Solitary re-entrant superconductivity in asymmetrical FSF structures

Solving the boundary value problem for the Eilenberger function, the superconducting and magnetic states of asymmetric ferromagnet–superconductor–ferromagnet (F₁SF₂) nanostructures are investigated. The dependences of critical temperature on an exchange field of the F metal, electronic correlations in the S and F metals, and thicknesses of layers F and S are derived. It is shown that the possibility of the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) state observation is especially increased in the asymmetrical trilayers F₁SF₂ for which solitary re-entrant superconductivity is predicted. The possibility of solitary re-entrant superconductivity for asymmetrical trilayers F₁SF₂ in the dirty limit is also shown.     

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.     

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 T _c than the known 1D LOFF states. It is shown that the nonmonotonic behavior of T _c 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 T _c on the F layer thickness d _f . An interpretation of the behavior of the experimental dependences T _c (d _f ) obtained for F/S structures is proposed.     

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.     

Screening properties of multiply connected ferromagnet–superconductor hybrid structures

Superconducting phase transition temperature T _c of a ferromagnet/superconductor (SF) hybrid structure consisting of a hollow superconducting (S) cylinder (shell) with the central part (core) filled with a ferromagnetic (F) metal has been analyzed on the basis of linearized Usadel equations. It has been shown that the proximity effect between the S and F metals, as well as the exchange interaction, may induce an inhomogeneous superconducting state with Δ ~ exp(iLθ + ipz), which is characterized by nonzero circulation of phase L and wavenumber p describing the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) instability along the cylinder axis. The transitions between the states with different values of L and p, which are accompanied by a nonmonotonic dependence of superconducting transition temperature T _c and effective magnetic field penetration depth Λ into the SF structure on the characteristic size of the ferromagnetic region, have been investigated.     

Peculiarities of the proximity effect in superconductor-multilayered ferromagnet structures with collinear magnetizations in ferromagnetic layers

The proximity effect is investigated theoretically in different superconducting structures including multilayered ferromagnet consisting of arbitrary number of metallic ferromagnet (F) layers. The in-plane exchange fields in the F-layers are supposed to be collinear. Different cases of the exchange fields ordering including the case of antiferromagnetic one. It is shown for the last case that the proximity effect (for the fixed thickness of the M-interlayer) increases with the growing number of the layers N and significantly depends on whether this number is odd or even. It is shown that under the condition of diffusive electron transport, the anomalous proximity effect is exhibited which is related with singlet component of the condensate Green’s function. Peculiarities of the proximity effect are analyzed for S-M, S-I-M-S, and S-M-S superconducting structures (S is a superconductor, I is an insulating layer). It is shown that when the M-structure consists of N seriously connected F₁-N-F₂-N links in which F layers are separated by normal metallic layers (N), for antiferro-magnetic ordering of the magnetization the exchange field induced enhancement of the critical current may occur.     

Angular dependence of the superconducting transition temperature in ferromagnet-superconductor-ferromagnet trilayers

The superconducting transition temperature T(c) of a ferromagnet (F)-superconductor (S)-ferromagnet trilayer depends on the mutual orientation of the magnetic moments of the F layers. This effect has been previously observed in F/S/F systems as a T(c) difference between parallel and antiparallel configurations of the F layers. Here we report measurements of T(c) in CuNi/Nb/CuNi trilayers as a function of the angle between the magnetic moments of the CuNi ferromagnets. The observed angular dependence of T(c) is in qualitative agreement with a F/S proximity theory that accounts for the odd triplet component of the condensate predicted to arise for noncollinear orientation of the magnetic moments of the F layers.     

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 T _c 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 T _c in the FM/S superlattices with S-layer thickness d _s less than the threshold value d _s ^π is due to the phase transition cascade 0π-ππ-0π At d _s >d _s ^π , the T _c 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.     

Critical temperature oscillations and reentrant superconductivity due to the FFLO like state in F/S/F trilayers

Ferromagnet/Superconductor/Ferromagnet (F/S/F) trilayers, in which the establishing of a Fulde‐Ferrell Larkin‐Ovchinnikov (FFLO) like state leads to interference effects of the superconducting pairing wave function, form the core of the superconducting spin valve. The realization of strong critical temperature oscillations in such trilayers, as a function of the ferromagnetic layer thicknesses or, even more efficient, reentrant superconductivity, are the key condition to obtain a large spin valve effect, i.e. a large shift in the critical temperature. Both phenomena have been realized experimentally in the Cu₄₁Ni₅₉/Nb/Cu₄₁Ni₅₉ trilayers investigated in the present work.     

Superconducting spin-valve and triplet superconductivity

Recent experimental results on the superconducting spin-valve effect and generation of the long-range triplet superconductivity in a F1/F2/S structure are reviewed (here, F1 and F2 are uncoupled ferromagnetic layers, and S is the superconducting layer). The main results are the following: (i) the maximum of the magnitude of the superconducting spin-valve effect increases with decreasing the exchange field h in the ferromagnetic layer; (ii) a full switching between the normal and superconducting states may be realized with the aid of the triplet contribution to the spin-valve effect.     

Triplet proximity effect in FSF trilayers

We study the critical temperature T _c of FSF trilayers (F is a ferromagnet, S is a singlet superconductor), where the triplet superconducting component is generated at noncollinear magnetizations of the F layers. An exact numerical method is employed to calculate T _c as a function of the trilayer parameters, in particular, mutual orientation of magnetizations. Analytically, we consider limiting cases. Our results determine the conditions necessary for the existence of recently investigated odd triplet superconductivity in SF multilayers.     

Change in the sign of the magnetoresistance effect in bilayer superconductor/ferromagnet structures under change in the type of the domain structure in the ferromagnet

The magnetoresistance effects in the bi- and trilayer hybrid planar superconductor/ferromagnet (S/F) structures based on Py (permalloy) and Nb near the superconducting transition temperature T _C are considered. It has been experimentally shown that the sign of the observed magnetoresistance peaks in the bilayer S/F systems changes from negative to positive at the permalloy layer thickness corresponding to the change in the type of domain walls from Néel to Bloch. For the Néel walls at the ferromagnet coercive fields, the negative magnetoresistance effect, which is due to a decrease in the depairing action of the exchange field E _ex, is observed in the S/F bilayers. For the Bloch domain walls, the magnetoresistance of the bilayer S/F structures is determined by the dissipative motion of Abrikosov vortices in the superconducting layer. In the trilayer F/S/F structures, the magnetoresistance is mainly due to the suppression of the superconducting order parameter in the superconducting layer under the action of the accumulation of the spin-polarized carriers near the S/F interfaces.     

Proximity effect in the finite and incommensurate ferromagnet/superconductor systems

The original theory of a proximity effect is proposed for the bi- and tri-layered system ferromagnetic metal/superconductor (F/S) in dirty limit. The F₁/S/F₂ trilayer is examined more closely. The distinctions in materials, in thicknesses of F layers (d_f1 and d_f2), in parameters interfaces, and in local environments of layers are considered among the causes of incommensurability of trilayer. The peculiar T_c(d_f1, d_f2) interference pattern is predicted for the F₁/S/F₂ systems. The reentrant superconductivity and possibility of the better observability of the spin-valve regime are discussed.     

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 T _c 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 d _f 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 T _s vs. d _f dependence reaches a plateau as d _f 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 T _c (d _f ) 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. Zh. éksp. Teor. Fiz. 113, 1708–1730 (May 1998)     

Effect of the variation of the exchange energy on the superconducting critical temperature of S/F/S trilayers

The effect of the exchange energy variation in weakly ferromagnetic alloys on the superconducting resistive transition of superconductor/ferromagnet/superconductor (S/F/S) trilayers is studied. Critical temperature, T _c , and resistive transitions versus the F-layer thickness, d _F , have been analyzed in Nb/Cu_0.41Ni_0.59/Nb and Nb/Pd_0.81Ni_0.19/Nb trilayers. We show that T _c (d _F ) dependence is sensitive to magnetic inhomogeneities in the F-layer for values of d _F corresponding to thickness range where the π-superconducting state is established.     

Resistive transitions in Nb/Cu0.41Ni0.59/Nb trilayers

The superconducting phase transition in Nb/Cu_0.41Ni_0.59/Nb trilayers, with superconducting (S) Nb and ferromagnetic (F) Cu_0.41Ni_0.59, has been experimentally studied as a function of the F-layer thickness by measuring the temperature dependence of the electrical resistance R(T). It is shown that the shape and the width of the R(T) curves depends on the Cu_0.41Ni_0.59 thickness, in particular in the regime where π is the coupling between the S layers, which can be expected. To explain the data, we developed a qualitative model which makes the interconnection between the superconducting phase transition and the 0 to π transition in SFS structures are more evident. The text was submitted by the authors in English.     

Magnetization modification by superconductivity in Nb/Ni80Fe20/Nb trilayers

We present experimental evidences for magnetization modification by superconductivity in a series of Nb/Ni₈₀Fe₂₀/Nb trilayers. By monitoring the magnetization in a zero field as a function of temperature, we observed an irreversibility in magnetization between the cooling and warming branches just above the superconducting transition temperature T_c. These results suggest that the magnetization of the ferromagnetic Ni₈₀Fe₂₀ layer is reduced by the mutual interactions between the ferromagnet and superconductor. Moreover, this effect diminishes with increasing thickness of the Ni₈₀Fe₂₀ layer, which indicates that the interaction between the superconducting and magnetic layers occurs mainly at the vicinity of the interfaces.     

Triplet pairing states with equal spins in ferromagnet/superconductor heterojunctions for noncollinear magnetizations

Four-component Bogoliubov-de Gennes equations are applied to study tunneling conductance spectra of ferromagnet/ferromagnet/d-wave superconductor (F₁/F₂/d-wave S) tunnel junctions and to find out signs of spin-triplet pairing correlations induced in the proximity structure. The pairing correlations with equal spins arises from the novel Andreev reflection (AR), which requires at least three factors: the usual AR at the F₂/S interface, spin flip in the F₂ layer, and superconducting coherence kept up in the F₂ layer. Effects of angle α between magnetizations of the two F layers, polarizations of the F₁ and F₂ layers, the thickness of the F₂ layer, and the orientation of the d-wave S crystal on the tunneling conductance are investigated. A conversion from a zero-bias conductance dip at α = 0 to a zero-bias conductance peak at a certain value of α can be seen as a sign of generated spin-triplet correlations.     

Proximity effect in normal metal/ferromagnet/d-wave superconductor structures

The superconducting proximity effect in normal metal/insulator/ferromagnet/d-wave superconductor (N/I/F/D) structures is studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. The transition from the “0” to “π” state is found in the conductance spectra with increasing thickness of F or the ferromagnetic exchange energy. The superconducting proximity effect is drastically changed by the orientation angle α, as α increases the proximity effect is enhanced, being strongest for α/π = 0.25.