Theory of proximity effect in superconductor/ferromagnet heterostructures

We present a microscopic theory of proximity effect in the ferromagnet/superconductor/ferromagnet (F/S/F) nanostructures where S is s-wave low-T_c superconductor and F's are layers of 3d transition ferromagnetic metal. Our approach is based on the 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 \xi_m^0 = \pi v_F/E_ex, where v_F is the Fermi velocity and E_ex is the exchange field, while damping is governed by the length l_0 = (1/l_{\uparrow} + 1/l_{\downarrow})^{-1} with l_{\uparrow} and l_{\downarrow} being spin-dependent mean free paths in the ferromagnet. The superconducting transition temperature T_c(d_F) of the F/S/F trilayer shows the damping oscillations as a function of the F-layer thickness d_F with period \xi_F = \pi/\sqrt{m E_ex}, where m is the effective electron mass. We show that strong spin-conserving scattering either in the superconductor or in the ferromagnet significantly suppresses these oscillations. The calculated T_c(d_F) dependences are compared with existing experimental data for Fe/Nb/Fe trilayers and Nb/Co multilayers.Comment: 13 pages, REVTeX4, 8 PS-figures; improved version, submitted to PR

Cryptoferromagnetic state in superconductor-ferromagnet multilayers

We study a possibility of a non-homogeneous magnetic order (cryptoferromagnetic state) in heterostructures consisting of a bulk superconductor and a ferromagnetic thin layer that can be due to the influence of the superconductor. The exchange field in the ferromagnet may be strong and exceed the inverse mean free time. A new approach based on solving the Eilenberger equations in the ferromagnet and the Usadel equations in the superconductor is developed. We derive a phase diagram between the cryptoferromagnetic and ferromagnetic states and discuss the possibility of an experimental observation of the CF state in different materials.Comment: 4 pages, 1 figur

Inhomogeneous magnetism induced in a superconductor at superconductor-ferromagnet interface

We study a magnetic proximity effect at superconductor (S) - ferromagnet (F) interface. It is shown that due to an exchange of electrons between the F and S metals ferromagnetic correlations extend into the superconductor, being dependent on interface parameters. We show that ferromagnetic exchange field pair breaking effect leads to a formation of subgap bands in the S layer local density of states, that accommodate only one spin-polarized quasiparticles. Equilibrium magnetization leakage into the S layer as function of SF interface quality and a value of ferromagnetic interaction have also been calculated. We show that a damped-oscillatory behavior versus distance from SF interface is a distinguished feature of the exchange-induced magnetization of the S layer.Comment: 10 pages, 7 Postscript figure

Critical temperature of superconductor/ferromagnet bilayers

Superconductor/ferromagnet bilayers are known to exhibit nontrivial dependence of the critical temperature T_c on the thickness d_f of the ferromagnetic layer. We develop a general method for investigation of T_c as a function of the bilayer's parameters. It is shown that interference of quasiparticles makes T_c(d_f) a nonmonotonic function. The results are in good agreement with experiment. Our method also applies to multilayered structures.Comment: 4 pages, 2 EPS figures; the style file jetpl.cls is included. Version 2: typos correcte

Ferromagnetic/superconducting proximity effect in La0.7Ca0.3MnO3 / YBa2Cu3O7 superlattices

We study the interplay between magnetism and superconductivity in high quality YBa2Cu3O7 (YBCO) / La0.7Ca0.3MnO3(LCMO)superlattices. We find evidence for the YBCO superconductivity depression in presence of the LCMO layers. We show that due to its short coherence length superconductivity survives in the YBCO down to much smaller thickness in presence of the magnetic layer than in low Tc superconductors. We also find that for a fixed thickness of the superconducting layer, superconductivity is depressed over a thickness interval of the magnetic layer in the 100 nm range. This is a much longer length scale than that predicted by the theory of ferromagnetic/superconducting proximity effect.Comment: 10 pages + 5 figures, submitted to Phys. Rev.

Structure and Magnetism of well-defined cobalt nanoparticles embedded in a niobium matrix

Our recent studies on Co-clusters embedded in various matrices reveal that the co-deposition technique (simultaneous deposition of two beams : one for the pre-formed clusters and one for the matrix atoms) is a powerful tool to prepare magnetic nanostructures with any couple of materials even though they are miscible. We study, both sharply related, structure and magnetism of the Co/Nb system. Because such a heterogeneous system needs to be described at different scales, we used microscopic and macroscopic techniques but also local selective absorption ones. We conclude that our clusters are 3 nm diameter f.c.c truncated octahedrons with a pure cobalt core and a solid solution between Co and Nb located at the interface which could be responsible for the magnetically inactive monolayers we found. The use of a very diluted Co/Nb film, further lithographed, would allow us to achieve a pattern of microsquid devices in view to study the magnetic dynamics of a single-Co cluster.Comment: 7 TeX pages, 9 Postscript figures, detailed heading adde

Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization

We calculate the dc Josephson current $I_J$ for two types of superconductor-ferromagnet (S/F) Josephson junctions. The junction of the first type is a S/F/S junction. On the basis of the Eilenberger equation, the Josephson current is calculated for an arbitrary impurity concentration. If $h\tau\ll1$ the expression for the Josephson critical current $I_c$ is reduced to that which can be obtained from the Usadel equation ($h$ is the exchange energy, $\tau$ is the momentum relaxation time). In the opposite limit $h\tau\gg1$ the superconducting condensate oscillates with period $$ and penetrates into the F region over distances of the order of the mean free path $l$. For this kind of junctions we also calculate $I_J$ in the case when the F layer presents a nonhomogeneous (spiral) magnetic structure with the period $2\pi /Q$. It is shown that for not too low temperatures, the $\pi$-state which occurs in the case of a homogeneous magnetization (Q=0) may disappear even at small values of $Q$. In this nonhomogeneous case, the superconducting condensate has a nonzero triplet component and can penetrate into the F layer over a long distance of the order of $\xi_{T}=$. The junction of the second type consists of two S/F bilayers separated by a thin insulating film. It is shown that the critical Josephson current $I_{c}$ depends on the relative orientation of the effective exchange field $h$ of the bilayers. In the case of an antiparallel orientation, $I_{c}$ increases with increasing $h$. We establish also that in the F film deposited on a superconductor, the Meissner current created by the internal magnetic field may be both diamagnetic or paramagnetic.Comment: 13 pages, 11 figures. To be published in Phys. Rev.

Depairing currents in the superconductor/ferromagnet proximity system Nb/Fe

We have investigated the behaviour of the depairing current J_{dp} in ferromagnet/superconductor/ferromagnet (F/S/F) trilayers as function of the thickness d_s of the superconducting layers. Theoretically, J_{dp} depends on the superconducting order parameter or the pair density function, which is not homogeneous across the film due to the proximity effect. We use a proximity effect model with two parameters (proximity strength and interface transparency), which can also describe the dependence of the superconducting transition temperature T_c on d_s. We compare the computations with the experimentally determined zero-field critical current J_{c0} of small strips (typically 5~ \mu m wide) of Fe/Nb/Fe trilayers with varying thickness d_{Nb} of the Nb layer. Near T_c the temperature dependence J_{c0}(T) is in good agreement with the expected behaviour, which allows extrapolation to T = 0. Both the absolute values of J_{c0}(0) and the dependence on d_{Nb} agree with the expectations for the depairing current. We conclude that J_{dp} is correctly determined, notwithstanding the fact that the strip width is larger than both the superconducting penetration depth and the superconducting coherence length, and that J_{dp}(d_s) is correctly described by the model.Comment: 10 pages, 5 figures, submitted to PR

Superconducting proximity effect in clean ferromagnetic layers

We investigate superconducting proximity effect in clean ferromagnetic layers with rough boundaries. The subgap density of states is formed by Andreev bound states at energies which depend on trajectory length and the ferromagnetic exchange field. At energies above the gap, the spectrum is governed by resonant scattering states. The resulting density of states, measurable by tunneling spectroscopy, exhibits a rich structure, which allows to connect the theoretical parameters from experiments.Comment: 11 pages, 5 figures (included

Spontaneous Spin Polarized Currents in Superconductor-Ferromagnetic Metal Heterostructures

We study a simple microscopic model for thin, ferromagnetic, metallic layers on semi-infinite bulk superconductor. We find that for certain values of the exchange spliting, on the ferromagnetic side, the ground states of such structures feature spontaneously induced spin polarized currents. Using a mean-field theory, which is selfconsistent with respect to the pairing amplitude $\chi$, spin polarization $\vec{m}$ and the spontaneous current $\vec{j}_s$, we show that not only there are Andreev bound states in the ferromagnet but when their energies $E_n$ are near zero they support spontaneous currents parallel to the ferromagnetic-superconducting interface. Moreover, we demonstrate that the spin-polarization of these currents depends sensitively on the band filling.Comment: 4 pages, 5 Postscript figures (included