Nematic versus ferromagnetic spin filtering of triplet Cooper pairs in superconducting spintronics

Abstract

We consider two types of magnetic Josephson junctions (JJ). They are formed by two singlet superconductors S and magnetic layers between them so that the JJ is a heterostructure of the S m /n/S m type, where S m includes two magnetic layers with non-collinear magnetization vectors. One layer is represented by a weak ferromagnet and another one-the spin filter-is either conducting strong ferromagnet (nematic or N-type JJ) or magnetic tunnel barrier with spin-dependent transparency (magnetic or M-type JJ). Due to spin filtering only fully polarized triplet component penetrates the normal n wire and provides the Josephson coupling between the superconductors S. Although both filters let to pass triplet Cooper pairs with total spin S parallel to the filter axes, the behavior of nematic and magnetic JJs is completely different. Whereas in the nematic case the charge and spin currents, I Q and I sp , do not depend on mutual orientation of the filter axes, both currents vanish in magnetic JJ in case of antiparallel filter axes, and change sign under reversing the filter direction. The obtained expressions for I Q and I sp show clearly a duality between the superconducting phase ϕ and the angle α between the exchange fields in the weak magnetic layers. PACS numbers: 74.78.Fk, 85.25.Cp, 74.45.+c Triplet Cooper pairing is known to exist in superfluid 3 He [1, 2]. As concerns superconductors, the situation is less clear. Although some indication for the triplet superconductors has been found in a number of completely different classes of materials [3][4][5], a general consensus about the existence of the triplet superconductivity in the organic metals, heavy fermions and other interesting materials investigated from this point of view has not been achieved [6,7]. In principle, the fact that the spins of the fermions of the Cooper pairs are equal to each other does not contradict the Pauli principle because the condensate wave function f (p) and the order parameter ∆ tr (p) in these triplet superconductors are odd functions of the momentum p. In contrast to the conventional BCS superconductivity, the triplet superconductivity with such a symmetry of the order parameter is sensitive to impurity scattering [8] and, therefore, it is usually strongly suppressed by disorder.However, the triplet Cooper pairs can appear already in conventional singlet superconductors provided an external magnetic (H) or an internal exchange (h) field acts on the spins of electrons. [8][9][10][11] A triplet component inevitably arises also in magnetic superconductors [12].The triplet condensate function arising from the singlet superconductivity in the presence of the magnetic or exchange field acting on spins is odd in frequency and therefore may still have an s-wave space symmetry without violating the Pauli principle. It has a component with the 0-spin projection f tr,0 ∝ 〈ĉ ↑ĉ↓ (t ) +ĉ ↓ĉ↑ (t )〉 on the direction of the field h or H but also the components with spin projection ±1. The zero projection component f tr,0 of the condensate functio...

Gauge theory of the long-range proximity effect and spontaneous currents in superconducting heterostructures with strong ferromagnets

“…The spontaneous phase shift of Josephson current has been obtained in several FM/SC systems [25,27,30,35,[41][42][43][44][45][46][47][48][49][50][51][52][53][54]]. Here we demonstrate that this effect is essential only for the case of strong ferromagnets.…”

Anomalous current in diffusive ferromagnetic Josephson junctions

“…Studies, based on quasiclassics, of the diffusive Josephson junctions through various noncoplanar structures, including a helix [40], magnetic vortex [41], and skyrmion [42], have shown no AJE. In contrast, in diffusive systems with half-metallic elements [29,31] and in junctions between magnetic superconductors with spin filters [35,36] a finite anomalous current has been predicted. From this apparent contradiction, the general condition for the AJE in diffusive systems still remains elusive.…”

“…Another type of system predicted to exhibit the AJE is conventional S/F/S junctions with a nonhomogeneous magnetization texture [29][30][31][32][33][34][35][36]. In such systems the current is a function of the magnetization distribution M, I = I (ϕ,M).…”

Electrical control of magnetization in superconductor/ferromagnet/superconductor junctions on a three-dimensional topological insulator

“…By now it is well-known that current-phase relation (CPR) in Josephson junctions with multi-layered ferromagnetic interlayers is strongly sensitive to the mutual orientation of the magnetizations in the layers [1][2][3][4][5][6][7][8][9][10][11][12] . CPRs of Josephson junctions with ferromagnetic interlayers in the presence of spin-orbit coupling also depends on the magnetization orientation.…”