Role of interface transparency and spin-dependent scattering in diffusive ferromagnet/superconductor heterostructures

Abstract

We present a numerical study of the density of states in a ferromagnet/superconductor junction and the Josephson current in a superconductor/ferromagnet/superconductor junction in the diffusive limit by solving the Usadel equation with Nazarov's boundary conditions. Our calculations are valid for an arbitrary interface transparency and arbitrary spin-dependent scattering rate, which allows us to explore the entire proximity-effect regime. We first investigate how the proximity-induced anomalous Green's function affects the density of states in the ferromagnet for three magnitudes of the exchange field h compared to the superconducting gapIn each case, we consider the effect of the barrier transparency and allow for various concentrations of magnetic impurities. We clarify features that may be expected in the various parameter regimes accessible for the ferromagnetic film, with regard to thickness and exchange field. In particular, we address how the zero-energy peak and minigap observed in experiments may be understood in terms of the interplay between the singlet and triplet anomalous Green's function and their dependence on the concentration of magnetic impurities. Our results should serve as a useful tool for quantitative analysis of experimental data. We also investigate the role of the barrier transparency and spin-flip scattering in a superconductor/ferromagnet/superconductor junction. We suggest that such diffusive Josephson junctions with large residual values of the supercurrent at the 0-π transition, where the first harmonic term in the current vanishes, may be used as efficient supercurrentswitching devices. We numerically solve for the Josephson current in such a junction to clarify to what extent this idea may be realized in an experimental setup. It is also found that uniaxial spin-flip scattering has very different effect on the 0-π transition points depending on whether one regards the width-or temperaturedependence of the current. Our theory takes into account vital elements that are necessary to obtain quantitative predictions of the supercurrent in such junctions.

General solution of 2D and 3D superconducting quasiclassical systems: coalescing vortices and nanoisland geometries

“…5a . The results are identical with the one-dimensional solution to the S/F bilayer, displaying an enhanced DOS at the Fermi level (ε = 0) and a spin-split minigap structure 45 46 47 48 49 50 51 . The spatial distribution of the DOS is nearly constant for this particular parameter set choice in F as illustrated by Fig.…”

“…Furthermore, a slight suppression of the DOS is found in the same regions, at the level of ε = ±h( r), which is typical for superconductor/ferromagnet hybrid structures. 51 The second line is placed opposite the lower superconductor, in the y-direction as shown in Fig. 8b.…”

Density of states in the presence of spin dependent scattering: numerical and analytical approach

“…For that purpose the Kupriyanov-Lukichev (KL) boundary conditions at the superconductor/ ferromagnet interface are perfectly suitable [81]. Previously, the DOS in SF bilayers has been studied numerically [82,83]. We revisit this question and propose an analytical model to describe the influence of spin-flip and spin-orbit scattering on the DOS behavior.…”

Odd-frequency Pairing in Conventional Josephson Junctions

“…Following the initial proposal for odd-ω superconductivity, several studies have been conducted dedicated to the thermodynamic stability of intrinsically odd-ω phases [6][7][8][9]. A growing list of systems expected to host this unusual pairing state have been identified, including: ferromagnet-superconductor heterostructures [10][11][12][13][14][15][16], topological insulator-superconductor systems [17][18][19][20][21], normal metal-superconductor junctions [22][23][24][25][26], twodimensional electron systems coupled to bulk superconductors [27,28], multiband superconductors with a finite interband hybridization [29][30][31][32], and conventional superconductors subjected to time-dependent drives [33,34]. In addition to theoretical studies, there are experimental indications of the realization of odd-ω pairing at the interface of Nb thin films and epitaxial Ho [35,36].…”

“…which can be obtained by Fourier transforming the expression in Eq (15). We evaluate Eq (16) at the interface r = 0 by integrating over the two independent momenta, k 1 , k 2 , to find…”