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

Abstract

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, JC , in the domains and critical current, IC, of SIFS structures are calculated as a function of domain wall parameters, as well as the thickness, dF , and the width, W, of the domains. We demonstrate that IC(dF , W ) dependencies exhibit damped oscillations with the ratio of the decay length, ξ1, and oscillation period, ξ2, 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 ξ1 and ξ2 observed experimentally in various types of SFS Josephson junctions.

Proximity effect in multilayer structures with alternating ferromagnetic and normal layers

“…In the limit of large d i values, the situation is actually determined by the properties of the first F layer, so that A → 0, ξ 1 and ξ 2 tend to the respective values for the first ferromagnetic film, and Eq. ( 34) transfers to the known formula simulating the penetration of superconductivity in the SF sandwich [36][37][38]. However, Eq.…”

“…The phase φ is obtained from Eq. ( 37) as (38) Then, since the second term in Ψ(x) (34) vanishes at the points x mid = , the parameter A is given by the expression (39) Finally, the last constant in Ψ(x) (34) can be determined by the formula (40)…”

Critical current oscillations of elliptical Josephson junctions with single-domain ferromagnetic layers

“…The simplest model of a diffusive S/F/S Josephson junction based on the Usadel equation 46 predicts that ξ F 1 = ξ F 2 = D F /E ex where D F and E ex are the diffusion constant and exchange energy of F, respectively, and has an overall phase offset φ ≡ (d 0−π /ξ F 2 ) − π/2 = π/4. In the presence of spinorbit or spin-flip scattering 50 , or when the F-layer contains domain walls 51 , one expects to find ξ F 1 < ξ F 2 . For strong ferromagnetic materials with large exchange energy, however, one often finds that ξ F 1 > ξ F 2 8 , a result that can be explained from a semi-ballistic calculation starting from the Eilenberger equation 44,45 .…”

The effect of normal and insulating layers on 0-πtransitions in Josephson junctions with a ferromagnetic barrier

“…When the dirty limit does not apply, the oscillation period of J d c F ( )may depend on many other parameters and does not have to be constant, but can change with the F layer thickness [57]. A multi-domain structured ferromagnet may also change J d c F ( ); for instance, the oscillation period decreases when the domain width increases [58].…”