Supercurrent in ferromagnetic Josephson junctions with heavy metal interlayers

The length scale 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 inhomogeneous magnetism is well established. Here, we describe an attempt to use spin-orbit coupling as an alternative mechanism to mediate singlet-triplet conversion in S-F-S Josephson junctions. We report that the addition of thin Pt spin-orbit-coupling layers in our Josephson junctions significantly increases supercurrent transmission, however the decay length of the supercurrent is not found to increase. We attribute the increased supercurrent transmission to Pt acting as a buffer layer to improve the growth of the Co F layer

Neutron skin uncertainties of Skyrme energy density functionals

Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of neutron-skin thickness and relate them to the equation of state of nuclear matter, and in particular to nuclear symmetry energy parameters. Methods: We use the nuclear superfluid Density Functional Theory with several Skyrme energy density functionals and density dependent pairing. To evaluate statistical errors and their budget, we employ the statistical covariance technique. Results: We find that the errors on neutron skin increase with neutron excess. Statistical errors due to uncertain coupling constants of the density functional are found to be larger than systematic errors, the latter not exceeding 0.06 fm in most neutron-rich nuclei across the nuclear landscape. The single major source of uncertainty is the poorly determined slope L of the symmetry energy that parametrizes its density dependence. Conclusions: To provide essential constraints on the symmetry energy of the nuclear energy density functional, next-generation measurements of neutron skins are required to deliver precision better than 0.06 fm.Comment: 5 pages, 4 figure

Interferometry of hyper-Rayleigh scattering by inhomogeneous thin films

The use of specific symmetry properties of the optical second-harmonic generation (the s,s-exclusion rule) has allowed us to observe high-contrast hyper-Rayleigh interference patterns in a completely diffuse light - an effect having no analog in case of linear (Rayleigh) scattering.Comment: 8 pages, 3 figure

Energy relaxation due to magnetic impurities in mesoscopic wires: Logarithmic approach

The transport in mesoscopic wires with large applied bias voltage has recently attracted great interest by measuring the energy distribution of the electrons at a given point of the wire, in Saclay. In the diffusive limit with negligible energy relaxation that shows two sharp steps at the Fermi energies of the two contacts, which are broadened due to the energy relaxation. In some of the experiments the broadening is reflecting an anomalous energy relaxation rate proportional to $E^{-2}$ instead of $E^{-3/2}$ valid for Coulomb electron-electron interaction, where $E$ is the energy transfer. Later it has been suggested that such relaxation rate can be due to electron-electron interaction mediated by Kondo impurities. In the present paper the latter is systematically studied in the logarithmic approximation valid above the Kondo temperature. In the case of large applied bias voltage Kondo resonances are formed at the steps of the distribution function and they are narrowed by increasing the bias. An additional Korringa energy broadening occurs for the spins which smears the Kondo resonances, and the renormalized coupling can be replaced by a smooth but essentially enhanced average coupling (factor of 8-10). Thus the experimental data can be described by formulas without logarithmic Kondo corrections, but with enhanced coupling. In certain regions of large bias, that averaged coupling depends weakly on the bias. In those cases the distribution function depends only on the ratio of the electron energy and the bias, showing scaling behavior. The impurity concentrations estimated from those experiments and other dephasing experiments can be very different, and a possible explanation considering the surface spin anisotropy due to strong spin-orbit interaction is the subject of our earlier paper.Comment: 12 pages, RevTex

Measuring the distribution of current fluctuations through a Josephson junction with very short current pulses

We propose to probe the distribution of current fluctuations by means of the escape probability histogram of a Josephson junction (JJ), obtained using very short bias current pulses in the adiabatic regime, where the low-frequency component of the current fluctuations plays a crucial role. We analyze the effect of the third cumulant on the histogram in the small skewness limit, and address two concrete examples assuming realistic parameters for the JJ. In the first one we study the effects due to fluctuations produced by a tunnel junction, finding that the signature of higher cumulants can be detected by taking the derivative of the escape probability with respect to current. In such a realistic situation, though, the determination of the whole distribution of current fluctuations requires an amplification of the cumulants. As a second example we consider magnetic flux fluctuations acting on a SQUID produced by a random telegraph source of noise.Comment: 6 pages, 6 figures; final versio

Supercurrent in ferromagnetic Josephson junctions with heavy-metal interlayers. II. Canted magnetization

It has been suggested by theoretical works that equal-spin triplet pair correlations can be generated in Josephson junctions containing both a ferromagnet and a source of spin-orbit coupling. Our recent experimental work suggested that such triplet correlations were not generated by a Pt spin-orbit coupling layer when the ferromagnetic weak link had entirely in-plane anisotropy [Satchell and Birge, Phys. Rev. B 97, 214509 (2018)]. Here, we revisit the experiment using Pt again as a source for spin-orbit coupling and a [Co(0.4 nm)/Ni(0.4 nm)]×8/Co(0.4 nm) ferromagnetic weak link with both in-plane and out-of-plane magnetization components (canted magnetization). The canted magnetization more closely matches theoretical predictions than our previous experimental work. Our results suggest that there is no supercurrent contribution in our junctions from equal-spin triplet pair correlations. In addition, this work includes systematic study of supercurrent dependence on Cu interlayer thickness, a common additional layer used to buffer the growth of the ferromagnet and which for Co may significantly improve the growth morphology. We report that the supercurrent in the [Co(0.4 nm)/Ni(0.4 nm)]×8/Co(0.4 nm) ferromagnetic weak links can be enhanced by over two orders of magnitude by tuning the Cu interlayer thickness. This result has important application in superconducting spintronics, where large critical currents are desirable for devices

Distortions to the penetration depth and coherence length of superconductor/normal-metal superlattices

Superconducting (S) thin film superlattices composed of Nb and a normal-metal spacer (N) have been extensively utilized in Josephson junctions given their favorable surface roughness compared to Nb films of comparable thickness. In this work, we characterize the London penetration depth and Ginzburg-Landau coherence lengths of S/N superlattices using polarized neutron reflectometry and electrical transport. Despite the normal-metal spacer layers being only approximately 8% of the total superlattice thickness, we surprisingly find that the introduction of these thin N spacers between S layers leads to a dramatic increase in the measured London penetration depth compared to that of a single Nb film of comparable thickness. Using the measured values for the effective in- and out-of-plane coherence lengths, we quantify the induced anisotropy of the superlattice samples and compare to a single Nb film sample. From these results, we find that the superlattices behave similarly to layered 2D superconductors

Robust optimization revisited via robust vector Farkas lemmas

This paper provides characterizations of the weakly minimal elements of vector optimization problems and the global minima of scalar optimization problems posed on locally convex spaces whose objective functions are deterministic while the uncertain constraints are treated under the robust (or risk-averse) approach, i.e. requiring the feasibility of the decisions to be taken for any possible scenario. To get these optimality conditions we provide Farkas-type results characterizing the inclusion of the robust feasible set into the solution set of some system involving the objective function and possibly uncertain parameters. In the particular case of scalar convex optimization problems, we characterize the optimality conditions in terms of the convexity and closedness of an associated set regarding a suitable point.This research was partially supported by MINECO of Spain and FEDER of EU, [grant number MTM2011-29064-C03-02] and by the project [B2015-28-04]: “A new approach to some classes of optimization problems”, Vietnam National University – HCMC, Vietnam