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

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

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices.

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Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications

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

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Superconducting Spintronics

Eilenberger's transportlike equations for a superconductor of type II can be simplified very much in the dirty limit. In this limit a diffusionlike equation is derived which is the generalization of the de Gennes-Maki theory for dirty superconductors to arbitrary values of the order parameter.

Generalized Diffusion Equation for Superconducting Alloys

The magnetic behavior of a type-II superconductor with very short electron mean free path (dirty limit) near its upper critical field ${B}_{c2}(T)$ is investigated. A calculation of the magnetization up to the second order in the difference between ${B}_{c2}(T)$ and the external magnetic field is presented which is valid for all temperatures. A triangular and a square lattice of flux lines are considered. A numerical calculation suggests that the triangular lattice remains stable despite the fact that the difference in the thermodynamical potentials between the two lattices decreases due to these second-order terms.

Magnetization of Dirty Superconductors near the Upper Critical Field

summary. An ocean-coast model which consists of a uniformly conducting half-space screened by a perfectly conducting half-plane (the model ocean) is studied. On the land the electric field decreases continuously to zero as the coast is approached. The horizontal magnetic field component is found to vary rapidly, but remains finite; the vertical component on the other hand, increases to infinity at the coast. On the surface of the model ocean as well as on the sea floor, electric field and vertical magnetic field are both nil, but the horizontal magnetic field becomes singular as the seashore is approached. This horizontal magnetic field however, is different on the sea floor and at the ocean surface, because the integrated ocean current is finite, even growing to infinity as the shore is approached. The very large ocean currents near the shore act as an extremely long line antenna, which radiates far afield. This antenna feature explains the very long range of the ocean-coast effects observed under E-polarization induction, compared to the corresponding H-polarization effects where no such antenna-like feature occurs. A similarly large difference of ranges can be expected for all shallow structures with large lateral conductivity contrasts. The present study may therefore be of some interest in relation to geomagnetic depth soundings by the inductive and magnetotelluric methods, as well as in understanding the ocean-coast effect known for some time from records of coastal observatories.

Electromagnetic response of an ocean-coast model to E-polarization induction

Samples in the shape of a double cross are analyzed, both theoretically and rheographically, as to their suitability for resistivity measurements. It is found, provided certain geometrical limitations are observed, that the presence of lateral arms instead of true point contacts has very little effect on the resistance observed. Typically, the voltage measured between the ends of lateral arms with half the cross section of the main sample body and separated by eight sample widths, is only 1% less than the voltage between two point contacts of similar separation placed on the main sample body. For known dimensions the effect of the side arms is calculated rigorously. Excellent agreement is found with measurements. The rheographic experiments also show that current and voltage arms need only be two or three times as long as they are wide to ensure the validity of the calculation.

Klaus D. Usadel

Papers

Generalized Diffusion Equation for Superconducting Alloys

Magnetization of Dirty Superconductors near the Upper Critical Field

Electromagnetic response of an ocean-coast model to E-polarization induction

Resistivity measurements with samples in the form of a double cross

Magnetization of strong-coupling superconductors for which K2(t) < K1(t) ≈ 1√2.