Superconductor-ferromagnet Structures Research Articles

Triplet odd-frequency superconductivity in hybrid superconductor–ferromagnet structures

We present an overview of the contributions made by Konstantin B. Efetov and the authors to the field of triplet odd-frequency superconductivity in hybrid ferromagnet–superconductor structures (Bergeret et al., 2005) and the repercussions they had on experimental and theoretical research. Konstantin B. Efetov passed away in August 2021. We hope the present short review gives a faithful testimony of an important part of his scientific legacy.

Current Rectification in Junctions with Spin-Split Superconductors

Spin-split superconductors exhibit an electron-hole asymmetric spin-resolved density of states, but the symmetry is restored upon averaging over spin. On the other hand, asymmetry appears again in tunneling junctions of spin-split superconductors with a spin-polarized barrier. As demonstrated recently in both theory and experiment, this fact leads to a particularly strong thermoelectric effect in superconductor-ferromagnet structures. In this work we show another important effect stemming from the electron-hole asymmetry - current rectification. We calculate the charge current in spin-polarized tunnel junctions of normal metal and a spin-split superconductor with AC and DC voltage bias. In the DC case, the I-V curve is not fully antisymmetric and has a voltage-symmetric component due to spin polarization. This translates to the existence of a rectified current in the AC case, which is proportional to the spin polarization of the junction and strongly depends on the frequency of the applied bias. We discuss possible applications of the rectification effect, including a diode for superconducting electronics and radiation detectors. The analysis of the rectified charge current is supplemented by the discussion of heat current and relevant noise correlators, where electron-hole asymmetry also plays an important role, and which are useful for applications in detectors.

Nonlocal thermoelectric effects in high-field superconductor-ferromagnet hybrid structures

We report on the experimental observation of nonlocal spin-dependent thermoelectric effects in superconductor-ferromagnet multiterminal structures. Our samples consist of a thin superconducting aluminum wire with several ferromagnetic tunnel junctions attached to it. When a thermal excitation is applied to one of the junctions in the presence of a Zeeman splitting of the density of states of the superconductor, a thermoelectric current is observed in remote junctions at distances exceeding $10~\mathrm{\mu m}$. The results can be explained by recent theories of coupled spin and heat transport in high-field superconductors.

Manifestation of the electromagnetic proximity effect in superconductor-ferromagnet thin film structures

Using the newly emerged theory model of an electromagnetic proximity effect, we demonstrate that it provides a good description of our previously reported anomalous Meissner screening observed in thin film superconductor-ferromagnet proximity structures. Using the low energy muon spin rotation measurement technique, we further investigate this new theory by probing directly the flux screening in various superconductor-ferromagnet proximity structures. We examine its main characteristics and find in general good agreement between theory and experiment. Understanding and control of this new proximity effect is an important step forward toward a new generation of superconducting spintronic devices.

Spin polarization and orbital effects in superconductor-ferromagnet structures

We study theoretically spontaneous currents and magnetic field induced in a superconductor-ferromagnet (S-F) bilayer due to direct and inverse proximity effects. The induced currents {are Meissner currents that appear even in the absence of an external magnetic field due to the magnetic moment in the ferromagnet }and {to the magnetization } in the superconductor . The latter is induced by the inverse proximity effect over a distance of the order of the superconducting correlation length $\xi _{S}$. On the other hand the magnetic induction $B$, caused by Meissner currents, penetrates the S film over the London length $\lambda _{S}$. Even though $\lambda _{S}$ usually exceeds considerably the correlation length, the amplitude and sign of $B$ at distances much larger than $\xi _{S}$ depends crucially on the strength of the exchange energy in the ferromagnet and on the magnetic moment induced in the in the S layer.

Electromagnetic proximity effect in planar superconductor-ferromagnet structures

The spread of Cooper pairs in a ferromagnet in proximity coupled superconductor-ferromagnet structures is shown to cause a strong inverse electromagnetic phenomenon, namely, the long-range transfer of the magnetic field from the ferromagnet to the superconductor. Contrary to the previously investigated inverse proximity effect resulting from the spin polarization of a superconducting surface layer, the characteristic length of the above inverse electrodynamic effect is of the order of the London penetration depth, which usually is much larger than the superconducting coherence length. The corresponding spontaneous currents appear even in the absence of the stray field of the ferromagnet and are generated by the vector-potential of magnetization near the S/F interface, and they should be taken into account in the design of nanoscale S/F devices. Similarly to the well-known Aharonov-Bohm effect, the discussed phenomenon can be viewed as a manifestation of the role of vector potential in quantum physics.

Giant Mesoscopic Fluctuations and Long-Range Superconducting Correlations in Superconductor-Ferromagnet Structures.

The fluctuating superconducting correlations emerging in dirty hybrid structures under the conditions of the strong proximity effect are demonstrated to affect the validity range of the widely used formalism of Usadel equations at mesoscopic scales. In superconductor-ferromagnet structures these giant mesoscopic fluctuations originating from the interference effects for the Cooper pair wave function in the presence of the exchange field can be responsible for an anomalously slow decay of superconducting correlations in a ferromagnet even when the noncollinear and spin-orbit effects are negligible. The resulting sample-to-sample fluctuations of the Josephson current in superconductor-ferromagnetic-superconductor junctions and the local density of states in superconductor-ferromagnetic hybrid structures can provide an explanation of the long-range proximity phenomena observed in mesoscopic samples with collinear magnetization.

Long-range supercurrents induced by the interference effect of opposite-spin triplet state in clean superconductor-ferromagnet structures

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 have shown an unusual long-range supercurrent, which can take place in clean junction with non-parallel orientation of magnetic moments. The mechanism behind the enhancement of Josephson current is provided by the interference of the opposite-spin triplet states deriving from and interfaces when both ferromagnetic layers have the same values of the length and exchange field. This discovery can offer a natural explanation for recent experiments (Robinson et al 2010 Phys. Rev. Lett. 104 207001; Baek et al 2014 Nat. Commun. 5 3888).

Long-Range Spin-Polarized Quasiparticle Transport in Mesoscopic Al Superconductors with a Zeeman Splitting

We report on nonlocal transport in multiterminal superconductor-ferromagnet structures, which were fabricated by means of e-beam lithography and shadow evaporation techniques. In the presence of a significant Zeeman splitting of the quasiparticle states, we find signatures of spin transport over distances of several μm, exceeding other length scales such as the coherence length, the normal-state spin-diffusion length, and the charge-imbalance length. The relaxation length of the spin signal shows a nearly linear increase with magnetic field, hinting at a freeze-out of relaxation by the Zeeman splitting. We propose that the relaxation length is given by the recombination length of the quasiparticles rather than a renormalized spin-diffusion length.

Triplet Superconductivity in a Ferromagnetic Vortex

We argue that triplet superconductivity can be conveniently realized in hybrid superconductor-ferromagnet (S-F) structures with a ferromagnetic vortex. We demonstrate that due to proximity-induced long-range triplet pairing such S-F-S junctions can sustain appreciable supercurrent which can be directly measured in experiments. Depending on the contact geometry either zero- or π-junction regime can be realized in the system under consideration.

Negative four-terminal resistance as a probe of crossed Andreev reflection

We report on the experimental investigation of electronic transport in superconductor-ferromagnet spin-valve structures. Our samples consist of two ferromagnetic iron leads forming planar tunnel contacts to a superconducting aluminum wire. Current is injected into one of the contacts while the voltage is monitored at the other, thus defining a four-probe resistance. At energies below the superconducting gap, we observe a negative four-probe resistance that can be explained by crossed Andreev reflection.

Odd triplet superconductivity in superconductor ferromagnet structures: a survey

We review the main features of odd triplet superconductivity in superconductor-ferromagnet (S/F) structures. We discuss the different types of superconducting condensate that can be experimentally observed and pay special attention to the triplet component induced in a ferromagnet which is in contact with a superconductor. The triplet component is an even function of the momentum and an odd function of the frequency and leads to novel phenomena.

Odd triplet superconductivity in superconductor–ferromagnet hybrid structures

We study the proximity effect in diffusive superconductor–ferromagnet structures. In particular we show that a triplet component of the condensate appears. This component is an odd function of the Matsubara frequency and an even function of the momentum. Therefore it is insensitive to the scattering by non-magnetic impurities. If the exchange field of the ferromagnet is homogeneous in space, only the triplet component with spin projection S z = 0 appears. The latter penetrates into the ferromagnet over the short length ξ h = D / h ( D is the diffusion coefficient and h the exchange field) like the singlet component. However, if the exchange is not homogeneous the condensate has also the components with projections S z = ± 1 . These are long-range components which penetrate the ferromagnet over the ξ T = D / T ( T is the temperature). We propose some experiments in order to detect the odd triplet component. To cite this article: F.S. Bergeret et al., C. R. Physique 7 (2006).

Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures

This review considers unusual effects in superconductor-ferromagnet structures, in particular, the triplet component of the condensate generated in those systems. This component is odd in frequency and even in momentum, which makes it insensitive to nonmagnetic impurities. If the exchange field is not homogeneous in the system, the triplet component is not destroyed even by a strong exchange field and can penetrate the ferromagnet over long distances. Some other effects considered here and caused by the proximity effect are enhancement of the Josephson current due to the presence of the ferromagnet, induction of a magnetic moment in superconductors resulting in a screening of the magnetic moment, and formation of periodic magnetic structures due to the influence of the superconductor. Finally, theoretical predictions are compared with existing experiments.

Long-range odd triplet superconductivity in superconductor-ferromagnet structures with Néel walls

We consider a multidomain superconductor/ferromagnet (SF) structure with an in-plane magnetization, assuming that the neighboring domains are separated by the Neel domain walls. We show that an odd triplet long-range component arises in the domain walls and spreads into domains over a long distance of the order \xi_T = \sqrt{D/2\pi T} (in the dirty limit). The density of states variation in the domains due to this component changes over distances of the order \xi_T and turns to zero in the middle of domains if the magnetization rotates in the same direction in all domain walls.

Inverse proximity effect in superconductor-ferromagnet structures: From the ballistic to the diffusive limit

The inverse proximity effect, i.e. the induction of a magnetic moment in the superconductor in superconductor-ferromagnet (S/F) junctions is studied theoretically. We present a microscopic approach which combines a model Hamiltonian with elements of the well established quasiclassical theory. With its help we study systems with arbitrary degree of disorder, interface transparency and thickness of the layers. In the diffusive limit we recover the result of previous works: the direction of the induced magnetization $M$ is opposite to the one of the F layer. However, we show that in the ballistic case the sign of $M$ may be positive or negative depending on the quality of the interface and thickness of the layers. {We show that, regardless of its sign, the penetration length of the magnetic moment into the superconductor is of the order of the superconductor coherence length, which demonstrates that the effect has a superconducting origin.}

Induced ferromagnetism due to superconductivity in superconductor-ferromagnet structures

We consider a superconductor-ferromagnet (S/F) structure and assume that above the superconducting transition temperature $T_{c}$ the magnetic moment exists only in F. {In a simple model of the ferromagnet (the exchange field is of the ferromagnetic type for all energies)}we show by an explicit calculation that below $T_{c}$ the magnetic moment may penetrate the superconductor. {In this model} its direction in S is opposite {to the magnetization of free electrons} in the ferromagnet. The magnetization spreads over a large distance which is of the order of the superconducting coherence length $\xi_{S}$ and can much exceed the ferromagnet film thickness. At the same time the magnetic moment in the ferromagnet is reduced. This inverse proximity effect may explain the reduction in magnetization observed in recent experiments and may lead to a strong interaction between the ferromagnetic layers in F/S/F structures.

Odd triplet superconductivity in superconductor-ferromagnet multilayered structures.

We demonstrate that in multilayered superconductor-ferromagnet structures a noncollinear alignment of the magnetizations of different ferromagnetic layers generates a triplet superconducting condensate which is odd in frequency. This triplet condensate coexists in the superconductors with the conventional singlet one but decays very slowly in the ferromagnet, which should lead to a large Josephson effect between the superconductors separated by the ferromagnet. Depending on the mutual direction of the ferromagnetic moments, the Josephson coupling can be both of 0 and of pi type.

Oscillations of the superconducting critical current in Nb-Cu-Ni-Cu-Nb junctions.

We report on experimental studies of superconductor-ferromagnet layered structures. Strong oscillations of the critical supercurrent were observed with the thickness variation of the ferromagnet. Using known microscopic parameters of Ni, we found reasonable agreement between the period of oscillations and the decay of the measured critical current, and theoretical calculations.

Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization

We calculate the dc Josephson current $I_J$ for two types of superconductor-ferromagnet (S/F) Josephson junctions. The junction of the first type is a S/F/S junction. On the basis of the Eilenberger equation, the Josephson current is calculated for an arbitrary impurity concentration. If $% h\tau\ll1$ the expression for the Josephson critical current $I_c$ is reduced to that which can be obtained from the Usadel equation ($h$ is the exchange energy, $\tau$ is the momentum relaxation time). In the opposite limit $h\tau\gg1$ the superconducting condensate oscillates with period $% v_F/h$ and penetrates into the F region over distances of the order of the mean free path $l$. For this kind of junctions we also calculate $I_J$ in the case when the F layer presents a nonhomogeneous (spiral) magnetic structure with the period $2\pi /Q$. It is shown that for not too low temperatures, the $\pi$-state which occurs in the case of a homogeneous magnetization (Q=0) may disappear even at small values of $Q$. In this nonhomogeneous case, the superconducting condensate has a nonzero triplet component and can penetrate into the F layer over a long distance of the order of $\xi_{T}=% \sqrt{D/2\pi T}$. The junction of the second type consists of two S/F bilayers separated by a thin insulating film. It is shown that the critical Josephson current $I_{c}$ depends on the relative orientation of the effective exchange field $h$ of the bilayers. In the case of an antiparallel orientation, $I_{c}$ increases with increasing $h$. We establish also that in the F film deposited on a superconductor, the Meissner current created by the internal magnetic field may be both diamagnetic or paramagnetic.