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

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.

Magnetic anisotropies of sputtered Fe films on MgO substrates

Ferromagnetic resonance (FMR) and superconducting quantum interference device (SQUID) measurements have been used to study the magnetic properties of rf sputtered Fe films on MgO(001) substrates. The dependences of the FMR spectra parameters on the direction of the dc magnetic field turning in the plane of the films were measured in a wide temperature range (20400 K) for films with thickness L in the range 25500. The analysis of the angular dependence of the resonance field H0 allowed us to determine the fourfold cubic anisotropy constant K1 and the effective magnetization value Meff. It was found that both values decrease with decreasing L and approach a constant value below a certain thickness. A theory of FMR is outlined demonstrating that for the case of the dc magnetic field lying in a film plane, the anisotropy constant can be interpreted as a combination of a volume anisotropy contribution and a 1/L-dependent contribution from the surface anisotropy up to the thickness L103. This means that for the experimentally studied thickness range the films may be considered as dynamically thin films with respect to surface perturbations. Then the peculiar thickness dependence of the K1 value can be explained assuming that the relaxation of the strain due to the mismatch between film and substrate extends to distances as far as 45 from the film-substrate interface. Since our SQUID measurements show that the saturation moment does not depend on the thickness, it is concluded that the thickness dependence of the effective magnetization Meff is caused by a second-order uniaxial anisotropy arising mainly from the broken symmetry of the crystal field at surfaces and near the edges of interfacial dislocations. © 1995 The American Physical Society

Possible origin for oscillatory superconducting transition temperature in superconductor/ferromagnet multilayers

We have studied superconducting and magnetic properties of sputtered Fe/Nb/Fe trilayers. For a fixed Nb thickness and with changing Fe thickness, dFe, a nonmonotonic behavior of the superconducting transition temperature Tc was observed with a maximum at dFe ≈ 10 Å. The analysis of the magnetization data revealed that for dFFe ≤7 Å the Fe layer is nonmagnetic. The interpretation of the observed Tc behavior is attributed to the existence of this magnetically "dead" layer and the change of the interaction of the Cooper pairs with this layer at the onset of ferromagnetism for dFe ≥ 7 Å

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

Superconducting and magnetic properties of epitaxial high-quality Fe/Nb bilayers

Single crystal Fe/Nb (110) bilayers with an Nb thickness d Nb in the range from 140 to 650 Å and with an Fe thickness d Fe in the range from 5 to 100 Å were prepared using molecular beam epitaxy (MBE) techniques. For d Fe≥20 Å a decrease of the superconducting transition temperature T c with decreasing d Nb was observed. For d Fe=20 Å the FMR data revealed a decrease of the effective magnetization of the Fe layer below the superconducting transition. This magnetization behavior is attributed to a spatial modulation of ferromagnetic order due to a modification of the RKKY interaction in the superconducting state. © 1997 American Institute of Physics

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.

FMR studies of magnetic properties of Co and Fe thin films on Al 2O3 and MgO substrates

The effect of substrates on the magnetic properties has been studied for Co and Fe films both on Al2O3 (112̄0) and MgO (001) substrates by using ferromagnetic resonance techniques. For Fe(001)/MgO(001) samples the thickness dependence of the magnetocrystalline constant and of the effective magnetization values have been determined from the in-plane angular variation of the resonance field H0. Different reasons for the thickness dependencies of these parameters are discussed. For Co(111)/Al 2O3(112̄0) the angular variation of H0 exhibits an uniaxial anisotropy, for which several causes are discussed. For Co(112̄0)/MgO(100) a four-fold in-plane anisotropy was observed which is due to the twinned structure of these samples