconducting order can greatly enhance central effects in spintronics such as spin injection and magnetoresistance Here, we review the experimental and theoretical advances in this field and provide an outlook for upcoming challenges in superconducting spintronics

/pdf/superconducting-spintronics-3kqdqwe8bp.pdf

Superconducting Spintronics

We report measurements of the temperature dependence of the critical current, Ic, in Josephson junctions consisting of conventional superconducting banks of Nb and a weakly ferromagnetic interlayer of a CuxNi1-x alloy, with x around 0.5. With decreasing temperature Ic generally increases, but for specific thicknesses of the ferromagnetic interlayer, a maximum is found followed by a strong decrease down to zero, after which Ic rises again. Such a sharp cusp can be explained only by assuming that the junction changes from a 0-phase state at high temperatures to a I� phase state at low temperatures.

/pdf/coupling-of-two-superconductors-through-a-ferromagnet-3w5q1nmeub.pdf

Coupling of two superconductors through a ferromagnet: evidence for a pi junction.

Coupling of Two Superconductors through a Ferromagnet

We report a direct observation of the transition of the superconductor-ferromagnet-superconductor (SFS) junctions to the \ensuremath{\pi} state This manifests itself in the half-period shift of the external magnetic field dependence of the transport critical current in the triangular SFS arrays The shift is associated with the appearance of spontaneous supercurrents in the array at zero external field, with the ground state degenerated with respect to the two possible current flow directions In conventional Josephson arrays this state can be observed only by imposing a frustrating external field equal to a half-integer number of magnetic flux quanta per array cell

Intrinsically frustrated superconducting array of superconductor-ferromagnet-superconductor π junctions

We have observed and studied critical supercurrents, I c , in cross-type Nb–Cu/Ni–Nb junctions with Josephson layers prepared from diluted ferromagnetic alloys. For suitable values of the exchange energy in the ferromagnet and the F-layer thickness we have observed I c ( T ) oscillation with vanishing I c for definite values of T and d F .

Supercurrents through the superconductor–ferromagnet–superconductor (SFS) junctions

The field dependence of the magnetic moment of square (100×100) Josephson networks was examined with the use of a SQUID magnetometer. The field dependence of the magnetic moment was found to be regular with features corresponding to integer and half-integer numbers of flux quanta per cell. At temperatures below 5.8 K, jumps in the magnetization curves associated with the entry and exit of avalanches of tens and hundreds of fluxons were observed. It was shown that the probability distribution of these processes corresponded to the theory of self-organized criticality. An avalanche character of flux motion was observed at temperatures at which the size of the fluxons did not exceed the size of the cell, that is, when a discrete vortex structure occurred.

A. V. Veretennikov

Papers

Coupling of two superconductors through a ferromagnet: evidence for a pi junction.

Coupling of Two Superconductors through a Ferromagnet

Intrinsically frustrated superconducting array of superconductor-ferromagnet-superconductor π junctions

Supercurrents through the superconductor–ferromagnet–superconductor (SFS) junctions

Magnetic properties of two-dimensional Josephson networks: Self-organized criticality in magnetic flux dynamics