Interference Phenomena and Long-Range Proximity Effect in Clean Superconductor-Ferromagnet Systems

Abstract

We study peculiarities of proximity effect in clean superconductor -ferromagnet structures caused by either spatial or momentum dependence of the exchange field. Even a small modulation of the exchange field along the quasiparticle trajectories is shown to provide a long range contribution to the supercurrent due to the specific interference of particle-and hole-like wave functions. The momentum dependence of the exchange field caused by the spin -orbit interaction results in the long -range superconducting correlations even in the absence of ferromagnetic domain structure and can explain the recent experiments on ferromagnetic nanowires.The exchange field h in ferromagnetic (F) metals is well known to destroy Cooper pairs resulting, thus, in a strong decay of superconducting (S) correlations in the F material and suppression of Josephson current in SFS junctions (see Refs. 1, 2 for review). Considering the quantum mechanics of quasiparticle excitations this destructive effect of the exchange field can be viewed as a consequence of a phase difference γ ∼ L/ξ h = 2Lh/ V F gained between the electron-and hole-like parts of the total wave function at the path of the length L. Both in the clean and dirty limits the measurable quantities should be calculated as superpositions of fast oscillating contributions e iγ from different trajectories and, thus, rapidly vanish with the increasing distance from the SF boundary.This textbook physical picture appears to be in sharp contrast with a number of recent experiments [3-8] which point to an anomalously large length of decay of superconducting correlations inside the F metal. As we can judge from the observation [8] of a noticeable supercurrent through a Co nanowire, this decay length can be of the order of half a micrometer which well exceeds typical coherence lengths in ferromagnets both in the clean and dirty limits. In the dirty limit such strong proximity effect can hardly be explained even taking account of long-range triplet correlations [2] induced by the exchange field inhomogeneity.Naturally, the inhomogeneity of the field h caused by the ferromagnetic domain structure can improve the conditions of Cooper pair survival in the clean limit as well. To suppress the destructive trajectory interference mentioned above the domain structure should cancel the phase gain γ for a certain group of quasiparticle trajectories. A simple example of such phase gain compensation can be realized in a clean junction consisting of two F layers with opposite orientations of magnetic moment [9,10]. On the other hand in the diffusive limit this compensation effect vanishes [11]. Note, that the exchange field inhomogeneity along the quasiclassical trajectory experiencing multiple reflections from the ferromagnet surface can appear even in the absence of the spatial domain structure. Indeed, the exchange field acting on band electrons in a solid with a finite spin -orbit interaction should obviously depend on the quasiparticle momentum [12]: h = h(k). The normal quasiparticle reflection...

Evidence for spin-triplet superconducting correlations in metal-oxide heterostructures with noncollinear magnetization

“…[18][19][20][21][22][23]. In a trilayer geometry, the first F layer helps to convert singlet Cooper pairs into triplet pairs with nonvanishing projection onto the channels with parallel electron spins along the (tilted) magnetization of the central F layer, which may thus propagate coherently over long distances.…”

“…The SF reflectivities R +− and R −+ depend only on the magnetic potential ρ SF (z) = B ⊥ (z). PNR thus allows the determination of depth profiles of the vector magnetization, and the experimental definition of the level of magnetic noncollinearity, which is an important parameter in the theory of triplet superconductivity [18][19][20][21][22][23].…”

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

“…Here, it should be noticed that the coefficient (1-2ξ 0 /d) of Eqs. (37) and (39) Finally, we shall approximately estimate ξ 0 and the amplitude of magnetization in the N. In clean normal metals, ξ 0 is in a range of several hundred nanometers. 18) Therefore, the magnetization in the N induced by the proximity effect has a finite value in this length scale.…”

“…Moreover, when the magnetization in the F is non-uniform in a S/F junction, the STC formed by electrons of equal spin (|S z | = 1) can also be induced in the F. This includes cases, for instance, where the F contains a magnetic domain wall, [24][25][26][27][28][29][30] the junction consisting of multilayers of Fs, [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46] or spin active interface at the S/F interface . [47][48][49][50][51][52][53][54] The penetration length of STC with spin…”

Magnetic field influence on the proximity effect atYBa2Cu3O7/LVisani1, Cuellar2, Pérez-Muñoz3 et al. 2015Phys. Rev. B14040View full textAdd to dashboardCite

“…In the case of half-metallic ferromagnets, the singlet-to-triplet conversion can be explained [11,[25][26][27] by two subsequent processes-(i) spin mixing and (ii) spin flip-which arise from (i) spin dependent electron scattering and (ii) magnetic inhomogeneities or other sources of misalignments of the spin quantization axis at the interface (e.g. spin-orbit coupling effects [28][29][30][31] MnO 3 (PCCO/LCMO) bilayers found a strong magnetic-field dependence of the spectral features that constitute the fingerprint of the long-range proximity effect [19]. The observed magnetic-field dependence was considered evidence for the role of magnetic inhomogeneities in the long-range proximity effects in LCMO.…”