We examine the appearance of a spontaneous bulk spin current in a triplet superconductor in contact with a metallic ferromagnet. The spin current results from the spin-flip of Cooper pairs upon reflection from the interface with the ferromagnet, and is shown to display strong similarities to the spontaneous charge current in a Josephson junction. We express the spin current in terms of the Andreev reflection coefficients, which are derived by the construction of the quasiclassical scattering wavefunctions. The dependence of the spin current upon a number of parameters is investigated, in particular the orientation of the magnetic moment of the ferromagnet, the exchange splitting, the temperature, and the orbital pairing state of the triplet superconductor.
We investigate charge pumping in ferromagnet/triplet superconductor junctions where the magnetization of the ferromagnet is inhomogeneous and dynamical. It is shown that charge current is pumped due to the coupling of the localized spin with triplet vector spin chirality, vector spin chirality formed by the triplet vector of Cooper pairing. Physical mechanism of the charge pumping is also discussed.
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.
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 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.
We develop a theory which describes hybrid structures consisting out of superconducting and ferromagnetic parts. We give two examples for applications. First, we consider a hybrid structure containing a strong ferromagnet in the ballistic limit. Second, we study for a weak ferromagnet the influence of a domain wall on the superconducting proximity effect. In both cases we account quantitatively for the mixing between singlet and triplet correlations.
Fundamental symmetry breaking and relativistic spin-orbit coupling give rise to fascinating phenomena in quantum materials. Of particular interest are the interfaces between ferromagnets and common s-wave superconductors, where the emergent spin-orbit fields support elusive spin-triplet superconductivity, crucial for superconducting spintronics and topologically-protected Majorana bound states. Here, we report the observation of large magnetoresistances at the interface between a quasi-two-dimensional van der Waals ferromagnet Fe0.29TaS2 and a conventional s-wave superconductor NbN, which prov…
We have investigated the proximity effect in superconductor/ferromagnet junctions in a systematic manner to discuss the relationship between the zero-energy peak (ZEP) of the local density of states (LDOS) and spin-triplet odd-frequency pairing. By exactly solving the nonlinear Usadel equations, we have found that the ZEP is realized in a wide range of geometrical and material parameters in the case of the noncollinear magnetization. This strongly suggests the robustness of the ZEP induced by spin-triplet odd-frequency pairing in such systems. We also found that the crossover from singlet pair…
We study the spin and charge currents flowing at the interface of an itinerant ferromagnet with a topological spin-triplet superconductor having different number of time-reversal-invariant Majorana helical modes. Depending on the number of helical modes, the capacity of carrying spin and charge currents is shown to be directly related to the amplitude and orientation of the ferromagnetic magnetization with respect to the superconducting $\vec{d}$-vector. Differently from the one-helical mode spin-triplet superconductor, we find that the presence of a finite amount of electronic hybridization w…
We discuss the Josephson effect in strongly spin-polarized ferromagnets where triplet correlations are induced by means of spin-active interface scattering, extending our earlier work [Phys. Rev. Lett. 102, 227005 (2009)] by including impurity scattering in the ferromagnetic bulk and the inverse proximity effect in a fully self-consistent way. Our quasiclassical approach accounts for the differences of Fermi momenta and Fermi velocities between the two spin bands of the ferromagnet, and thereby overcomes an important short-coming of previous work within the framework of Usadel theory. We show …
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 condition the standard supercurrent, carried by the singlet part of current-carrying density of states, 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 nonequilibrium …
Cooper pairs in superconductors are normally spin singlet. Nevertheless, recent studies suggest that spin-triplet Cooper pairs can be created at carefully engineered superconductor-ferromagnet interfaces. If Cooper pairs are spin-polarized they would transport not only charge but also a net spin component, but without dissipation, and therefore minimize the heating effects associated with spintronic devices. Although it is now established that triplet supercurrents exist, their most interesting property - spin - is only inferred indirectly from transport measurements. In conventional spintroni…
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 θ. At small angles the LRTC decays in the ferromagnet exponentially in a monotonic way. If the angle θexceeds a certain value, the exponential decay of the L…
We investigate spin-dependent quasiparticle and Cooper-pair transport through a central node interfaced with two superconductors and two ferromagnets. We demonstrate that voltage biasing of the ferromagnetic contacts induces superconducting triplet correlations on the node and reverses the supercurrent flowing between the two superconducting contacts. We further find that such triplet correlations can mediate a tunable spin current flow into the ferromagnetic contacts. Our key finding is that unequal spin-mixing conductances for the two interfaces with the ferromagnets result in equal-spin tri…
We calculate the conductance of a superconductor/ferromagnet (S/F) mesoscopic structure in the dirty limit. First we assume that the ferromagnet exhibits a homogeneous magnetization and consider the case that the penetration of the condensate into the F wire is negligible and the case in which the proximity effect is taken into account. It is shown that if the exchange field is large enough, the conductance below the critical temperature $T_C$, is always smaller than the conductance in the normal state. At last, we calculate the conductance for a F/S structure with a local inhomogeneity of the…
The coexistence of a homogeneous (Meissner-like) phase of spin-triplet superconductivity and ferromagnetism is investigated within the framework of a phenomenological model of spin-triplet ferromagnetic superconductors. The results are discussed in view of application to metallic ferromagnets as UGe$_2$, ZrZn$_2$, URhGe, and Fe.
In the past year, several groups have observed evidence for long-range spin-triplet supercurrent in Josephson junctions containing ferromagnetic (F) materials. In our work, the spin-triplet pair correlations are created by non-collinear magnetizations between a central Co/Ru/Co "synthetic antiferromagnet" (SAF) and two outer thin F layers. Here we present data showing that the spin-triplet supercurrent is enhanced up to 20 times after our samples are subject to a large in-plane magnetizing field. This surprising result can be explained if the Co/Ru/Co SAF undergoes a "spin-flop" transition, wh…
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
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 have studied the dependence of the superconducting (SC) transition temperature on the mutual orientation of magnetizations of Fe1 and Fe2 layers in the spin valve system CoO_x/Fe1/Cu/Fe2/Pb. We find that this dependence is nonmonotonic when passing from the parallel to the antiparallel case and reveals a distinct minimum near the orthogonal configuration. The analysis of the data in the framework of the SC triplet spin valve theory gives direct evidence for the long-range triplet superconductivity arising due to noncollinearity of the two magnetizations.
In 2010, several experimental groups obtained compelling evidence for spin-triplet supercurrent in Josephson junctions containing strong ferromagnetic materials. Our own best results were obtained from large-area junctions containing a thick central Co/Ru/Co "synthetic antiferromagnet" and two thin outer layers made of Ni or PdNi alloy. Because the ferromagnetic layers in our samples are multi-domain, one would expect the sign of the local current-phase relation inside the junctions to vary randomly as a function of lateral position. Here we report measurements of the area dependence of the cr…
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.
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…
Magnetic susceptibility, entropy and specific heat are calculated at the equilibrium points of phase transition to a phase of coexistence of ferromagnetic order and superconductivity in a new class of spin-triplet ferromagnetic superconductors. The results are discussed in view of application to metallic ferromagnets as UGe$_2$, ZrZn$_2$, URhGe.
We investigate thermodynamic phases, including the phase of coexistence of superconductivity and ferromagnetism, the possible phase transitions of first and second order, and the shape of the phase diagram in mean-field approximation for a phenomenological model of spin-triplet ferromagnetic superconductors. The results are discussed in view of application to metallic ferromagnets as UGe$_2$, ZrZn$_2$, URhGe, and Fe.
The existence of spin-triplet superconductivity in non-collinear magnetic heterostructures with superconductors is by now well established. This observation lays the foundation of superconducting spintronics with the aim to create a low-power consuming devices in order to replace the conventional electronics limited by heating. From a fundamental point of view the investigation of the structure and properties of spin-triplet Cooper pairs continues. Recently, spectroscopic evidence has shown to offer more detailed insights in the structure of triplet Cooper pairs than the supercurrent. Hence, w…
Josephson junctions containing multiple ferromagnetic layers can carry spin-triplet supercurrent under certain conditions. Large-area junctions containing multiple domains are expected to have a random distribution of 0 or pi coupling across the junction surface, whereas magnetized samples should have uniquely pi coupling everywhere. We have measured the area dependence of the critical current in such junctions, and confirm that the critical current scales linearly with area in magnetized junctions. For as-grown (multi-domain) samples, the results are mixed. Samples grown on a thick Nb base ex…
At the interface between a ferromagnetic insulator and a superconductor there is a coupling between the spins of the two materials. We show that when a supercurrent carried by triplet Cooper pairs flows through the superconductor, the coupling induces a magnon spin current in the adjacent ferromagnetic insulator. The effect is dominated by Cooper pairs polarized in the same direction as the ferromagnetic insulator, so that charge and spin supercurrents produce similar results. Our findings demonstrate a way of converting Cooper pair supercurrents to magnon spin currents.
The long-range proximity effect in superconductor/ferromagnet (S/F) hybrid nano-structures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the fer- romagnet 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 con- densate 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 …
We have studied the proximity-induced superconducting triplet pairing in CoO$_x$/Py1/Cu/Py2/Cu/Pb spin-valve structure (where Py = Ni$_{0.81}$Fe$_{0.19}$). By optimizing the parameters of this structure we found a triplet channel assisted full switching between the normal and superconducting states. To observe an "isolated" triplet spin-valve effect we exploited the oscillatory feature of the magnitude of the ordinary spin-valve effect $ΔT_c$ in the dependence of the Py2-layer thickness $d_{Py2}$. We determined the value of $d_{Py2}$ at which $ΔT_c$ caused by the ordinary spin-valve effect (th…
Using the $ϕ$-mapping method, we argue that ferromagnetic spin-triplet superconductors allow formation of unstable magnetic monopoles. In particular, we show that the limit points and the bifurcation points of the $ϕ$-mapping will serve as the interaction points of these magnetic monopoles.
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…
In general, conventional superconductivity should not occur in a ferromagnet, though it has been seen in iron under pressure. Moreover, theory predicts that the current is always carried by pairs of electrons in a spin singlet state, so conventional superconductivity decays very rapidly when in contact with a ferromagnet, which normally prohibits the existence of singlet pairs. It has been predicted that this rapid spatial decay would not occur when spin triplet superconductivity could be induced in the ferromagnet. Here we report a Josephson supercurrent through the strong ferromagnet CrO2, f…
We present a theoretical study of a ferromagnet/s-wave superconductor junction to investigate the signatures of induced triplet correlations in the system. We apply the extended BTK-formalism and allow for an arbitrary magnetization strength/direction of the ferromagnet, a spin-active barrier, Fermi-vector mismatch, and different effective masses in the two systems. It is found that the phase associated with the $xy$-components of the magnetization in the ferromagnet couples with the superconducting phase and induces spin-triplet pairing correlations in the superconductor, if the tunneling bar…
The spin susceptibility in the uranium ferromagnet superconductors is calculated. There is shown that the absence of superconductivity paramagnetic limitation for the field directions perpendicular to the direction of the spontaneous magnetization is explained by the itinerant ferromagnet band splitting rather than by a rotation of magnetization toward the external field direction. The qualitative description of the upper critical field temperature dependence is given.
We consider some properties of odd frequency triplet superconducting condensates. In order to describe fluctuations we construct a supermatrix sigma-model for the superconductor/ferromagnet or superconductor/normal-metal structures. We show that an odd frequency triplet superconductor, when in isolation or coupled to a normal metal, generally displays behaviour comparable to a superconductor with the usual singlet pairings. However, for spin dependent systems such as the superconductor/ferromagnet the two types of superconductor have quite different behaviour. We discuss this difference by con…
We analyze the proximity effect of superconductor/ferromagnet nanostructures and point out that the scattering of quasiparticle of spin-triplet pairs by local magnetic moments leads to large resistance peak slightly below the superconducting transition temperature of the superconductor. Both the temperature and the magnitude of the resistance peak decrease with increasing magnetic field, which agree quite well with the experimental results reported in [Nature Phys. 6, 389 (2010)].
Using the quasiclassical Green's function formalism, we study the influence of the odd-frequency spin-triplet superconductivity on the local density of states (LDOS) in a diffusive ferromagnet (DF) attached to a superconductor. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli's principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of these states, the pairing state…
It has been commonly accepted that magnetic field suppresses superconductivity by inducing the ordered motion of Cooper pairs. We demonstrate that magnetic field can instead provide a generation of superconducting correlations by inducing the motion of superconducting condensate. This effect arises in superconductor/ferromagnet heterostructures in the presence of Rashba spin-orbital coupling. We predict the odd-frequency spin-triplet superconducting correlations called the Berezinskii order to be switched on at large distances from the superconductor/ferromagnet interface by the application of…
The superconducting critical temperature $T_C$ of a superconductor/ferromagnet (S/F) bilayer with spin-flip scatterings at the interface is calculated as a function of the ferromagnet thickness $d_F$ in the dirty limit employing the Usadel equation. The appropriate boundary conditions from the spin-flip scatterings at the S/F interface are derived for the Usadel equation which includes the spin triplet pairing components as well as the spin singlet one. The spin-flip processes induce the spin triplet pairing components with s-wave in momentum and odd symmetry in frequency from the s-wave singl…
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…
We study Superconductor-Ferromagnet-Superconductor (Nb-Cu0.47 Ni0.53-Nb) Josephson junctions with spatial variations in the barrier thickness. Critical current vs. magnetic flux diffraction patterns indicate that the critical current density changes sign along the width of the junctions, creating interfaces between 0 and pi junction regions around which spontaneous currents can circulate. Shapiro steps observed at half-integer Josephson voltages can be explained by the phase-locking of the spontaneous circulating currents to the applied rf modulation.
We have previously shown that a ferromagnet-superconductor heterostructure may possess a spontaneous current circulation parallel to the interface. This current is caused by Andreev bound states in the thin ferromagnetic layer, and can be fully spin-polarized. Here we investigate the total energy of the system in cases where the current either does or does not flow. We show that the current is a true quantum ground state effect, and examine the effect of the current on the different contributions to the total energy.
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 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 t…
Ferromagnetic spin valves offer the key building blocks to integrate giant- and tunneling-magnetoresistance effects into spintronics devices. Starting from a generalized Blonder-Tinkham-Klapwijk approach, we theoretically investigate the impact of interfacial Rashba and Dresselhaus spin-orbit couplings on the tunneling conductance, and thereby the magnetoresistance characteristics, of ferromagnet/superconductor/ferromagnet spin-valve junctions embedding thin superconducting spacers between the either parallel or antiparallel magnetized ferromagnets. We focus on the unique interplay between usu…
Recent results for the coexistence of ferromagnetism and unconventional superconductivity with spin-triplet Cooper pairing are reviewed on the basis of the quasi-phenomenological Ginzburg-Landau theory. New results are reported. The results are discussed in view of applications to metallic compounds as UGe2, URhGe, ZrZn2.
We calculate the diamagnetic susceptibility in zero external magnetic field above the phase transition from ferromagnetic phase to phase of coexistence of ferromagnetic order and unconventional superconductivity. For this aim we use generalized Ginzburg-Landau free energy of unconventional ferromagnetic superconductor with spin-triplet electron pairing. A possible application of the result to some intermetallic compounds is briefly discussed.
We characterize the coexistence of itinerant ferromagnetism and spin-triplet superconductivity within a single mechanism involving local (Hund's rule) exchange among $d$ electrons. The ratio of transition temperatures and the spin anisotropy of the superconducting gap is estimated for $ZrZn_2$. The $A$ phase is stable in very low applied and molecular fields, whereas the $A1$ phases persists in higher fields. A small residual magnetic moment is present below the Stoner threshold in the superconducting phase.
We propose that screened pairing interactions mediated by phonons could give rise to a spin triplet superconductivity in ferromagnetic compounds such as UGe_2. It is pointed out that the pairing interactions include anisotropic components such as those of p, d, f-waves in addition to dominant s-wave component due to the momentum dependence. Since the ferromagnetic long-range order coexists, there is a large splitting of the Fermi surfaces of up and down spin electrons, which suppresses singlet pairing. Therefore, triplet pairing occurs at last due to the sub-dominant anisotropic interactions, …
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…
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 …
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.
Ferromagnets can sustain supercurrents through the formation of equal spin triplet Cooper pairs and the mechanism of odd-frequency pairing. Since such pairs are not broken by the exchange energy of the ferromagnet, superconducting triplet correlations are long-ranged and spin-polarized, with promises for superconducting spintronics devices. The main challenge is to understand how triplets are generated at the superconductor (S)/ ferromagnet (F) interface. Here we use the concept of a so-called triplet spin valve (TSV) to investigate the conversion of singlets in a conventional superconductor t…
We study experimentally nanoscale Josephson junctions and Josephson spin-valves containing strong Ni ferromagnets. We observe that in contrast to junctions, spin valves with the same geometry exhibit anomalous Ic(H) patterns with two peaks separated by a dip. We develop several techniques for in-situ characterization of micromagnetic states in our nano-devices, including magnetoresistance, absolute Josephson fluxometry and First-Order-Reversal-Curves analysis. They reveal a clear correlation of the dip in supercurrent with the antiparallel state of a spin-valve and the peaks with two noncollin…
Scanning tunneling spectroscopy measurements conducted on epitaxially grown bilayers of half-metallic ferromagnetic La2/3Ca1/3MnO3 (LCMO) on superconducting (SC) (100)YBa2Cu3O7-delta (YBCO) reveal long-range penetration of superconducting order into the LCMO. This anomalous proximity effect manifests itself in the tunneling spectra measured on the LCMO layer as gaps and zero bias conductance peaks. Remarkably, these proximity-induced spectral features were observed for bilayers with LCMO thickness of up to 30 nm, an order of magnitude larger than the expected ferromagnetic coherence length in …
We have measured a long-range supercurrent in Josephson junctions containing Co (a strong ferromagnetic material) when we insert thin layers of either PdNi or CuNi weakly-ferromagnetic alloys between the Co and the two superconducting Nb electrodes. The critical current in such junctions hardly decays for Co thicknesses in the range of 12-28 nm, whereas it decays very steeply in similar junctions without the alloy layers. The long-range supercurrent is controllable by the thickness of the alloy layer, reaching a maximum for a thickness of a few nm. These experimental observations provide stron…
A general quasi-phenomenological theory that describes phases and phase transitions of ferromagnetic superconductors with spin-triplet electron Cooper pairing is presented. The theory is based on extended Ginzburg-Landau expansion in powers of superconducting and ferromagnetic order parameters. A simple form for the dependence of theory parameters on the pressure ensures a correct theoretical outline of the temperature-pressure phase diagram where a stable phase of coexistence of p-wave superconductivity and itinerant ferromagnetism appears. This new theory is in an excellent agreement with th…
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 …
A model for coexistence of p-wave spin-triplet superconductivity (SC) and itinerant ferromagnetism (FM) is presented. The Hamiltonian can be diagonalized by using the so(5) algebraic coherent state. We obtain the coupling equations of the magnetic exchange energy and superconducting gaps through the double-time Green function. It is found that the ferromagnetisation gives rise to the phase transitions of p-wave superconducting states or superfluid of $^{3}He$.
