Long-range Triplet Component Research Articles

Триплетные сверхпроводящие корреляции гибридной меза-структуры с двухслойной ферромагнитной прослойкой

We present results on electron transport in hybrid Josephson mesa-structure Sd/F1F2/S, consisting of epitaxial films of cuprate superconductor YBa2Cu3O7-δ (Sd), bi-layer ferromagnetic interlayer (F1F2), thin film of metallic Nb was deposited on the top of a thin protective Au film layer used as the upper superconducting electrode (S). The long-range triplet component of superconducting correlations arises when strontium ruthenate SrRuO3 F1 and manganiteLa0.7Sr0.3MnO3 with non-collinear magnetizations are used as ferromagnetic material F2. Superconducting current took place up to the thickness d = 52 nm of the F1F2 interlayer. Superconducting current disappeared in the case of a single ferromagnetic interlayer of manganite (La0.7Sr0.3MnO3 or La0.7Ca0.3MnO3) and SrRuO3 with minimized thicknesses, limited by the occurrence of pinholes. The magnetic field properties of mesa-structure are discussed as well, along with the impact of the second harmonic in the superconducting current-phase relation.

Charge and spin supercurrents in magnetic Josephson junctions with spin filters and domain walls

We analyze theoretically the influence of domain walls (DWs) on the DC Josephson current in magnetic superconducting S$_{m}$/Fl/F/Fl/S$_{m}$ junctions. The Josephson junction consists of two "magnetic" superconductors S$_{m}$ (superconducting film covered by a thin ferromagnetic layer), spin filters Fl and a ferromagnetic layer F with or without DW (DWs). The spin filters Fl allow electrons to pass with one specific spin orientation, such that the Josephson coupling is governed by a fully polarized long-range triplet component. In the absence of DW(s), the Josephson and spin currents are nonzero when the right and left filters, Fl$_{r,l}$, pass electrons with equal spin orientation and differ only by a temperature-independent factor. They become zero when the \textbf{spins} of the triplet Cooper pairs passing through the Fl$_{r,l}$ have opposite directions. Furthermore, for the different chiralities of the injected triplet Cooper pairs the spontaneous currents arise in the junction yielding a diode effect. Once a DW is introduced, it reduces the critical Josephson current $I_{c}$ in the case of equal spin polarization and makes it finite in the case of opposite spin orientation. The critical current $I_{c}$ is maximal when the DW is in the center of the F film. A deviation of the DW from the center generates a force that pushes the DW to the center of the F film. In addition, we consider the case of an arbitrary number $N$ of DW's, with the case $N=2$ corresponding to a model system for a magnetic skyrmion.

Proximity Effect in Heterostructures Based on a Superconductor/Half-Metal System

We demonstrated that with increasing the exchange splitting of the conduction band of a ferromagnet and, respectively, of the degree of the spin polarization, the probability of transmission of the superconducting Cooper pairs through the S/F interface decreases. We concluded that the spin imbalance plays a key role in the processes taking place at the interface between a superconductor and a ferromagnet with spin-polarized conduction electrons. We have studied the superconducting spin-valve effect in F1/F2/S heterostructures containing the Heusler alloy Co2Cr1−xFexAly as one of two ferromagnetic (F1 or F2) layers. We used the Heusler alloy layer in two roles: as a weak ferromagnet on the place of the F2 layer and as a half-metal on the place of the F1 layer. In the first case, we obtained the full switching between the normal and superconducting states is realized with the dominant aid of the long-range triplet component of the superconducting pair condensate which occurs at the perpendicular mutual orientation of magnetizations. In the second case, we observed separation between the superconducting transitions for perpendicular and parallel configurations of magnetizations reaching 0.5 K. We also find a good agreement between our experimental data and theoretical results.

Switchable Josephson current in junctions with spin-orbit coupling

We study the Josephson current in two types of lateral junctions with spin-orbit coupling and an exchange field. The first system (type 1 junction) consists of superconductors with heavy metal interlayers linked by a ferromagnetic bridge, such that the spin-orbit coupling is finite only at the superconductor/heavy metal interface. In the second type (type 2) of system we assume that the spin-orbit coupling is finite in the bridge region. The length of both junctions is larger than the magnetic decay length such that the Josephson current is carried uniquely by the long-range triplet component of the condensate. The latter is generated by the spin-orbit coupling via two mechanisms, spin precession and inhomogeneous spin relaxation. We show that the current can be controlled by rotating the magnetization of the bridge or by tuning the strength of the spin-orbit coupling in type 2 junctions and also discuss how the ground state of the junction can be tuned from a 0 to a $\ensuremath{\pi}$ phase difference between the superconducting electrodes. In leading order in the spin-orbit coupling, the spin precession dominates the behavior of the triplet component and both junctions behave similarly. However, when spin relaxation effects are included the type 2 junction offers a wider parameter range in which 0-$\ensuremath{\pi}$ transitions take place.

Superconducting switching due to a triplet component in the Pb/Cu/Ni/Cu/Co2Cr1 -x Fe x Al y spin-valve structure.

We report the superconducting properties of the Co2Cr1−xFexAly/Cu/Ni/Cu/Pb spin-valve structure the magnetic part of which comprises the Heusler alloy layer HA = Co2Cr1−xFexAly with a high degree of spin polarization (DSP) of the conduction band and a Ni layer of variable thickness. The separation between the superconducting transition curves measured for the parallel (α = 0°) and perpendicular (α = 90°) orientation of the magnetization of the HA and the Ni layers reaches up to 0.5 K (α is the angle between the magnetization of two ferromagnetic layers). For all studied samples the dependence of the superconducting transition temperature Tc on α demonstrates a deep minimum in the vicinity of the perpendicular configuration of the magnetizations. This suggests that the observed minimum and the corresponding full switching effect of the spin valve is caused by the long-range triplet component of the superconducting condensate in the multilayer. Such a large effect can be attributed to a half-metallic nature of the HA layer, which in the orthogonal configuration efficiently draws off the spin-polarized Cooper pairs from the space between the HA and Ni layers. Our results indicate a significant potential of the concept of a superconducting spin-valve multilayer comprising a half-metallic ferromagnet, recently proposed by A. Singh et al., Phys. Rev. X 2015, 5, 021019, in achieving large values of the switching effect.

Superconducting spin-valve effect in a heterostructure containing the Heusler alloy as a ferromagnetic layer

We have studied the superconducting spin-valve effect in a F1/F2/S heterostructure containing a Heusler alloy layer standing for an F2 layer. The Heusler alloy layer was grown at the substrate temperature Tsub=300K. According to our previous data in such preparation conditions this layer is a weak ferromagnet. For the samples with the Heusler layer thickness dHeusler=1 and 4 nm the full switching between the normal and superconducting states is realized with the dominant aid of the long-range triplet component of the superconducting pair condensate which occurs at the perpendicular mutual orientation of magnetizations.

Superconductor-ferromagnet-superconductor nanojunctions from perovskite materials

The lateral superconductor-ferromagnet–superconductor (SFS) nanojunctions based on high critical temperature superconductor YBa2Cu3Ox (YBCO) and half-metallic ferromagnet La0.67Sr0.33MnO3 (LSMO) thin films were prepared to investigate a possible presence of long range triplet component (LRTC) of Cooper pairs in the LSMO. We applied Ga3+ focused ion beam patterning to create YBCO/LSMO/YBCO lateral type nanojunctions with LSMO length as small as 40nm. The resistivity vs. temperature, critical current density vs. temperature and resistance vs. magnetic field dependence were studied to recognize the LRTC of Cooper pairs in the LSMO. A non-monotonic temperature dependence of junction critical current density and a decrease of the SFS nanojunction resistance in increased magnetic field were observed. Only weak manifestations of LRTC and some qualitative agreement with theory were found out in SFS nanojunctions realized from the perovskite materials. The presence of equal-spin triplet component of Cooper pairs in half-metallic LSMO ferromagnet is not such apparent as in SFS junctions prepared from low temperature superconductors NbTiN and half-metallic ferromagnet CrO2.

Thickness dependence of the triplet spin-valve effect in superconductor-ferromagnet-ferromagnet heterostructures.

Background: In nanoscale layered S/F1/N/F2/AF heterostructures, the generation of a long-range, odd-in-frequency spin-projection one triplet component of superconductivity, arising at non-collinear alignment of the magnetizations of F1 and F2, exhausts the singlet state. This yields the possibility of a global minimum of the superconducting transition temperature Tc, i.e., a superconducting triplet spin-valve effect, around mutually perpendicular alignment.Results: The superconducting triplet spin valve is realized with S = Nb a singlet superconductor, F1 = Cu41Ni59 and F2 = Co ferromagnetic metals, AF = CoOx an antiferromagnetic oxide, and N = nc-Nb a normal conducting (nc) non-magnetic metal, which serves to decouple F1 and F2. The non-collinear alignment of the magnetizations is obtained by applying an external magnetic field parallel to the layers of the heterostructure and exploiting the intrinsic perpendicular easy-axis of the magnetization of the Cu41Ni59 thin film in conjunction with the exchange bias between CoOx and Co. The magnetic configurations are confirmed by superconducting quantum interference device (SQUID) magnetic moment measurements. The triplet spin-valve effect has been investigated for different layer thicknesses, dF1, of F1 and was found to decay with increasing dF1. The data is described by an empirical model and, moreover, by calculations using the microscopic theory.Conclusion: The long-range triplet component of superconducting pairing is generated from the singlet component mainly at the N/F2 interface, where the amplitude of the singlet component is suppressed exponentially with increasing distance dF1. The decay length of the empirical model is found to be comparable to twice the electron mean free path of F1 and, thus, to the decay length of the singlet component in F1. Moreover, the obtained data is in qualitative agreement with the microscopic theory, which, however, predicts a (not investigated) breakdown of the triplet spin-valve effect for dF1 smaller than 0.3 to 0.4 times the magnetic coherence length, ξF1.

Long range triplet Josephson current and 0−π transitions in tunable domain walls

The order parameter of superconducting pairs penetrating an inhomogeneous magnetic material can acquire a long range triplet component (LRTC) with non-zero spin projection. This state has been predicted and generated in proximity systems and Josephson junctions. We show, using a realistic domain wall of an exchange spring bilayer, how the LRTC emerges and can be tuned with the twisting of the magnetization. We also introduce a new kind of Josephson current reversal, the singlet-LRTC 0–π transition, that can be observed in one and the same system either by tuning the domain wall or by varying temperature.

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present a complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. We demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. We also consider a S/F bilayer in contact with normal metal with SO coupling and show that the latter can be used as a source for the LRTC. Our work gives a global description of the singlet-triplet conversion in hybrids structures in terms of generic spin-fields and our results are particularly important for the understanding of the physics underlying spintronics devices with superconductor elements.

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.

Triplet superconducting correlations in oxide heterostructures with a composite ferromagnetic interlayer

The superconducting current induced by the penetration of the long-range triplet component of superconducting correlations into a composite ferromagnetic interlayer has been detected in mesa-heterostructures based on oxide cuprate superconductors YBa2Cu3O7 - delta and Au/Nb bilayer films with the composite oxide interlayer that is made of ferromagnetic films of manganite La0.7Sr0.3MnO3 and ruthenate SrRuO3 and has a thickness much larger than the length of correlations determined by the exchange field. The deviation of the superconducting current in the mesa-heterostructure with the fraction of the second harmonic of 13% from a sinusoidal current-phase relation has been detected; this deviation can also be due to the generation of the triplet component of superconducting correlations in the ferromagnet.

Singlet-triplet conversion and the long-range proximity effect in superconductor-ferromagnet structures with generic spin dependent fields.

The long-range proximity effect in superconductor-ferromagnet (S/F) hybrid nanostructures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the ferromagnet over large distances. It is commonly believed that this happens only in the presence of magnetic inhomogeneities. We show that there are other sources of the long-range triplet component (LRTC) of the condensate and establish general conditions for their occurrence. As a prototypical example, we consider first a system where the exchange field and spin-orbit coupling can be treated as time and space components of an effective SU(2) potential. We derive a SU(2) covariant diffusive equation for the condensate and demonstrate that an effective SU(2) electric field is responsible for the long-range proximity effect. Finally, we extend our analysis to a generic ferromagnet and establish a universal condition for the LRTC. Our results open a new avenue in the search for such correlations in S/F structures and make a hitherto unknown connection between the LRTC and Yang-Mills electrostatics.

Influence of spin-dependent quasiparticle distribution on the Josephson current through a ferromagnetic weak link

The Josephson current flowing through weak links containing ferromagnetic elements is studied theoretically under the condition that the quasiparticle distribution over energy states in the interlayer is spin dependent. It is shown that the interplay between the spin-dependent quasiparticle distribution and the triplet superconducting correlations induced by the proximity effect between the superconducting leads and ferromagnetic elements of the interlayer leads to the appearence of an additional contribution to the Josephson current. This additional contribution ${j}_{t}$ can be extracted from the full Josephson current in experiment. The features of the additional supercurrent ${j}_{t}$, which are of main physical interest are the following: i) We propose the experimental setup, where the contributions given by the short-range triplet component (SRTC) and long-range triplet component (LRTC) of superconducting correlations in the interlayer can be measured separately. It can be realized on the basis of a S/N/F/N/S junction, where the interlayer is composed of two normal metal regions with a spiral ferromagnet layer sandwiched between them. For the case of tunnel junctions, the measurement of ${j}_{t}$ in such a system can provide direct information about the energy-resolved anomalous Green's function components describing SRTC and LRTC. ii) In some cases the exchange field-suppressed supercurrent can be not only recovered but also enhanced with respect to its value for a nonmagnetic junction with the same interface resistances by the presence of a spin-dependent quasiparticle distribution. This effect is demonstrated for the S/N/S junction with magnetic S/N interfaces. In addition, it is also found that under the considered conditions the dependence of the Josephson current on temperature can be nontrivial: At first, the current rises upon the temperature increasing and only after that starts to decline.

Electrical Transport Study of Patterned Lateral Niobium-Permalloy Junctions

In order to investigate the interplay between magnetic domain walls and superconductivity we study the electrical transport property of lateral Nb-permalloy-Nb junctions where the permalloy thickness is varied from 50 to 90 nm. Magnetic force microscopy images confirm the presence of domain walls in the ferromagnetic portion between the two superconducting electrodes for samples with permalloy thickness of 60, 70 and 90 nm. Below superconducting transition temperature, the zero bias conductance (ZBC) for these samples shows a sharp reduction in the magnetic field range of 0 to 0.15 T and after that it stays almost at a constant level until a high field is applied. The phenomenon is attributed to domain wall assisted crossed Andreev reflection (CAR) and/or long range triplet component (LRTC) of superconductivity. On the contrary, the decreasing trend of ZBC at low field is absent for the sample with 50 nm thick NiFe which indicates that the conductance contribution from CAR and/or LRTC is absent in this sample. This is presumably due the fact that the permalloy in the gap region for this sample is in a single domain state. A quantitative analysis for conductance contribution from domain wall assisted CAR is provided.

Spin orbit scattering effect on long-range odd frequency triplet pairing in ferromagnet/superconductor bilayers

A formulation of triplet proximity effect in a ferromagnet/superconductor bilayer based on the de Gennes correlation function method is presented by extending the Takahashi–Tachiki theory. The inhomogeneous in-plane spiral magnetic order is employed in this approach the superconducting order parameter is a conventional spin singlet s-wave pairing, and the induced triplet pair amplitude arises as a result of the broken time-reversal invariance due to the presence of the rotating exchange field. A new type of triplet condensate still possesses the s-wave state but the symmetry requires an odd frequency parity. We find that the inhomogeneous exchange interaction leads to the appearance of the long-range odd frequency triplet pair amplitude, and the inclusion of the spin orbit scattering affects both short-range and long-range triplet components. The superconducting critical temperature of the diffusive ferromagnet/superconductor sandwiches is determined from the secular equation of the linearized gap equation in order to investigate the behavior of the induced triplet pairing. It is found that the induced long-range triplet component exists which arises from the modulation of the in-plane pair amplitudes in the transverse direction. Moreover, the possibility of the cryptoferromagnetic state is demonstrated in favor of superconductivity and this may explain a possible origin of the magnetically dead layer.

Josephson effect due to the long-range odd-frequency triplet superconductivity inSFSjunctions with Néel domain walls

We consider a SFS Josephson junction made of two superconductors S and a multidomain ferromagnet F with an in-plane magnetization. We assume that the neighboring domains of the ferromagnet are separated by Neel domain walls. An odd-frequency triplet long-range component of superconducting correlations arises in the domain walls and spreads into the domains over a long distance of the order $\xi_T = \sqrt{D / 2 \pi T}$, where $D$ is the diffusion coefficient (dirty limit is implied). We calculate the contribution of this component to the Josephson current in the situation when conventional short-range components exponentially decay over the thickness of the F layer and can be neglected. In the limit when the thickness of the F layer is much smaller than the penetration length of the long-range component, we find that the junction is in the $\pi$ state. We also analyze a correction to the density of states due to the long-range triplet component.

Odd triplet superconductivity in a superconductor/ferromagnet system with a spiral magnetic structure

We analyze a superconductor-ferromagnet $(S∕F)$ system with a spiral magnetic structure in the ferromagnet F for a weak and strong exchange field. The long-range triplet component (LRTC) penetrating into the ferromagnet over a long distance is calculated for both cases. In the dirty limit (or weak ferromagnetism) we study the LRTC for conical ferromagnets. Its spatial dependence undergoes a qualitative change as a function of the cone angle $\ensuremath{\vartheta}$. At small angles $\ensuremath{\vartheta}$ the LRTC decays in the ferromagnet exponentially in a monotonic way. If the angle $\ensuremath{\vartheta}$ exceeds a certain value, the exponential decay of the LRTC is accompanied by oscillations with a period that depends on $\ensuremath{\vartheta}$. This oscillatory behavior leads to a similar dependence of the Josephson critical current in SFS junctions on the thickness of the $F$ layer. In the case of a strong ferromagnet the LRTC decays over the length which is determined by the wave vector of the magnetic spiral and by the exchange field.