Yu. N. Proshin

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.

Current switches based on asymmetric ferromagnet-superconductor nanostructures with allowance for a triplet channel in an external magnetic field

We analyze the properties of asymmetric three-layer (FSF and FFS) heterostructures consisting of a ferromagnet (F) and a superconductor (S) in an external magnetic field. The asymmetry of FS systems can be due to the difference in the parameters characterizing the F layers (in particular, noncollinearity of the magnetizations of the ferromagnets, leading to the generation of the long-range triplet component of the superconducting condensate). We consider the case of strong scattering of conduction electrons from non-magnetic impurities (the so-called dirty limit), for which we derive the equations for the pair amplitude and corresponding boundary conditions to these equations, which are valid in the presence of an external magnetic field. We discuss possible applications of these FS heterostructures as spin switches on the basis of analysis of their phase diagrams, and we give recommendations for determining the optimal parameters required for their stable operation. The occurrence of peculiar re-entrant superconductivity in the FFS systems on an increase of the external magnetic field is predicted.

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.

The influence of an external magnetic field on the triplet proximity effect in ferromagnet/superconductor trilayers

The properties of the ferromagnet/superconductor (FS) system are theoretically studied in an external magnetic field. We consider the boundary value problem for the Usadel-like equations in the case of the so-called ?dirty? limit. Based on a fit of theoretical and known experimental data for the real symmetrical CuNi/Nb/CuNi trilayer, we expand upon numerical predictions on the asymmetrical F1SF2 and F1F2S systems. It is shown that the asymmetry essentially influences the critical properties of both the trilayers. The appearance of peculiar solitary re-entrant superconductivity caused by an external magnetic field is predicted for the F1F2S system.

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.

Solitary superconductivity in a ferromagnet–superconductor heterostructure

A ferromagnet (F)–superconductor (S) (F1F2S) three-layer heterostructure has been studied using Usadel equations with allowance for the pair electron–electron interaction in ferromagnetic layers. The appearance of regions with solitary superconductivity on the phase diagram has been predicted for the antiparallel configuration of the magnetization in F layers. Conditions for the possible experimental observation of solitary superconductivity in FFS three-layer structures, as well as for the detection of the electron–electron interaction in ferromagnets, have been discussed.

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.