We study induced triplet pairing correlations in clean ferromagnet/superconductor/ferromagnet heterostructures. The pairing state in the superconductor is the conventional singlet s-wave, and the angle $α$ between the magnetizations of the two ferromagnetic layers is arbitrary. We use a numerical fully self-consistent solution of the microscopic equations and obtain the time-dependent triplet correlations via the Heisenberg equations of motion. We find that in addition to the usual singlet correlations, triplet correlations, odd in time as required by the Pauli principle, are induced in both the ferromagnets and the superconductor. These time-dependent correlations are largest at times of order of the inverse of the Debye cutoff frequency, $ω_D$, and we find that within that time scale they are often spatially very long ranged. We discuss the behavior of the characteristic penetration lengths that describe these triplet correlations. We also find that the ferromagnets can locally magnetize the superconductor near the interface, and that the local magnetization then undergoes strongly damped oscillations. The local density of states exhibits a variety of energy signatures, which we discuss, as a function of ferromagnetic strength and $α$.
We study theoretically the influence of ferromagnetic metals on a superconducting film in the clean limit. Using a self-consistent solution of the Bogoliubov--de Gennes equation for a ferromagnet-superconductor-ferromagnet double junction we calculate the pair potential and conductance spectra as a function of the superconducting layer thickness $d$ for different strengths of ferromagnets and interface transparencies. We find that the pair potential and the critical temperature are weakly perturbed by the exchange interaction and do not drop to zero for any finite $d$. On the other hand, for t…
We demonstrate that in a wide class of multilayered superconductor - ferromagnet structures (e.g., S/F, S/F/N and S/F/F') the vanishing Meissner effect signals the appearance of the in-plane Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superconducting phase. In contrast to the bulk superconductors the FFLO instability in these systems can emerge at temperatures close to the critical one and is effectively controlled by the S layer thickness and the angle between magnetization vectors in the F/F' bilayers. The predicted FFLO state reveals through the critical temperature oscillations vs th…
We study the thermodynamics of clean structures composed of superconductor (S) and ferromagnet (F) layers and consisting of one or more SFS junctions. We use fully self consistent numerical methods to compute the condensation free energies of the possible order parameter configurations as a function of temperature $T$. As $T$ varies, we find that there are phase transitions between states characterized by different junction configurations (denoted as ``0'' or ``$π$'' according to the phase difference of the order parameter in consecutive S layers). We show that these transitions are of first o…
We study peculiarities of proximity effect in clean superconductor -- ferromagnet structures caused by either spatial or momentum dependence of the exchange field. Even a small modulation of the exchange field along the quasiparticle trajectories is shown to provide a long range contribution to the supercurrent due to the specific interference of particle- and hole- like wave functions. The momentum dependence of the exchange field caused by the spin -- orbit interaction results in the long -- range superconducting correlations even in the absence of ferromagnetic domain structure and can expl…
We analyze the local density of states (LDOS) of heterostructures consisting of alternating ferromagnet, $F$, and superconductor, $S$, layers. We consider structures of the $SFS$ and $SFSFSFS$ type, with thin nanometer scale $F$ and $S$ layers, within the ballistic regime. The spin-splitting effects of the ferromagnet and the mutual coupling between the $S$ regions, yield several nontrivial stable and metastable pair amplitude configurations, and we find that the details of the spatial behavior of the pair amplitude govern the calculated electronic spectra. These are reflected in discernible s…
We present a microscopic calculation of the energy dissipation in the core of a vortex moving in a two-dimensional or layered superconductor in the moderately clean regime. In this regime, the quasiclassical Bardeen--Stephen result remains valid in spite of the strong correlations between the energy levels. We find that the quasiclassical expression applies both in the limit of fast vortex motion (with transitions between smeared levels) and in the limit of slow vortex motion (with nearly adiabatic dynamics). This finding can be related to the similar result known for the unitary random-matrix…
We investigate the structure of quasiparticle states localized in a core of an Abrikosov vortex in a clean layered superconductor in the presence of planar defects. It is shown that even a highly transparent defect opens a minigap at the Fermi energy. Its magnitude, $E_g\simΔ\sqrt{R}$, exceeds the mean level spacing for the chiral branch, $ω_0\simΔ^2/E_F$, already for very small values of the reflection coefficient off the defect, $R\ll1$ ($Δ$ is the bulk gap). For $R\gtrsim\sqrt{Δ/E_F}$, formation of the minigap is accompanied by the appearance of subgap states localized along the defect, in …
We study parametric level statistics of the discretized excitation spectra inside a moving vortex core in layered superconductors with impurities. The universal conductivity is evaluated numerically for the various values of rescaled vortex velocities $κ$ from the clean case to the dirty limit case. The random matrix theoretical prediction is verified numerically in the large $κ$ regime. On the contrary in the low velocity regime, we observe $σ_{xx} \propto κ^{2/3}$ which is consistent with the theoretical result for the super-clean case, where the energy dissipation is due to the Landau-Zener…
We study triplet pairing correlations in clean Ferromagnet (F)/Superconductor (S) nanojunctions, via fully self consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle $α$ between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and $α$. The triplet amplitudes are largest at times on the order of the inver…
We investigate clean mutilayered structures of the SFS and SFSFS type, (where the S layer is intrinsically superconducting and the F layer is ferromagnetic) through numerical solution of the self-consistent Bogoliubov-de Gennes equations for these systems. We obtain results for the pair amplitude, the local density of states, and the local magnetic moment. We find that as a function of the thickness $d_F$ of the magnetic layers separating adjacent superconductors, the ground state energy varies periodically between two stable states. The first state is an ordinary "0-state", in which the order…
The proximity effect and the Josephson current in a superconductor-insulator-ferromagnet-superconductor (SIFS) junction are investigated within the framework of the quasiclassical Eilenberger equations. This investigation allows us to compare the dirty and the clean limits, to investigate an arbitrary impurity scattering, and to determine the applicability limits of the Usadel equations for such structures. The role of different types of the FS interface is analyzed. It is shown that the decay length and the spatial oscillation period of the Eilenberger function may exhibit a nonmonotonic depe…
By now it is known that in an s-wave superconductor-ferromagnet-superconductor ($SFS$) structure the supercurrent induced by spin singlet pairs can only transmit a short distance of the order of magnetic coherence length. The long-range supercurrent, taking place on the length scale of the normal metal coherence length, will be maintained by equal-spin triplet pairs, which can be generated by magnetic inhomogeneities in the system. In this paper, we show an unusual long-range supercurrent, which can take place in clean $SF_1F_2S$ junction with non-parallel orientation of magnetic moments. The …
We study the Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction for arbitrarily large spin polarizations. The Andreev reflection at a clean Ferromagnet-Superconductor interface is incomplete, and Andreev channels with a large incidence angle are progressively suppressed with increasing exchange energy. As a result, the critical current exhibits oscillations as a function of the exchange energy and of the length of the ferromagnet and has a temperature dependence which deviates from the one predicted by the quasiclassical theory.
We study the thermodynamics of clean, layered superconductor/ferromagnet nanostructures using fully self consistent methods to solve the microscopic Bogoliubov-deGennes equations. From these self-consistent solutions the condensation free energies are obtained. The trilayer SFS junction is studied in particular detail: first order transitions between 0 and $π$ states as a function of the temperature $T$ are located by finding where the free energies of the two phases cross. The occurrence of these transitions is mapped as a function of the thickness $d_F$ of the F layer and of the Fermi waveve…
Transport phenomena in clean ferromagnet-superconductor-ferromagnet (FSF) trilayers are studied theoretically for a general case of arbitrary orientation of in-plane magnetizations and interface transparencies. Generalized expressions for scattering probabilities are derived and the differential conductance is computed using solutions of the Bogoliubov-de Gennes equation. We focus on size and coherence effects that characterize ballistic transport, in particular on the subgap transmission and geometrical oscillations of the conductance. We find a monotonic dependence of conductance spectra and…
We have studied the nuclear magnetic resonance (NMR) of 51V nuclei in the superconductor/ferromagnet thin film heterostructures Ni/V/Ni and Pd{1-x}Fe{x}/V/Pd{1-x}Fe{x} in the normaland superconducting state. Whereas the position and shape of the NMR line in the normal state for the trilayers is identical to that observed in a single V-layer, in the superconducting state the line shape definitely changes, developing a systematic distortion of the high-field wing of the resonance line. We consider this as the first experimental evidence for the penetration of ferromagnetism into the superconduct…
We investigate the influence of Landau quantization on the superconducting instability for a pure layered superconductor in the magnetic field directed perpendicular to the layers. We demonstrate that the quantization corrections to the Cooper-pairing kernel with finite Zeeman spin splitting promote the formation of the nonuniform state in which the order parameter is periodically modulated along the magnetic field, i.e., between the layers (Fulde-Ferrell-Larkin-Ovchinnikov [FFLO] state). The conventional uniform state experiences such a quantization-induced FFLO instability at low temperature…
The behavior of clean layered superconductors in the presence of a finite electric current and in zero-magnetic field behavior is addressed. The structure of the current temperature phase diagram and the properties of each of the four regions will be explained. We will discuss the expected current voltage and resistance characteristics of each region as well as the effects of finite size and weak disorder on the phase diagram. In addition, the reason for which a weakly non-ohmic region exists above the transition temperature will be explained.
We fabricated a nanolayered hybrid superconductor-ferromagnet spin-valve structure, the resistive state of which depends on the preceding magnetic field polarity. The effect is based on a strong exchange bias (about -2 kOe) on a diluted ferromagnetic copper-nickel alloy and generation of a long range odd in frequency triplet pairing component. The difference of high and low resistance states at zero magnetic field is 90% of the normal state resistance for a transport current of 250 μA and still around 42% for 10 μA. Both logic states of the structure do not require biasing fields or currents i…
We present a transfer matrix approach that combines the Blonder-Tinkham-Klapwijk (BTK) formalism and self-consistent solutions to the Bogolibuov-de Gennes (BdG) equations and use it to study the tunneling conductance and spin transport in ferromagnet (${\rm F}$)-superconductor (${\rm S}$) trilayers (${\rm F_1F_2 S}$) as functions of bias voltage. The self-consistency ensures that the spin and charge conservation laws are properly satisfied. We consider forward and angularly averaged conductances over a broad range of the strength of the exchange fields and ${\rm F}$ thicknesses, as the relativ…
The four-layered F/S/F$'$/S$'$ nanostructure consisting of rather dirty superconducting (S) and ferromagnetic (F) metals is studied within the theory of the proximity effect taking detailed account of the boundary conditions. The F/S structures with four F and S layers are shown to have considerably richer physics than the F/S/F trilayer (due to the interplay between the 0 and $π$ phase superconductivity and the 0 and $π$ phase magnetism) and even the F/S superlattices. The extra $π$ phase superconducting states obtained for the four-layered F/S/F$^{\prime }$/S$^{\prime }$ system are found to …
The theoretical statements about a restoration of a superconductivity at magnetic fields higher than the quasiclassical upper critical field and a reentrance of superconductivity at temperatures $T_c(H)\approx T_c(0)$ in the superconductors with open Fermi surfaces are reinvestigated taking into account a scattering of quasiparticles on the impurities. The system of integral equations for determination of the upper critical field parallel to the conducting planes in a layered conventional and unconventional superconductors with impurities are derived. The $H_{c2}(T)$ values for the "clean" cas…
We use the quasiclassical theory of superconductivity to calculate the response of the currents in the core of a vortex to an alternating electric field. We consider relatively clean superconductors with a mean free path larger than the coherence length (but still not in the 'superclean limit'). The current response of the core is dominated by the bound states of Caroli, de Gennes and Matricon, and differs significantly from the response obtained from the model of a ``normal core'' introduced by Bardeen and Stephen. The model of Bardeen and Stephen describes the limit of a dirty core and fails…
We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions, where S is a clean conventional (s-wave) superconductor, while F' and middle layers are clean or moderately diffusive ferromagnets. Middle layers consist of two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations that are not collinear with magnetizations in the neighboring F' layers. We use fully self-consistent numerical solutions of the Eilenberger equations to calculate the superconducting pair amplitudes and the Josephson current for arbitrary thickness of ferromagnetic layers and the angle be…
We study Superconductor/Ferromagnet/Superconductor junctions with CuNi, PtNi, or Ni interlayers. Remarkably, we observe that supercurrents through Ni can be significantly larger than through diluted alloys. The phenomenon is attributed to the dirtiness of disordered alloys leading to a short coherence length despite a small exchange energy. To the contrary, pure Ni is clean resulting in a coherence length as long as in a normal metal. Analysis of temperature dependencies of critical currents reveals a crossover from short (dirty) to long (clean) range proximity effects in Pt1-xNix with increas…
We investigate the superconducting proximity effect in a clean magnetic structure consisting of two ferromagnetic layered domains with antiparallel magnetizations in contact with a superconductor. Within the quasiclassical Green's function approach we find that the penetration of the superconducting correlations into the magnetic domains can be enhanced as compared to the corresponding single domain structure. This enhancement depends on an effective exchange field which is determined by the thicknesses and the exchange fields of the two domains. The pair amplitude function oscillates spatiall…
Motivated by the recent discovery of helical magnetic structure in RbEuFe$_{4}$As$_{4}$, we investigate interlayer ordering of magnetic moments in materials composed of spatially-separated superconducting and ferromagnetically-aligned layers. We consider the interplay between the normal and superconducting indirect exchange interaction mediated by tunneling between the conducting layers. We elaborate a recipe to evaluate the normal interlayer interaction via two-dimensional density of states of an isolated layer and demonstrate that for bands with small fillings, such interaction is typically …
We examined the proximity effect in granular films made of Pb, a superconductor, and Ni, a ferromagnet, with various compositions. Slow decay of the critical temperature as a function of the relative volume concentration of Ni per sample was demonstrated by our measurements, followed by a saturation of T$_c$. Using an approximate theoretical description of our granular system in terms of a layered one, we show that our data can only be reasonably fitted by a multilayer model. This indicates the importance of the interplay between different ferromagnetic grains; when non-collinearly magnetized …
Interfaces between materials with differently ordered phases present unique opportunities to study fundamental problems in physics. One example is the interface between a singlet superconductor and a half-metallic ferromagnet, where Cooper pairing occurs between electrons with opposite spin on one side, while the other displays 100% spin polarisation. The recent surprising observation of a supercurrent through half-metallic CrO_2 therefore requires a mechanism for conversion between unpolarised and completely spin polarised supercurrents. Here we suggest a conversion mechanism based on electro…
The uniformly frustrated layered XY model is analyzed in its Villain form. A decouple pancake vortex liquid phase is identified. It is bounded by both first-order and second-order decoupling lines in the magnetic field versus temperature plane. These transitions, respectively, can account for the flux-lattice melting and for the flux-lattice depinning observed in the mixed phase of clean high-temperature superconductors.
We study the Josephson effect and pairing correlations in SFFS junctions that consist of conventional superconductors (S) connected through two metallic monodomain ferromagnets (F) with transparent and spin inactive interfaces. We solve the Eilenberger equations for arbitrary relative orientation of magnetizations of the two F layers in the clean limit and for moderate disorder in ferromagnets. Spatial variation of pair amplitudes, singlet $f_s$, and odd in frequency triplet $f_{t0}$ and $f_{t1}$, with 0 and $\pm1$ spin projections, as well as the Josephson current-phase relations are calculat…
Ru based perovskites demonstrate an amazing richness in their magnetic properties, including 3D and quasi-2D ferromagnetism, antiferromagnetism, and unconventional superconductivity. Tendency to ferromagnetism, stemming from the unusually large involvement of O in magnetism in ruthenates, leads to ferromagnetic spin fluctuations in Sr2RuO4 and eventually to p-wave superconductivity. A related compound Ca2RuO4 was measured to be antiferromagnetic, suggesting a possibility of antiferromagnetic fluctuations in Sr2RuO4 as well. Here we report first principles calculations that demonstrate that in …
Theories of proximity effect in layered superconductor-normal metal structures usually deal with a hypothetic normal metal with no interaction between electrons and with finite temperatures often close to the superconductor critical temperature. We present an asymptotic solution of the Gor'kov equations in the opposite low-temperature limit for a clean normal metal with a repulsive interaction between electrons. The order parameter in the metal exhibits a power-law decay, Delta(x) is proportional to 1/x, as a function of the distance from the SN boundary, x, with a proximity length strongly de…
The stationnary Josephson effect in a clean Superconductor-Ferromagnet-Superconductor junction is revisited for arbitrarily large spin polarizations. The quasiclassical calculation of the supercurrent assumes that the Andreev reflection is complete for all channels. However, De Jong and Beenakker have shown that the Andreev reflection at a clean FS interface is incomplete, due to the exchange interaction in the ferromagnet. Taking into account this incomplete Andreev reflection, we investigate the quasiparticle spectrum, the Josephson current and the $0-π$ transition in a ballistic single chan…
The nature of decoupling in the mixed phase of extremely type-II layered superconductors is studied theoretically through a duality transformation of the layered XY model with frustration. In the limit of weak coupling, we generally find that the Josephson effect is absent if and only if the phase correlations within isolated layers are short range. In the case specific to uniform frustration, we notably identify a decoupled pancake vortex liquid phase that is bounded by first-order and second-order decoupling lines in the magnetic field vs. temperature plane. These transitions potentially acc…
We consider the quasiparticle c-axis conductivity in highly anisotropic layered compounds in the presence of the magnetic field parallel to the layers. We show that at low temperatures the quasiparticle interlayer conductivity depends strongly on the orientation of the in-plane magnetic field if the excitation gap has nodes on the Fermi surface. Thus measurements of the angle-dependent c-axis (out-of-plane) magnetoresistance, as a function of the orientation of the magnetic field in the layers, provide information on the momentum dependence of the superconducting gap (or pseudogap) on the Ferm…
We theoretically study the proximity effect in the thin-film layered ferromagnet (F) - superconductor (S) heterostructures in F$_1$F$_2$S design. We consider the boundary value problem for the Usadel-like equations in the case of so-called "dirty" limit. The "latent" superconducting pairing interaction in F layers taken into account. The focus is on the recipe of experimental preparation the state with so-called solitary superconductivity. We also propose and discuss the model of the superconducting spin valve based on F$_1$F$_2$S trilayers in solitary superconductivity regime.
We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anom…
