Theory of proximity effect in superconductor/ferromagnet heterostructures

Abstract

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.

Ferromagnet-superconductor proximity effect: The clean limit

“…2,3,4,5,6,7,8 and 9, 10,11,12,13,14,15,16,17,18,19,20 ). The interplay of ferromagnetism and superconductivity results in characteristic proximity effects near the contacts between two metals: the Andreev reflection is suppressed in the presence of a ferromagnet; 21 conversely, the superconducting correlations, described via the pair amplitude, extend in the ferromagnetic material in an oscillatory way.…”

Ferromagnetic proximity effect ina-CoxSi1−x/Nbbilayers: Role of magnetic disorder and interface transparency

“…The value d F = 40 nm has been chosen so that it is larger than typical values of F length even for weak ferromagnets ͑ F Ϸ 1-15 nm͒. 7,12,13,20,21,23,27,30,40 Thus, we can make the initial assumption that the bilayers are in the thick layer limit and the proximity effect is saturated. The validity of this hypothesis will be revised later in Sec.…”

“…1 The study of hybrid structures, such as superconducting/magnetic multilayers, [2][3][4][5][6][7][8] superconducting/ magnetic/superconducting junctions, 9 or superconducting magnetic nanostructures, 10 has revealed many remarkable phenomena such as direct and inverse proximity effect, 11 reentrant superconductivity 12 and critical temperature oscillations, or infinite magnetoresistance in superconducting spin valves. 13,14 Active theoretical work [15][16][17][18][19][20][21][22] in this field is helping to disentangle the subtle interplay between superconductivity and magnetism, depending on the different structural parameters of the superconducting/ferromagnetic ͑F͒ materials and the oscillating behavior of the superconducting order parameter within the ferromagnetic layers.…”

Adjustment of superconductivity and ferromagnetism in few-layered ferromagnet-superconductor nanostructures

“…The solution of the boundary value problem [8][9][10][11][12][13][14][15] has revealed an additional mechanism of nonmonotonic dependence of T c due to modulation of the pair amplitude flux from the S layer to the F layer. This modulation is caused by the change of the FM layer thickness d f .…”

“…The LOFF pairs momentum k I/v f 2 is determined by the Fermi surface splitting caused by the internal exchange field I (where v f is the Fermi velocity in the F layers). Usually it is assumed [5,6,[8][9][10][11][12][13][14][15]20,21] that the momentum of the LOFF pairs is directed across the F/S interface (the so-called one-dimensional (1D) case).…”