We study the Andreev bound states in a Josephson junction between a singlet and a triplet superconductors. Because of the mismatch in the spin symmetries of pairing, the energies of the spin up and down quasiparticles are generally different. This results in imbalance of spin populations and net spin accumulation at the junction in equilibrium. This effect can be detected using probes of local magnetic field, such as the scanning SQUID, Hall, and Kerr probes. It may help to identify potential triplet pairing in $\rm(TMTSF)_2X$, $\rm Sr_2RuO_4$, and oxypnictides.
We predict a novel type of Josephson effect to occur in triplet superconductor - ferromagnet - triplet superconductor Josephson junctions. We show that the Josephson current, I_J, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d-vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional temperature dependence of I_J in which I_J changes sign with increasing temperature
The Josephson effect between triplet and singlet superconductors is studied. Josephson current can flow between triplet and singlet superconductors due to the spin-orbit coupling in the spin-triplet superconductor but it is finite only when triplet superconductor has $L_z=-S_z=\pm 1$, where $L_z$ and $S_z$ are the perpendicular components of orbital angular momentum and spin angular momentum of the triplet Cooper pairs, respectively. The recently observed temperature and orientational dependence of the critical current through a Josephson junction between UPt$_3$ and Nb is investigated by cons…
We study AC Josephson effect in a superconductor-ferromagnet heterostructure with a variable magnetic configuration. The system supports triplet proximity correlations whose dynamics is coupled to the magnetic dynamics. This feedback dramatically modifies the behavior of the junction. The current-phase relation becomes double-periodic at both very low and high Josephson frequencies $ω_J$. At intermediate frequencies, the periodicity in $ω_J t$ may be lost.
We examine a Josephson junction involving two arbitrary equal-spin-pairing unitary triplet superconductors and a ferromagnetic tunneling barrier. Using perturbation theory, we show how the interaction of the barrier moment with the spin of the tunneling triplet Cooper pairs can reverse the sign of the Josephson charge current. This also results in a Josephson spin current, which contains a phase-independent contribution due to reflection processes at the barrier. We verify our analytic predictions using a non-perturbative Bogoliubov-de Gennes method.
We study the Josephson current through a long ferromagnetic bilayer in the diffusive regime. For non-collinear magnetizations, we find that the current-phase relation is dominated by its second harmonic, which corresponds to the long-range coherent propagation of two triplet pairs of electrons.
We study theoretically the Josephson effect and pairing correlations in planar SF1F2S junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We obtain both spin-singlet and -triplet pair amplitudes and the Josephson current-phase relations for arbitrary orientation of the magnetizations using the self-consistent solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that the long-range spin-triplet correlations cannot prevail in symmetric junctions …
The induced magnetic moment, provided by the bands electrons, is calculated in a variety of Josephson junctions with multilayered ferromagnetic (F) weak link. The noncollinear magnetization of the F layers provides the conditions necessary to generate triplet superconducting correlations. It leads to the long-range induced magnetic moment, emerging in the superconducting (S) layers. It is shown to be dependent on the Josephson phase. By tuning the Josephson current, one may control the long-range induced magnetic moment. Alternatively, applying the voltage we can generate an oscillatory magnet…
This paper theoretically discusses the spin current in spin-triplet superconductor / insulator / spin-triplet superconductor junctions. At low temperatures, a midgap Andreev resonant state anomalously enhances not only the charge current but also the spin current. The coupling between the Cooper pairs and the electromagnetic fields leads to the Frounhofer pattern in the direct current spin flow in magnetic fields and the alternative spin current under applied bias-voltages.
Charge and spin transport in a junction involving two triplet superconductors and a ferromagnetic barrier are studied. We use Bogoliubov-de Gennes wavefunctions to construct the Green's function, from which we obtain the Josephson currents in terms of the Andreev reflection coefficients. We focus on the consequences of a finite barrier width for the occurrence of 0-πtransitions and for the spin currents, and examine the appropriateness of the common δ-function approximation for the tunneling region.
Josephson junctions made with conventional s-wave superconductors and containing multiple layers of ferromagnetic materials can carry spin-triplet supercurrent in the presence of certain types of magnetic inhomogeneity. In junctions containing three ferromagnetic layers, the triplet supercurrent is predicted to be maximal when the magnetizations of adjacent layers are orthogonal, and zero when the magnetizations of any two adjacent layers are parallel. Here we demonstrate on-off control of the spin-triplet supercurrent in such junctions, achieved by rotating the magnetization direction of one …
Josephson junctions with s-wave superconductors (S) and multiple ferromagnetic (F) layers carry spin-triplet supercurrents in the presence of magnetically inhomogeneous spin-mixer interfaces. Here, we report magnetic Josephson junctions with exchange-spring and double exchange-spring ("spin-mixer") Co/Py interfaces. At the Co/Py interface, exchange coupling is strong with respect to the magnetic anisotropy of Py and so, depending on the direction and magnitude of an external magnetic field, a non-collinear magnetic structure forms in Py creating the necessary magnetic inhomogeneity for singlet…
Motivated by a recent experiment evidencing triplet superconductivity in a ferromagnetic Josephson junction with a Cu$_2$MnAl-Heusler barrier, we construct a theoretical model accounting for this observation. The key ingredients in our model which generate the triplet supercurrent are \textit{spin-active zones}, characterised by an effective canted interface magnetic moment. Using a numerical solution of the quasiclassical equations of superconductivity with spin-active boundary conditions, we find qualitatively very good agreement with the experimentally observed supercurrent. Further experim…
Charge and spin Josephson currents in a ballistic superconductor-ferromagnet-superconductor junction with spin-triplet pairing symmetry are studied using the quasiclassical Eilenberger equation. The gap vector of superconductors has an arbitrary relative angle with respect to magnetization of the ferromagnetic layer. We clarify the effects of the thickness of ferromagnetic layer and magnitude of the magnetization on the Josephson charge and spin currents. We find that 0-πtransition can occur except for the case that the exchange field and d-vector are in nearly perpendicular configuration. We …
We study the Josephson effect of a $\rm{T_1 F T_2}$ junction, consisting of spin-triplet superconductors (T), a weak ferromagnetic metal (F), and ferromagnetic insulating interfaces. Two types of the triplet order parameters are considered; $(k_x +ik_y)\hat{z}$ and $k_x \hat{x}+k_y\hat{y}$. We compute the current density in the ballistic limit by using the generalized quasiclassical formalism developed to take into account the interference effect of the multilayered ferromagnetic junction. We discuss in detail how the current-phase relation is affected by orientations of the d-vectors of super…
We study the appearance of a Josephson spin current in a model triplet superconductor junction with a magnetically-active tunnelling barrier. We find three distinct mechanisms for producing a spin current, and we provide a detailed discussion of the symmetry properties and the physical origins of each. By combining these three basic mechanisms, we find that it is possible to exercise fine control over the spin currents. In particular, we show that unlike the charge current, the spin currents on either side of the barrier need not be identical.
We study the long-range triplet Josephson current in a clean junction composed of two s-wave superconductors and a normal-metal/ferromagnet/normal-metal trilayer. Through applying the bias voltages on the metal regions by two antiparallel half-metal electrodes, we show that the amplitude and direction of this long-range current can be controlled easily and flexibly. Such current arises from the fact that the applied voltage can produce a nonequilibrium spin-dependent quasiparticle distribution in the metal regions so that the Cooper pairs acquire an extra momenta, which will lead to a spin-fli…
We have studied Josephson junctions with barriers prepared from the Heusler compound Cu$_2$MnAl. In the as-prepared state the Cu$_2$MnAl layers are non ferromagnetic and the critical Josephson current density $j_{c}$ decreases exponentially with the thickness of the Heusler layers $d_{F}$. On annealing the junctions at 240\degree C the Heusler layers develop ferromagnetic order and we observe a dependence $j_{c}(d_{F}$) with $j_{c}$ strongly enhanced and weakly thickness dependent in the thickness range 7.0 nm < $d_{F}$ < 10.6 nm. We attribute this feature to a triplet component in the superco…
We study the Josephson effect in a triplet superconductor--ferromagnet--singlet superconductor junction. We show that the interaction of tunneling Cooper pairs with the interface magnetization can permit a Josephson current at the lowest order of a tunneling Hamiltonian perturbation theory. Two conditions must be satisfied for this to occur: the magnetization of the ferromagnet has a component parallel to the ${\bf d}$-vector of the triplet superconductor, and the gaps of the superconductors have the same parity with respect to the interface momentum. The resulting charge current displays an u…
We have investigated the Josephson coupling between two s-wave superconductors separated by the ferromagnetic trilayers with noncollinear magnetization. We find that the long-range triplet critical current will oscillate with the strength of the exchange field and the thickness of the interface layer, when the interface magnetizations are orthogonal to the central magnetization. This feature is induced by the spatial oscillations of the spin-triplet state |\uparrow\downarrow>+|\downarrow\uparrow> in the interface layer. Moreover, the critical current can exhibit a characteristic nonmonotonic b…
The study of superconductor-ferromagnet interfaces has generated great interest in the last decades, leading to the observation of spin-aligned triplet supercurrents and 0-pi transitions in Josephson junctions where two superconductors are separated by an itinerant ferromagnet. Recently, spin-filter Josephson junctions with ferromagnetic barriers have shown unique transport properties, when compared to standard metallic ferromagnetic junctions, due to the intrinsically nondissipative nature of the tunneling process. Here we present the first extensive characterization of spin polarized Josephs…
We theoretically study static and dynamic properties of short Josephson junctions (JJ) with singlet and triplet Josephson coupling. In singlet Josephson weak links, two singlet superconductors S are connected with each other by a normal film (N) or wire. Triplet JJs, which we denote S$_{\text{m}}$/N(F)/S$_{\text{m}}$, are formed by two singlet BCS superconductors covered by a thin layer of a weak ferromagnet F$_{\text{w}}$. These superconductors S$_{\text{m}}$ are separated from the N (or F) layer by spin filters, which pass electrons with only one spin orientation. The triplet Cooper pairs pr…
In this paper we extend our earlier analysis of the novel Josephson effect in triplet superconductor--ferromagnet--triplet superconductor (TFT) junctions [B. Kastening \emph{et al.}, Phys. Rev. Lett. {\bf{96}}, 047009 (2006)]. In our more general formulation of the TFT junction we allow for potential scattering at the barrier and an arbitrary orientation of the ferromagnetic moment. Several new effects are found upon the inclusion of these extra terms: for example, we find that a Josephson current can flow even when there is vanishing phase difference between the superconducting condensates on…
The critical current modulation and the spontaneous flux of the vortex states in corner Josephson junctions between Sr$_2$RuO$_4$ and a conventional s-wave superconductor are calculated as a function of the crystal orientation, and the magnetic field. For Sr$_2$RuO$_4$ we assume two nodeless p-wave pairing states. Also we use the nodal $f$-wave states $B_{1g}\times E_u$ and $B_{2g} \times E_u$, and one special p-wave state having line nodes. It is seen that the critical current depends solely on the topology of the gap.
The increased capabilities of coupling more and more materials through functional interfaces are paving the way to a series of exciting experiments and extremely advanced devices. Here we focus on the capability of magnetically inhomogeneous superconductor/ferromagnet (S/F) interfaces to generate spin-polarized triplet pairs. We build on previous achievements on spin-filter ferromagnetic Josephson junctions (JJs) and find unique correspondence between neat experimental benchmarks in the temperature behavior of the critical current and theoretical modeling based on microscopic calculations, whi…
We study the Josephson effect in planar $SF_1F_2S$ junctions that consist of conventional $s$-wave superconductors ($S$) connected by two metallic monodomain ferromagnets ($F_1$ and $F_2$) with arbitrary transparency of interfaces. We solve the scattering problem in the clean limit based on the Bogoliubov-de Gennes equation for both spin-singlet and odd in frequency spin-triplet pairing correlations. We calculate numerically the Josephson current-phase relation $I(ϕ)$. While the first harmonic of $I(ϕ)$ is completely generated by spin-singlet and short-range spin-triplet superconducting correl…
A thin ferromagnetic layer on a bulk equal-spin-pairing triplet superconductor is shown to mediate a Josephson coupling between the spin $\uparrow$ and $\downarrow$ condensates of the superconductor. By deriving analytic expressions for the bound states at the triplet superconductor-ferromagnet interface, we show that this spin Josephson effect establishes an effective anisotropy axis in the ferromagnetic layer. The associated Josephson spin current is predicted to cause a measurable precession of the magnetization about the vector order parameter of the triplet superconductor.
Dynamic states offer extended possibilities to control the properties of quantum matter. Recent efforts are focused on studying the ordered states which appear exclusively under the time-dependent drives. Here we demonstrate a class of systems which feature dynamic spin-triplet superconducting order stimulated by the alternating electric field. The effect is based on the interplay of ferromagnetism, interfacial spin-orbital coupling (SOC) and the condensate motion driven by the field, which converts hidden static p-wave order, produced by the joint action of the ferromagnetism and the SOC, int…
The Josephson current through a long s-wave superconductor/weak ferromagnet/s-wave superconductor weak link is studied theoretically in the regime of nonequilibrium spin-dependent occupation of electron states in the ferromagnetic intelayer. While under the considered nonequilibrium conditions the standard supercurrent, carried by the singlet part of current-carrying density of states, practically is not modified, the additional supercurrent flowing via the triplet part of the current-carrying density of states appears. Depending on voltage, controlling the particular form of spin-dependent no…
Josephson effects in the spin-triplet superconductor/altermagnet/spin-triplet superconductor junctions: the detection of the intrinsic $\bf{d}$-vector
School of Science, Qingdao University of Technology（青岛理工大学理学院）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料科学中心）；Hefei National Laboratory（合肥国家实验室）
The experimental achievements during the past year in demonstrating the existence of long-ranged spin-triplet supercurrents in ferromagnets proximity coupled to singlet superconductors open up the possibility for new interesting physics and applications [for a review, see M. Eschrig, Phys. Today 64(1), 43 (2011)]. Our group reported the injection of triplet supercurrents into a magnetically uniform ferromagnet (Co) by sandwiching it between two helimagnet/superconductor (Ho/Nb) bilayers to form a Nb/Ho/Co/Ho/Nb-type Josephson device. In the function of the Ho layer thicknesses, the supercurren…
In diffusive Josephson junctions the phase-difference $ϕ$ between the superconductors strongly influences the spectroscopic features of the layer separating them. The observation of a uniform minigap and its phase modulation were only recently experimentally reported, demonstrating agreement with theoretical predictions up to now - a vanishing minigap at $ϕ=π$. Remarkably, we find that in the presence of intrinsic spin-orbit coupling a giant proximity effect due to spin-triplet Cooper pairs can develop at $ϕ=π$, in complete contrast to the suppressed proximity effect without spin-orbit couplin…
Triplet supercurrents in multilayer ferromagnetic Josephson junctions with misaligned magnetization can penetrate thicker ferromagnetic barriers compared to the singlet component. Although the static properties of these junctions have been extensively studied, the dynamic characteristics remain largely unexplored. Here we report a comprehensive electrodynamic characterization of multilayer ferromagnetic Josephson junctions composed of Co and Ho. By measuring the temperature-dependent current-voltage characteristics and the switching current distributions down to 0.3 K, we show that phase dynam…
We calculate the Andreev bound states and the corresponding Josephson current for an asymmetric 2-dimensional Josephson junction by solving Bogoliubov-de-Gennes equations. The junction consists of a non-centrosymmetric superconductor (NCS) separated by a tunneling barrier with a variable height to a conventional s-wave superconductor. In addition to the antisymmetric spin-orbit coupling in the NCS on the one side, this asymmetric junction gives rise to a Rashba spin-orbit coupling at the interface. We explore the rich parameter space and recover various limiting cases such as s-wave/p-wave jun…
On the basis of the Usadel equation we study a multi-terminal Josephson junction. This junction is composed by "magnetic" superconductors S$_{\text{m}}$ which have singlet pairing and are separated from the normal n~wire by spin filters so that the Josephson coupling is caused only by fully polarized triplet components. We show that there is no interaction between triplet Cooper pairs with antiparallel total spin orientations. The presence of an additional singlet superconductor S attached to the n wire leads to a finite Josephson current $I_{\text{Q}}$ with an unusual current--phase relation.…
We have measured spin-triplet supercurrent in Josephson junctions of the form S/F'/F/F'/S, where S is superconducting Nb, F' is a thin Ni layer with in-plane magnetization, and F is a Ni/[Co/Ni]n multilayer with out-of-plane magnetization. The supercurrent in these junctions decays very slowly with F-layer thickness, and is much larger than in similar junctions not containing the two F' layers. Those two features are the characteristic signatures of spin-triplet supercurrent, which is maximized by the orthogonality of the magnetizations in the F and F' layers. Magnetic measurements confirm the…
We study the current-phase relation of a ballistic SIFIT junction, consisting of a spin-singlet superconductor (S), a weak ferromagnetic metal (F), a spin-triplet superconductor (T), and insulating ferromagnetic interfaces (I). We use the generalized quasiclassical formalism developed by A. Millis et al. to compute the current density and the free energy of the junction for arbitrary orientation of the magnetizations of the junction barrier. We investigate in detail the effect of the distribution of magnetization on the various harmonics of the current-phase relation and the transition of the …
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 the Josephson effect in spin-singlet superconductor/helical $p$-wave superconductor junctions with a ferromagnetic barrier using the quasiclassical Green function method. It is found that both $\sinϕ$-type and $\cosϕ$-type current-phase relations always exist, irrespective of the gap symmetries in superconductors. The indispensable condition for the $\sinϕ$-type and $\cosϕ$-type current is that the magnetization must have a component parallel to the crystallographic $a$ or $b$ axis, which is distinct from the case of $p$-wave superconductor described by a $\vect{d}$-vector with a unif…
We predict that long-range triplet correlations (LRTC) in superconductor/ferromagnet (S/F) hybrids with extrinsic impurity spin-orbit coupling (SOC) can be generated and manipulated by supercurrent flowing in the superconducting leads along the S/F interfaces. The LRTC appear via two basic mechanisms. The essence of the first one is the generation of triplets by the superconducting spin Hall effect. These pairs are long-range in the ferromagnet under the appropriate mutual orientation of the condensate momentum and the ferromagnet magnetization. The second mechanism is based on the singlet-tri…
We study the Josephson current through a ferromagnetic trilayer, both in the diffusive and clean limits. For colinear (parallel or antiparallel) magnetizations in the layers, the Josephson current is small due to short range proximity effect in superconductor/ferromagnet structures. For non colinear magnetizations, we determine the conditions for the Josephson current to be dominated by another contribution originating from long range triplet proximity effect.
The lengthscale over which supercurrent from conventional BCS, $s$-wave, superconductors ($S$) can penetrate an adjacent ferromagnetic ($F$) layer depends on the ability to convert singlet Cooper pairs into triplet Cooper pairs. Spin aligned triplet Cooper pairs are not dephased by the ferromagnetic exchange interaction, and can thus penetrate an $F$ layer over much longer distances than singlet Cooper pairs. These triplet Cooper pairs carry a dissipationless spin current and are the fundamental building block for the fledgling field of superspintronics. Singlet-triplet conversion by inhomogen…
Josephson junctions containing three ferromagnetic layers with non-collinear magnetizations between adjacent layers carry spin-triplet supercurrent under certain conditions. The signature of the spin-triplet supercurrent is a relatively slow decay of the maximum supercurrent as a function of the thickness of the middle ferromagnetic layer. In this work we focus on junctions where the middle magnetic layer is a [Co/Pd]$_N$ multilayer with perpendicular magnetic anisotropy (PMA), while the outer two layers have in-plane anisotropy. We compare junctions where the middle PMA layer is or is not con…
We study the dc Josephson effect in a diffusive multilayered SF'FF'S structure, where S is a superconductor and F,F' are different ferromagnets. We assume that the exchange energies in the F' and F layers are different ($% h $ and $H$, respectively) and the middle F layer consists of two layers with parallel or antiparallel magnetization vectors $M$. The $M$ vectors in the left and right F' layers are generally not collinear to those in the F layer. In the limit of a weak proximity effect we use a linearized Usadel equation. Solving this equation, we calculate the Josephson critical current fo…
We study the impact of the long-range spin-triplet proximity effect on the density of states (DOS) in planar SF1F2S Josephson junctions that consist of conventional superconductors (S) connected by two metallic monodomain ferromagnets (F1 and F2) with transparent interfaces. We determine the electronic DOS in F layers and the Josephson current for arbitrary orientation of the magnetizations using the solutions of Eilenberger equations in the clean limit and for a moderate disorder in ferromagnets. We find that fully developed long-range proximity effect can occur in highly asymmetric ferromagn…
We show that the Josephson effect between triplet superconductors is sensitive to the relative orientation of the d-vectors across the junction. In addition, we point out that the temperature and angular dependence of the Josephson effect can help distinguish between different order parameter symmetries. We discuss coherent and incoherent tunneling processes, and the role of surface bound states within the framework of non-local lattice Bogoliubov-deGennes equations.
We consider a Josephson junction with an arbitrary transmission coefficient $\mathcal{D}$ between a singlet and a triplet superconductor with the latter order parameter characterized by a d-vector of the form ($k_x\hat{y}-k_y\hat{x}$). Various quantities such as the tunnelling current, spin accumulation, and spin current are calculated via the quasiclassical Green's functions. We also present a symmetry argument on the existence of these quantities and their dependencies on the phase difference across the junction. A physical picture is also given in terms of the Andreev states near the juncti…
We show that the fully polarized triplet s-wave component is characterized not only by the spin direction, but also by chirality. Interaction of a polarized triplet component and a singlet one results in creation of triplet Cooper pairs with opposite spin direction or of different chiralities. Such spin transformation leads to interesting phenomena in multiterminal magnetic Josephson junctions. We calculate the dc Josephson current $I_{\text{J}}$ in a multiterminal Josephson contact of the S$_{\text{m}}$/n/S$_{\text{m}}^{\prime}$ type with "magnetic" superconductors S$_{\text{m}}$ that generat…
It has been predicted theoretically that an unconventional odd-frequency spin-triplet component of superconducting order parameter can be induced in multilayered ferromagnetic structures with non-collinear magnetization. In this work we study experimentally nano-scale devices, in which a ferromagnetic spin valve is embedded into a Josephson junction. We demonstrate two ways of in-situ analysis of such Josephson spin valves: via magnetoresistance measurements and via in-situ magnetometry based on flux quantization in the junction. We observe that supercurrent through the device depends on the r…
We study a singlet-triplet Josephson junction between a conventional s-wave superconductor and an unconventional p$_{\rm x}$-wave superconductor. The Andreev spectrum of the junction yields a spontaneous magnetization in equilibrium. This allows manipulating the occupation of the Andreev levels using an ac Zeeman field. The induced Rabi oscillations manifest themselves as a resonance in the current-phase relation. For a circularly polarized magnetic field, we find a spin selection rule, yielding Rabi oscillations only in a certain interval of the superconducting phase difference.
We show that a supercurrent carried by spinless singlet Cooper pairs can induce a spin accumulation in the normal metal interlayer of a Josephson junction. This phenomenon occurs when a nonequilibrium spin-energy mode is excited in the normal metal, for instance by an applied temperature gradient between ferromagnetic electrodes. Without supercurrent, the spin accumulation vanishes in the Josephson junction. With supercurrent, a spatially antisymmetric spin accumulation is generated that can be measured by tunneling to a polarized detector electrode. We explain the physical origin of the induc…
The long-range spin-triplet supercurrent transport is an interesting phenomenon in the superconductor/ferromagnet ($S/F$) heterostructure containing noncollinear magnetic domains. Here we study the long-range superharmonic Josephson current in asymmetric $S/F_1/F_2/S$ junctions. It is demonstrated that this current is induced by spin-triplet pairs $\mid\uparrow\uparrow\rangle-$$\mid\downarrow\downarrow\rangle$ or $\mid\uparrow\uparrow\rangle+$$\mid\downarrow\downarrow\rangle$ in the thick $F_1$ layer. The magnetic rotation of the particularly thin $F_2$ layer will not only modulate the amplitu…
A stationary Josephson effect in a weak-link between misorientated nonunitary triplet superconductors is investigated theoretically. The non-self-consistent quasiclassical Eilenberger equation for this system has been solved analytically. As an application of this analytical calculation, the current-phase diagrams are plotted for the junction between two nonunitary bipolar $f-$wave superconducting banks. A spontaneous current parallel to the interface between superconductors has been observed. Also, the effect of misorientation between crystals on the Josephson and spontaneous currents is stud…
We demonstrate that in multilayered superconductor-ferromagnet structures a non-collinear 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 $π$ type.
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 recently in proximity systems and Josephson junctions. We show using an analytically derived domain wall of an exchange spring 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 triplet $0-π$ transition, that can be observed in one and the same system either by tuning the domain wall or by v…
We present measurements of Josephson junctions containing three magnetic layers with noncolinear magnetizations. The junctions are of the form $S/F^{\prime}/N/F/N/F^{\prime \prime}/S$, where $S$ is superconducting Nb, $F^\prime$ is either a thin Ni or Permalloy layer with in-plane magnetization, $N$ is the normal metal Cu, $F$ is a synthetic antiferromagnet (SAF) with magnetization perpendicular to the plane, composed of Pd/Co multilayers on either side of a thin Ru spacer, and $F^{\prime \prime}$ is a thin Ni layer with in-plane magnetization. The supercurrent in these junctions decays more s…
We show that injecting nonequilibrium spins into the superconducting leads strongly enhances the stationary Josephson current through a superconductor-ferromagnet-superconductor junction. The resulting long-range super-current through a ferromagnet is carried by triplet Cooper pairs that are formed in s-wave superconductors by the combined effects of spin injection and exchange interaction. We quantify the exchange interaction in terms of Landau Fermi-liquid factors. The magnitude and direction of the long-range Josephson current can be manipulated by varying the angles of the injected polariz…
