Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization

Abstract

We calculate the dc Josephson current IJ for two types of superconductor-ferromagnet (S/F) Josephson junctions. The junction of the first type is a S/F/S junction. On the basis of the Eilenberger equation, the Josephson current is calculated for an arbitrary impurity concentration. If hτ ≪ 1 the expression for the Josephson critical current Ic is reduced to that which can be obtained from the Usadel equation (h is the exchange energy, τ is the momentum relaxation time). In the opposite limit hτ ≫ 1 the superconducting condensate oscillates with period vF /h and penetrates into the F region over distances of the order of the mean free path l. For this kind of junctions we also calculate IJ in the case when the F layer presents a nonhomogeneous (spiral) magnetic structure with the period 2π/Q. It is shown that for not too low temperatures, the π-state which occurs in the case of a homogeneous magnetization (Q = 0) may disappear even at small values of Q. In this nonhomogeneous case, the superconducting condensate has a nonzero triplet component and can penetrate into the F layer over a long distance of the order of ξT = D/2πT . The junction of the second type consists of two S/F bilayers separated by a thin insulating film. It is shown that the critical Josephson current Ic depends on the relative orientation of the effective exchange field h of the bilayers. In the case of an antiparallel orientation, Ic increases with increasing h. We establish also that in the F film deposited on a superconductor, the Meissner current created by the internal magnetic field may be both diamagnetic or paramagnetic.

Spin-triplet supercurrent through inhomogeneous ferromagnetic trilayers

“…One of the most intriguing phenomena in the context of this interplay is the generation of a long-ranged spin-triplet supercurrent flowing through a Josephson junction with magnetic elements. The main criterion for generation of such a current is that some form of magnetic inhomogeneity must be present in the junction, as first shown by Bergeret et al [20][21][22] and Volkov et al [23][24][25] . In the diffusive limit of transport, being often the experimentally most relevant regime, such a nonuniform magnetization can induce exotic long-range superconducting correlations which are odd under time-reversal: the so-called odd-frequency superconducting state.…”

Odd triplet superconductivity in a superconductor/ferromagnet system with a spiral magnetic structure

“…The formula (2) is valid for a short mean free path ( hτ << 1). If the exchange field h is strong enough (hτ >> 1), the condensate penetrates the ferromagnet over a distance of the order of l (if τ T < 1) and oscillates with the period ∼ v/h [4,5]. Note that a short length of the condensate penetration is related to the fact that Cooper pairs in a conventional superconductor are formed by two electrons with opposite spins.…”

Theoretical Study of Magnetism Induced by Proximity Effect in a Ferromagnetic Josephson Junction with a Normal Metal

“…Substituting Eqs (19)- (23) into Eq. (25) and then performing the integration with respect to x in Eq.…”

“…18) Moreover, it is expected that the amplitude of anomalous Green's function becomes due to the mismatch of the Fermi surfaces between F and S, since F has the exchange splitting between up and down Fermi surfaces. 19) Therefore, the linearization of Eilenberger equation can be suitable to the 4/18 present system.…”

“…1,2) The proximity effect in s-wave superconductor/ferromagnetic metal (S/F) hybrid junctions provides interesting phenomena which are not observed in S/N hybrid junctions and thus has been extensively studied both theoretically and experimentally. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In a S/F junction, due to the proximity effect, spin-singlet Cooper pairs (SSCs) penetrate into the F. Because of the exchange splitting of the electronic density of states for up and down electrons, the SSC in the F acquires the finite center-of-mass momentum, and the pair amplitude shows a damped oscillatory behavior with the thickness of the F. [20][21][22] Interesting phenomenon induced by the damped oscillatory behavior of the pair amplitude is a π-state in a S/F/S junction, where the current-phase relation in the Josephson current is shifted by π from that of the ordinary S/I/S and S/N/S junctions (called 0-state). [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]…”