Superconducting proximity effects in magnetic metals

Demler, Eugene; Arnold, G.; Beasley, M. R.

doi:10.1103/physrevb.55.15174

Cited by 438 publications

(460 citation statements)

References 9 publications

(7 reference statements)

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“…We consider that F layers are 3d transition metals and assume that the main mechanism of spinconserving electron scattering in F layers is s-d scattering, while S layer is s-wave superconductor with s-s scattering. We find the characteristic lengths determining the periods of oscillations and damping of critical temperature T c and Cooper pair wave function, and show that in the given model these lengths differ from length scales predicted by quasiclassical theories 3,4,15,16 . We show that strong spin-conserving scattering either in the superconductor or in the ferromagnet significantly suppresses the oscillations of T c .…”

Section: Introductionmentioning

confidence: 99%

Theory of proximity effect in superconductor/ferromagnet heterostructures

2003

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We present a microscopic theory of proximity effect in the ferromagnet/superconductor-/ferromagnet (F/S/F) nanostructures where S is s-wave low-Tc superconductor and F's are layers of 3d transition ferromagnetic metal. Our approach is based on the direct analytical solution of Gor'kov equations for the normal and anomalous Green's functions together with a self-consistent evaluation of the superconducting order parameter. We take into account the elastic spin-conserving scattering of the electrons assuming s-wave scattering in the S layer and s-d scattering in the F layers. In accordance with the previous quasiclassical theories, we found that due to exchange field in the ferromagnet the anomalous Green's function F (z) exhibits the damping oscillations in the F-layer as a function of distance z from the S/F interface. In the given model a half of period of oscillations is determined by the length ξ 0 m = πvF /εex, where vF is the Fermi velocity and εex is the exchange field, while damping is governed by the length l0 = (1/l ↑ + 1/l ↓ ) −1 with l ↑ and l ↓ being spin-dependent mean free paths in the ferromagnet. The superconducting transition temperature Tc(dF ) of the F/S/F trilayer shows the damping oscillations as a function of the F-layer thickness dF with period ξF = π/ √ mεex, where m is the effective electron mass. The oscillations of Tc(dF ) are a consequence of the oscillatory behavior of the superconducting order parameter at the S/F interface vs thickness dF , that in turn is caused by the oscillations of F (z) in the F-region. We show that strong spin-conserving scattering either in the superconductor or in the ferromagnet significantly suppresses these oscillations. The calculated Tc(dF ) dependences are compared with existing experimental data for Fe/Nb/Fe trilayers and Nb/Co multilayers.

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Section: Introductionmentioning

confidence: 99%

Theory of proximity effect in superconductor/ferromagnet heterostructures

2003

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“…The intriguing nature of this 'superconducting proximity effect' in S/F systems arises due to the exchange field in F, which imposes a phase shift on the two electrons of a Cooper pair as they propagate across F. Cooper pairs in conventional superconductors consist of two electrons with equal and opposite momenta and opposite spin. When such a pair crosses the S/F boundary, one electron goes into the majority, or up-spin, band in F and the other goes into the minority, or down-spin, band, causing the two electrons to acquire a net centre-of-mass momentum ±hQ = ±(hk F ↑ −hk F ↓ ), wherehk F ↑ andhk F ↓ are the Fermi momenta of the majority and minority bands, respectively 13 . Alternatively, one can say that the electron pair correlation function oscillates in F with wavevector Q perpendicular to the S/F interface.…”

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confidence: 99%

Controllable 0–π Josephson junctions containing a ferromagnetic spin valve

et al. 2016

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“…In ferromagnet/superconductor (F/S) junctions Cooper pairs penetrating into the F layer from the S layer have a nonzero momentum due to the influence of exchange field 1,2,3 . This results in oscillating behavior of the pair amplitude or a π-phase shift of the order parameter in the ferromagnet.…”

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Resonant peak in the density of states in normal-metal/diffusive-ferromagnet/superconductor junctions

2005

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The conditions for the formation of zero-energy peak in the density of states (DOS) in the normal metal / insulator / diffusive ferromagnet / insulator / s-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel equations. The DOS of the DF is calculated in various regimes for different magnitudes of the resistance, Thouless energy and the exchange field of the DF, as well as for various resistances of the insulating barriers. The conditions for the DOS peak are formulated for the cases of weak proximity effect (large resistance of the DF/S interface) and strong proximity effect (small resistance of the DF/S interface).In ferromagnet/superconductor (F/S) junctions Cooper pairs penetrating into the F layer from the S layer have a nonzero momentum due to the influence of exchange field 1,2,3 . This results in oscillating behavior of the pair amplitude or a π-phase shift of the order parameter in the ferromagnet. A negative sign of the real part of the order parameter may occur when the thickness of the F layer is larger than the coherence length of the F layer. The occurrence of the π-phase shift makes it possible to realize the SFS π -junctions 1 , as was confirmed experimentally 4,5,6,7,8 . The order parameter oscillations also lead to nonmonotonous dependence of T c in SF bilayers on the F-layer thickness 9,10,11,12,13 . Effects of resonant transmission in conductivity of SF structures were discussed in Ref 14,15,16 .Another interesting consequence of the oscillations of the pair amplitude is the spatially damped oscillating behavior of the density of states (DOS) in a ferromagnet predicted theoretically 17,18,19,20 in various regimes. The energy dependent DOS calculated in the clean 18 and the dirty 21 limits exhibits rich structures. Experimentally DOS in F/S bilayers was measured by Kontos et al. who found a broad DOS peak around zero energy when the π-phase shift occurs 22 . In diffusive ferromagnet/superconductor (DF/S) junctions the zeroenergy DOS may have a sharp peak 21 . However the conditions for the appearance of such anomaly have not been studied systematically so far.The purpose of the present paper is to calculate DOS in N/DF/S junctions and to formulate the conditions for the zero-energy DOS peak in two regimes corresponding to the weak proximity effect (large DF/S interface resistance) and strong proximity effect (small DF/S interface resistance). We will show that in the former case the condition is equivalent to the one of Ref. 21 , while in the latter case the new condition is found. The calculation will be performed in the zero-temperature regime by varying the interface resistances as well as the resistance, the exchange field and the Thouless energy of the DF layer.We consider a junction consisting of normal and superconducting reservoirs connected by a quasi-onedimensional diffusive ferromagnet conductor (DF) with a resistance R d and a length L much larger than the mean free path. The DF/N interface located at x = 0 has the resistance R ′ b , while the DF/S interface...

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Superconducting proximity effects in magnetic metals

Cited by 438 publications

References 9 publications

Theory of proximity effect in superconductor/ferromagnet heterostructures

Theory of proximity effect in superconductor/ferromagnet heterostructures

Controllable 0–π Josephson junctions containing a ferromagnetic spin valve

Resonant peak in the density of states in normal-metal/diffusive-ferromagnet/superconductor junctions

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