Josephson current in a superconductor-ferromagnet junction with two non-collinear magnetic domains

We study the Josephson effect in a superconductor--ferromagnet--superconductor (SFS) junction with ferromagnetic domains of non-collinear magnetization. As a model for our study we consider a diffusive junction with two ferromagnetic domains along the junction. The superconductor is assumed to be close to the critical temperature $T_c$, and the linearized Usadel equations predict a sinusoidal current-phase relation. We find analytically the critical current as a function of domain lengths and of the angle between the orientations of their magnetizations. As a function of those parameters, the junction may undergo transitions between 0 and $\pi$ phases. We find that the presence of domains reduces the range of junction lengths at which the $\pi$ phase is observed. For the junction with two domains of the same length, the $\pi$ phase totally disappears as soon as the misorientation angle exceeds $\pi/2$. We further comment on possible implication of our results for experimentally observable 0--$\pi$ transitions in SFS junctions.Comment: 9 pages, 4 figures, minor changes, references adde

Enhancement of superconductivity in NbN nanowires by negative electron-beam lithography with positive resist

We performed comparative experimental investigation of superconducting NbN nanowires which were prepared by means of positive-and negative electron-beam lithography with the same positive tone Poly-methyl-methacrylate (PMMA) resist. We show that nanowires with a thickness 4.9 nm and widths less than 100 nm demonstrate at 4.2 K higher critical temperature and higher density of critical and retrapping currents when they are prepared by negative lithography. Also the ratio of the experimental critical-current to the depairing critical current is larger for nanowires prepared by negative lithography. We associate the observed enhancement of superconducting properties with the difference in the degree of damage that nanowire edges sustain in the lithographic process. A whole range of advantages which is offered by the negative lithography with positive PMMA resist ensures high potential of this technology for improving performance metrics of superconducting nanowire singe-photon detectors

Transport Properties in Ferromagnetic Josephson Junction between Triplet Superconductors

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-\pi transition can occur except for the case that the exchange field and d-vector are in nearly perpendicular configuration. We also show how spin current flows due to misorientation between the exchange field and d-vector.Comment: 6 pages, 8 figure

Surface effects in magnetic superconductors with a spiral magnetic structure

We consider a magnetic superconductor MS with a spiral magnetic structure. On the basis of generalized Eilenberger and Usadel equations we show that near the boundary of the MS with an insulator or vacuum the condensate (Gor'kov's) Green's functions are disturbed by boundary conditions and differ essentially from their values in the bulk. Corrections to the bulk quasiclassical Green's functions oscillate with the period of the magnetic spiral, $2\pi /Q$, and decay inside the superconductor over a length of the order $v/\pi T$ (ballistic limit) or $\sqrt{D/\pi T}$ (diffusive limit). We calculate the dc Josephson current in an MS/I/MS tunnel junction and show that the critical Josephson current differs substantially from that obtained with the help of the tunnel Hamiltonian method and bulk Green's functions.Comment: 10 pages 3 Figs; some misprints in fromulae corrected; submitted to Phys. Rev.

Mesoscopic fluctuations of the supercurrent in diffusive Josephson junctions

We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference across the junction. Technically, fluctuations on top of the spatially inhomogeneous proximity effect in the normal region are described by the replicated version of the \sigma-model. For the case of diffusive junctions with transparent interfaces, the magnitude of mesoscopic fluctuations of the critical current appears to be nearly 3 times larger than the prediction of the previous theory which did not take the proximity effect into account.Comment: 19 pages, 14 figures, 2 table

Odd spin-triplet superconductivity in a multilayered superconductor-ferromagnet Josephson junction

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 ($$ and $H$, respectively) and the middle F layer consists of two layers with parallel or antiparallel magnetization vectors $M$. The $M$ vectors in the left and right F' layers are generally not collinear to those in the F layer. In the limit of a weak proximity effect we use a linearized Usadel equation. Solving this equation, we calculate the Josephson critical current for arbitrary temperatures, arbitrary thicknesses of the F' and F layers ($$ and $L_{H}$) in the case of parallel and antiparallel $M$ orientations in the F layer. The part of the critical current $I_{cSR}$ formed by the short-range (SRC) singlet and S=0 triplet condensate components decays on a short length $\xi_{H}=\sqrt{D/H}$, whereas the part $$ due to the long-range triplet $|S|=1$ component (LRTC) decreases with increasing $L_{H}$ on the length $\xi_{N}=\sqrt{D/\pi T}$. Our results are in agreement with the experiment \cite{Birge}.Comment: 13 pages, 6 figures; some references updated and adde

Considerable enhancement of the critical current in a superconducting film by magnetized magnetic strip

We show that a magnetic strip on top of a superconducting strip magnetized in a specified direction may considerably enhance the critical current in the sample. At fixed magnetization of the magnet we observed diode effect - the value of the critical current depends on the direction of the transport current. We explain these effects by a influence of the nonuniform magnetic field induced by the magnet on the current distribution in the superconducting strip. The experiment on a hybrid Nb/Co structure confirmed the predicted variation of the critical current with a changing value of magnetization and direction of the transport current.Comment: 6 pages, 7 figure

Odd triplet superconductivity in a superconductor/ferromagnet structure 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 \theta. At small angles the LRTC decays in the ferromagnet exponentially in a monotonic way. If the angle \theta exceeds a certain value, the exponential decay of the LRTC is accompanied by oscillations with a period that depends on \theta. This oscillatory behaviour 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.Comment: 15 pages, 4 figures; to be published in Phys. Rev. B 73 (10) (2006