M. G. Khusainov

Nonmonotonic behavior of the superconducting transition temperature in bimetallic ferromagnet-superconductor structures

For layered ferromagnet/superconductor (F/S) structures we develop a theory of the proximity effect. In contrast to previous approaches, this theory allows for a finite transmission coefficient of the interface between the two metals and competition between the diffusion and spin-wave types of quasiparticle motion in the ferromagnet’s strong exchange field. The superconductivity in F/S systems proves to be a superposition of BCS pairing with a constant-sign pair amplitude in the S-layers and Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) pairing with an oscillating wave function in the F-layers. We show that the oscillatory behavior of the superconducting transition temperature Tc is due to oscillations of the Cooper pair flux from the S-layer to the F-layer, which are the result of oscillations of the discontinuity (jump) of the pair amplitude at the F/S boundary as the thickness df of the F-layer increases. The presence of nonmagnetic impurities leads to heavy damping of the oscillations of the LOFF pair amplitude and rapid deterioration of the coherent coupling of the boundaries of the F-layer in which the Ts vs. df dependence reaches a plateau as df increases. In F/S superlattices, in contrast to F/S double-layer junctions, there are two forms of the LOFF state, the 0-phase and the π-phase, which differ in their symmetry with respect to the center of the F layer. This gives rise to additional oscillations in the Tc (df) dependence due to the 0-π transitions. As the most vivid manifestation of LOFF states in F/S-systems, we predict the existence of recurrent and periodically recurrent superconductivities. We give a qualitative explanation of the different behavior of the superconducting transition temperature observed by different groups of experimenters dealing with the same ferromagnet-superconductor structures.

Separate re-entrant superconductivity in asymmetric ferromagnet/superconductor/ferromagnet trilayers

The superconducting and magnetic states of asymmetric ferromagnet/superconductor/ferromagnet (F/S/F′) nanostructures have been investigated using the boundary value problem for the Eilenberger function. It has been shown that 0- and π-phase superconducting states of pure thin F/S/F′ trilayers are controlled by the magnitude and sign of electron correlations in the F and F′ layers, as well as by the competition between homogeneous Bardeen-Cooper-Schrieffer (BCS) pairing and inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) pairing. The LOFF-BCS-LOFF separate re-entrant superconductivity has been predicted for F/S/F′ trilayers. A continuous control of the pair-breaking factor in the Eilenberger function and transition to the state with re-entrant superconductivity is achieved by varying the thickness of the F′ layer. Sine-modulated 2D LOFF states in asymmetric F/S/F′ trilayers are possible not only for parallel, but also for antiparallel orientations of the magnetizations of the F and F′ layers; this fact significantly facilitates the experimental implementation of the predicted phenomena.

Spontaneous symmetry breaking and a boundary value problem for the proximity effect in ferromagnet/superconductor nanostructures

A three-dimensional (3D) boundary value problem for the Eilenberger function has been microscopically derived. It is applicable for describing the proximity effect in ferromagnet/superconductor (F/S) nanostructures, where the superconductivity is the superposition of the BCS pairing with zero total momentum in the S layers and the pairing through the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) mechanism with nonzero 3D momentum of pairs k in the F layers. It has been shown that continuous matching at the F/S interface occurs only for the pair amplitudes with the same space symmetry. When two pairing types are simultaneously present, the processes of mutual transformations between LOFF and BCS pairs at the F/S interface occur as Umklapp processes through surface states. The phase diagrams of the surface states with the mixed BCS + LOFF pairing type have been analyzed. Superconductivity localized at the F/S interface has been predicted.

Superconducting probe of electronic correlations and exchange field based on the proximity effect in F/S nanostructures

The proximity effect and competition between the BCS and LOFF states are studied in the Cooper limit for thin F/S and F/S/F nanostructures, where F is a ferromagnet and S is a superconductor. The dependences of the critical temperature on the exchange field I, electron correlations λf, and the thickness df of the F layer are derived for F/S bilayers and F/S/F trilayers. In addition, two new π-phase superconducting states with electron-electron repulsion in the F layers of F/S/F trilayers are predicted. A two-dimensional LOFF state in F/S/F trilayers is possible only in the presence of a weak magnetic field and the appropriate parameters of the F and S layers. The absence of the suppression of three-dimensional superconductivity in short-period Gd/La superlattices is explained and the electron-electron coupling constant in gadolinium is predicted. A method of superconducting sounding spectroscopy based on the proximity effect is proposed for determining the symmetry of the order parameter, the magnitude and sign of electron correlations, and the exchange field in various nanomagnets F.

Multicritical behavior of the phase diagrams of ferromagnet/superconductor layered structures

For ferromagnet/superconductor (F/S) layered structures, new 3D Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states are predicted. In most cases, these states are characterized by a higher critical temperature Tc than the known 1D LOFF states. It is shown that the nonmonotonic behavior of Tc is determined by the oscillations of the Cooper pair flux through the F/S boundary, which occur as a result of the 3D-1D-3D phase transitions at the Lifshits triple points. The appearance of the new 3D LOFF states and the presence of nonmagnetic impurities leads to a strong damping of the 1D oscillations of the LOFF pair amplitude and to a considerable smoothing of the dependence of Tc on the F layer thickness df. An interpretation of the behavior of the experimental dependences Tc(df) obtained for F/S structures is proposed.

Manifestations of the Larkin-Ovchinnikov-Fulde-Ferrell state in bimetal ferromagnet-superconductor structures

Reentrant and periodically reentrant superconductivity in contacts and ferromagnet/superconductor (F/S) superlattices are predicted on the basis of the theory developed in this letter. These effects are consequences of the realization of the Larkin-Ovchinnikov-Fulde-Ferrell state in F layers. An explanation is given for the qualitatively different behavior of the critical temperature observed by different experimental groups on identical F/S structures.

Spin screening of magnetic moments and inverse proximity effect in ferromagnet/superconductor nanostructures

It is shown that the short-range oscillating spin polarization of conduction electrons around a magnetic moment embedded in a superconducting film is screened by a long-range antiferromagnetic term, which has its origin in Cooper pairing. Using these results, an exchange model of the proximity effect in ferromagnet/superconductor (F/S) nanostructures is proposed. The mutual accommodation of inhomogeneous superconducting and magnetic order parameters in the F/S nanostructures is studied within the framework of this model. It is shown that F/S nanostructures of the first type allow only the presence of homogeneous ferromagnetic ordering in the F layers that coexists with superconductivity in the S layers if the exchange fields h are lower than a critical field hc. It is found that in the F/S nanostructures of the second type for exchange fields h between hc1 and hc2, where hc1(2) is the lower (upper) critical exchange field, a nonuniform cryptoferromagnetic modulation is induced in the spin structure of the...

Effect of a magnetic field on the critical temperature of a ferromagnet-superconductor transition in layered heterostructures

Effect of an external magnetic field H on the superconductivity of bilayer (FS) and trilayer (FSF) heterostructures consisting of layers of ferromagnetic (F) and superconducting (S) metals has been studied. The case has been considered where the scattering in both metals is sufficiently strong (the so-called “dirty limit”), which makes it possible to use the Usadel equations to describe the proximity effect. For the Gor’kov function, a boundary problem is formulated that is free of restrictions on the magnitudes of the transparency of the FS (SF) interface and takes into account both the wave and diffusional types of motion of quasi-particles. Special attention is given to the case of a trilayer system, for which a detailed analysis of two states with parallel (P) and antiparallel (AP) directions of the magnetizations in the F layers has been performed. Based on the results obtained, the possibility of a technical application of the FSF system is considered.

π-phase magnetism in ferromagnet-superconductor superlattices

New 0π and ππ Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states with antiferromagnetic orientation of magnetizations in the neighboring layers of a ferromagnetic metal (FM) are predicted for FM/superconductor (FM/S) superlattices. Under certain conditions, the critical temperature Tc of these states is higher than for the known 00 and π0 LOFF states with ferromagnetic ordering of the FM layers. It is shown that the nonmonotonic behavior of Tc in the FM/S superlattices with S-layer thickness ds less than the threshold value dsπ is due to the phase transition cascade 0π-ππ-0π At ds>dsπ, the Tc oscillations are caused by the 00-π0-00 transitions. New logic elements based on the FM/S structures and combining the advantages of the superconducting and magnetic data-record channels in a single sample are proposed.

Superconducting spintronic devices based on nanostructures ferromagnet/superconductor

The layered nanostructures ferromagnet/superconductor (F/S) due to combination of incompatible in homogeneous materials properties are the most perspective materials for use in the new field of electronics – a superconducting spintronics. A new type of logical devices based on the layered F/S nanostructures and combining the advantages of the superconducting and magnetic recording channels in one sample is offered. Each channel can be separately controlled by weak magnetic field or current pulse and the switching time is of order of 10−10 – 10−11 s. The implementation of such devices on base of high-temperature superconductors will allow using nitrogen instead of expensive helium for cooling.