Odd Triplet Pairing in Clean Superconductor/Ferromagnet Heterostructures

Abstract

We study triplet pairing correlations in clean Ferromagnet (F)/Superconductor (S) nanojunctions, via fully self consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle α between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and α. The triplet amplitudes are largest at times on the order of the inverse "Debye" frequency, and at that time scale they are long ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.PACS numbers: 74.45.+c, 74.25.Bt, 74.78.Fk The proximity effects in superconductor/ferromagnet (SF) heterostructures lead to the coexistence of ferromagnetic and superconducting ordering and to novel transport phenomena [1,2]. Interesting effects that arise from the interplay between these orderings have potential technological applications in fields such as spintronics [3]. For example, the relative orientation of the magnetizations in the F layers in FSF trilayers can have a strong influence on the conductivity [4,5,6,7,8], making them good spin valve candidates. Such trilayers were first proposed[9] for insulating F layers and later for metallic [10,11] ones. This interplay also results in fundamental new physics. An outstanding example is the existence of "odd" triplet superconductivity. This is an s-wave pairing triplet state that is even in momentum, and therefore not destroyed by nonmagnetic impurities, but with the triplet correlations being odd in frequency, so that the equal time triplet amplitudes vanish as required by the Pauli principle. This exotic pairing state with total spin one was proposed long ago [12] as a possible state in superfluid 3 He. Although this type of pairing does not occur there, it is possible in certain FSF systems [1,2,13,14] with ordinary singlet pairing in S. This arrangement can induce, via proximity effects, triplet correlations with m = 0 and m = ±1 projections of the total spin. If the magnetization orientations in both F layers are unidirectional and along the quantization axis, symmetry arguments show that only the m = 0 projection along that axis can exist.Odd triplet pairing in F/S structures has been studied in the dirty limit through linearized Usadel-type quasiclassical equations [2,13,14,15]. In this case, it was found that m = 0 triplet pairs always exist. They are suppressed in F over short length scales, just as the singlet pairs. The m = ±1 components, for which the exchange field is not pair-breaking, can be long ranged, and were found to exist for nonhomogeneous magnetization. For FSF trilayers [2,16,17], the quasiclassical methods predict that the structure contains a superposition of all three spin triplet projections except when the magnetizations of the F layers are collinear, in wh...

Spin-triplet supercurrent through inhomogeneous ferromagnetic trilayers

“…26,35,38,39. Over the last couple of years, induction of triplet-correlations in layered heterostructures with ferromagnets (F) and superconductors (S) in the clean limit has been studied by using different formalisms and configurations in Refs. [40][41][42]. On the experimental side, Keizer et al 44 observed a long-range supercurrent through half-metallic CrO 2 , whereas very recent work also reports observation of a long-range supercurrent through an inhomogeneous magnetic layer 6,27 .…”

Induced triplet pairing in cleans-wave superconductor/ferromagnet layered structures

“…Until both better theoretical models and more varied experimental observations are made available, one cannot conclusively say that there is indeed an induced triplet state in these systems, but at this point the facts fit this explanation and no better one has been proposed. 17 Many theoretical studies agree that it is possible to induce this exotic state in certain SF systems 17,18,19,20,21,22,23,24,25,26,27,28,29 (perhaps even in the nonmagnetic 30 case) with ordinary singlet pairing in S. Some studies use an SFF ′ S arrangement in which the F and F ′ layers have different magnetization orientations. Others assume that a domain structure in a single F layer is responsible for the symmetry breaking.…”

“…28 To understand and probe the underlying triplet state, investigations have been done on conductance spectra in simpler FS structures 31 with arbitrary magnetization alignment and with spin active interfaces, as well as in diffusive 29 SF junctions, through characterizing the possible superconductor symmetry classes consistent with Pauli's principle. With the exception of our early work 18 on SFS trilayers and some recent work on SFS Josephson junctions, 28 the studies above are done in the dirty limit through linearized Usadel-type or other quasiclassical equations. The disadvantage of a quasiclassical approach is that it is unsuitable for magnets with an exchange field on the order of the Fermi energy.…”

Spin nutation effects in molecular nanomagnet–superconductor tunnel junctions

“…As a result a nonzero Josephson current flows through the strong ferromagnets (such as half metals) [33,34,35]. The triplet correlations also penetrate into the superconductors however their amplitudes are small in comparison to the bulk singlet component [36]. The triplet correlations are also generated by magnetization dynamics such as spin precession and magnonic excitations.…”