Nonsinusoidal current-phase relations and the 0−π0-\pi transition in diffusive ferromagnetic Josephson junctions

We study the effect of the interfacial transparency on the Josephson current in a diffusive ferromagnetic contact between two superconductors. In contrast to the cases of the fully transparent and the low-transparency interfaces, the current-phase relation is shown to be nonsinusoidal for a finite transparency. It is demonstrated that even for the nearly fully transparent interfaces the small corrections due to weak interfacial disorders contribute a small second-harmonic component in the current-phase relation. For a certain thicknesses of the ferromagnetic contact and the exchange field this can lead to a tiny minimum supercurrent at the crossover between 0 and $\pi$ states of the junction. Our theory has a satisfactory agreement with the recent experiments in which a finite supercurrent was observed at the transition temperature. We further explain the possibility for observation of a large residual supercurrent if the interfaces have an intermediate transparency.Comment: 7 pages, 4 figure

Theory of superconducting and magnetic proximity effect in S∣\midF structures with inhomogeneous magnetization textures and spin-active interfaces

We present a study of the proximity effect and the inverse proximity effect in a superconductor$\mid$ferromagnet bilayer, taking into account several important factors which mostly have been ignored in the literature so far. These include spin-dependent interfacial phase shifts (spin-DIPS) and inhomogeneous textures of the magnetization in the ferromagnetic layer, both of which are expected to be present in real experimental samples. Our approach is numerical, allowing us to access the full proximity effect regime. In Part I of this work, we study the superconducting proximity effect and the resulting local density of states in an inhomogeneous ferromagnet with a non-trivial magnetic texture. Our two main results in Part I are a study of how Bloch and N\'eel domain walls affect the proximity-induced superconducting correlations and a study of the superconducting proximity effect in a conical ferromagnet. The latter topic should be relevant for the ferromagnet Ho, which was recently used in an experiment to demonstrate the possibility to generate and sustain long-range triplet superconducting correlations. In Part II of this work, we investigate the inverse proximity effect with emphasis on the induced magnetization in the superconducting region as a result of the "leakage" from the ferromagnetic region. It is shown that the presence of spin-DIPS modify conclusions obtained previously in the literature with regard to the induced magnetization in the superconducting region. In particular, we find that the spin-DIPS can trigger an anti-screening effect of the magnetization, leading to an induced magnetization in the superconducting region with \textit{the same sign} as in the proximity ferromagnet.Comment: 16 pages, 18 figures. Accepted for publication in Phys. Rev.

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

Superconducting Phase Domains for Memory Applications

In this work we study theoretically the properties of S-F/N-sIS type Josephson junctions in the frame of the quasiclassical Usadel formalism. The structure consists of two superconducting electrodes (S), a tunnel barrier (I), a combined normal metal/ferromagnet (N/F) interlayer and a thin superconducting film (s). We demonstrate the breakdown of a spatial uniformity of the superconducting order in the s-film and its decomposition into domains with a phase shift $\pi$ . The effect is sensitive to the thickness of the s layer and the widths of the F and N films in the direction along the sIS interface. We predict the existence of a regime where the structure has two energy minima and can be switched between them by an electric current injected laterally into the structure. The state of the system can be non-destructively read by an electric current flowing across the junction

Josephson effect in SIFS-tunnel junctions with domain walls in weak link region

We study theoretically the properties of SIFS type Josephson junctions composed of two superconducting (S) electrodes separated by an insulating layer (I) and a ferromagnetic (F) film consisting of periodic magnetic domains structure with antiparallel magnetization directions in neighboring domains. The two-dimensional problem in the weak link area is solved analytically in the framework of the linearized quasiclassical Usadel equations. Based on this solution, the spatial distributions of the critical current density, $J_{C},$ in the domains and critical current, $I_{C},$ of SIFS structures are calculated as a function of domain wall parameters, as well as the thickness, $d_{F},$ and the width, $W,$ of the domains. We demonstrate that $I_{C}(d_{F},W)$ dependencies exhibit damped oscillations with the ratio of the decay length, $\xi_{1},$ and oscillation period, $\xi_{2},$ being a function of the parameters of the domains, and this ratio may take any value from zero to unity. Thus, we propose a new physical mechanism that may explain the essential difference between $\xi_{1}$ and $\xi_{2}$ observed experimentally in various types of SFS Josephson junctions.Comment: The paper will be published in JETP letters vol 101, issue 11, 201

Protected 0-pi states in SIsFS junctions for Josephson memory and logic

We study the peculiarities in current-phase relations (CPR) of the SIsFS junction in the region of $0$ to $\pi$ transition. These CPR consist of two independent branches corresponding to $0-$ and $\pi-$ states of the contact. We have found that depending on the transparency of the SIs tunnel barrier the decrease of the s-layer thickness leads to transformation of the CPR shape going in the two possible ways: either one of the branches exists only in discrete intervals of the phase difference $\varphi$ or both branches are sinusoidal but differ in the magnitude of their critical currents. We demonstrate that the difference can be as large as $10\%$ under maintaining superconductivity in the s layer. An applicability of these phenomena for memory and logic application is discussed.Comment: 5 pages, 5 figure

Dissipative charge transport in diffusive superconducting double-barrier junctions

We solve the coherent multiple Andreev reflection (MAR) problem and calculate current-voltage characteristics (IVCs) for Josephson SINIS junctions, where S are local-equilibrium superconducting reservoirs, I denotes tunnel barriers, and N is a short diffusive normal wire, the length of which is much smaller than the coherence length, and the resistance is much smaller than the resistance of the tunnel barriers. The charge transport regime in such junctions qualitatively depends on a characteristic value \gamma = \Delta \tau_d of relative phase shifts between the electrons and retro-reflected holes accumulated during the dwell time \tau_d. In the limit of small electron-hole dephasing \gamma << 1, our solution recovers a known formula for a short mesoscopic connector extended to the MAR regime. At large dephasing, the subharmonic gap structure in the IVC scales with 1/ \gamma, which thus plays the role of an effective tunneling parameter. In this limit, the even gap subharmonics are resonantly enhanced, and the IVC exhibits portions with negative differential resistance.Comment: 8 pages, 3 figures, typos corrected, to be published in Phys. Rev.

Current-phase relations in SIsFS junctions in the vicinity of 0-π\pi transition

We consider the current-phase relation (CPR) in the Josephson junctions with complex insulator-superconductor-ferromagnetic interlayers in the vicinity of 0-$\pi$ transition. We find a strong impact of the second harmonic on CPR of the junctions. It is shown that the critical current can be kept constant in the region of 0-pi transition, while the CPR transforms through multi-valued hysteretic states depending on the relative values of tunnel transparency and magnetic thickness. Moreover, CPR in the transition region has multiple branches with distinct ground states.Comment: Submitted in Phys. Rev.