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 presents a summary and evaluation of the experimental properties of unconventional superconductivity in ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ as they were known in the spring of 2002. At the same time, the paper is intended to be useful as an introduction to the physics of spin-triplet superconductivity. First, the authors show how the normal-state properties of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ are quantitatively described in terms of a quasi-two-dimensional Fermi liquid. Then they summarize its phenomenological superconducting parameters in the framework of the Ginzburg-Landau model, and discuss the existing evidence for spin-triplet pairing. After a brief introduction to the vector order parameter, they examine the most likely symmetry of the triplet state. The structure of the superconducting energy gap is discussed, as is the effect of symmetry-breaking magnetic fields on the phase diagram. The article concludes with a discussion of some outstanding issues and desirable future work. Appendixes on additional details of the normal state, difficulty in observing the bulk Fermi surface by angle-resolved photoemission, and the enhancement of superconducting transition temperature in a two-phase ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}\ensuremath{-}\mathrm{Ru}$ system are included.

The superconductivity of Sr 2 RuO 4 and the physics of spin-triplet pairing

Since the 1950s, Heisenberg and others have addressed the problem of how to explain the appearance of countable particles in continuous fields. Stable localized field configurations were searched for an ingredient for a general field theory of elementary particles, but the majority of nonlinear field models were unable to predict them. As an exception, Skyrme succeeded in describing nuclear particles as localized states, so-called 'skyrmions'. Skyrmions are a characteristic of nonlinear continuum models ranging from microscopic to cosmological scales. Skyrmionic states have been found under non-equilibrium conditions, or when stabilized by external fields or the proliferation of topological defects. Examples are Turing patterns in classical liquids, spin textures in quantum Hall magnets, or the blue phases in liquid crystals. However, it has generally been assumed that skyrmions cannot form spontaneous ground states, such as ferromagnetic or antiferromagnetic order, in magnetic materials. Here, we show theoretically that this assumption is wrong and that skyrmion textures may form spontaneously in condensed-matter systems with chiral interactions without the assistance of external fields or the proliferation of defects. We show this within a phenomenological continuum model based on a few material-specific parameters that can be determined experimentally. Our model has a condition not considered before: we allow for softened amplitude variations of the magnetization, characteristic of, for instance, metallic magnets. Our model implies that spontaneous skyrmion lattice ground states may exist generally in a large number of materials, notably at surfaces and in thin films, as well as in bulk compounds, where a lack of space inversion symmetry leads to chiral interactions.

Spontaneous skyrmion ground states in magnetic metals

This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

The hunt for new materials exhibiting high-temperature superconductivity is on again. A complex iron-based oxide, containing lanthanum and arsenic, was recently found to exhibit a transition temperature (Tc) of about 26 K when doped with fluoride ions. That's respectable, but far from the heights achieved in copper oxide superconductors. Now Takahashi et al. show that the application of around 40,000 atmospheres of pressure can raise the Tc of this material substantially, to about 43 K. This is the highest tc yet reported for a non-copper-based material. What is more, this record is unlikely to last for long: the complexity of 'iron oxypnictides' of this type offers considerable flexibility for chemical modification, and we can expect to hear of yet higher transition temperatures. This paper — and the prospect of a new wave of superconductor fever — is the subject of an Editorial in the 24 April issue of Nature (452, 914; 2008). The application of pressure can raise the superconducting transition temperature of oxypnictide (a pnicogen being a group V element) substantially, to a maximum value of about 43 K. This is the highest transition temperature yet reported for a non-copper-based material, but this record is unlikely to last for long: the material system offers considerable flexibility for chemical modification, and we can reasonably anticipate that this record will soon be superseded. The iron- and nickel-based layered compounds LaOFeP (refs 1, 2) and LaONiP (ref. 3) have recently been reported to exhibit low-temperature superconducting phases with transition temperatures Tc of 3 and 5 K, respectively. Furthermore, a large increase in the midpoint Tc of up to ∼26 K has been realized4 in the isocrystalline compound LaOFeAs on doping of fluoride ions at the O2- sites (LaO1-xFxFeAs). Experimental observations5,6 and theoretical studies7,8,9 suggest that these transitions are related to a magnetic instability, as is the case for most superconductors based on transition metals. In the copper-based high-temperature superconductors, as well as in LaOFeAs, an increase in Tc is often observed as a result of carrier doping in the two-dimensional electronic structure through ion substitution in the surrounding insulating layers, suggesting that the application of external pressure should further increase Tc by enhancing charge transfer between the insulating and conducting layers. The effects of pressure on these iron oxypnictide superconductors may be more prominent than those in the copper-based systems, because the As ion has a greater electronic polarizability, owing to the covalency of the Fe–As chemical bond, and, thus, is more compressible than the divalent O2- ion. Here we report that increasing the pressure causes a steep increase in the onset Tc of F-doped LaOFeAs, to a maximum of ∼43 K at ∼4 GPa. With the exception of the copper-based high-Tc superconductors, this is the highest Tc reported to date. The present result, together with the great freedom available in selecting the constituents of isocrystalline materials with the general formula LnOTMPn (Ln, Y or rare-earth metal; TM, transition metal; Pn, group-V, ‘pnicogen’, element), indicates that the layered iron oxypnictides are promising as a new material platform for further exploration of high-temperature superconductivity.

Superconductivity at 43 K in an iron-based layered compound LaO 1-x F x FeAs

The absence of simple examples of superconductivity adjoining itinerant-electron ferromagnetism in the phase diagram has for many years cast doubt on the validity of conventional models of magnetically mediated superconductivity. On closer examination, however, very few systems have been studied in the extreme conditions of purity, proximity to the ferromagnetic state and very low temperatures required to test the theory definitively. Here we report the observation of superconductivity on the border of ferromagnetism in a pure system, UGe2, which is known to be qualitatively similar to the classic d-electron ferromagnets. The superconductivity that we observe below 1 K, in a limited pressure range on the border of ferromagnetism, seems to arise from the same electrons that produce band magnetism. In this case, superconductivity is most naturally understood in terms of magnetic as opposed to lattice interactions, and by a spin-triplet rather than the spin-singlet pairing normally associated with nearly antiferromagnetic metals.

P. Monthoux

Papers

Superconductivity on the border of itinerant-electron ferromagnetism in UGe2

Superconductivity on the border of itinerant electron ferromagnetism in UGe2