Stability of π\pi junction configurations in ferromagnet-superconductor heterostructures

We investigate the stability of possible order parameter configurations in clean layered heterostructures of the $SFS...FS$ type, where $S$ is a superconductor and $F$ a ferromagnet. We find that for most reasonable values of the geometric parameters (layer thicknesses and number) and of the material parameters (such as magnetic polarization, wavevector mismatch, and oxide barrier strength) several solutions of the {\it self consistent} microscopic equations can coexist, which differ in the arrangement of the sequence of ``0'' and ``$\pi$'' junction types (that is, with either same or opposite sign of the pair potential in adjacent $S$ layers). The number of such coexisting self consistent solutions increases with the number of layers. Studying the relative stability of these configurations requires an accurate computation of the small difference in the condensation free energies of these inhomogeneous systems. We perform these calculations, starting with numerical self consistent solutions of the Bogoliubov-de Gennes equations. We present extensive results for the condensation free energies of the different possible configurations, obtained by using efficient and accurate numerical methods, and discuss their relative stabilities. Results for the experimentally measurable density of states are also given for different configurations and clear differences in the spectra are revealed. Comprehensive and systematic results as a function of the relevant parameters for systems consisting of three and seven layers (one or three junctions) are given, and the generalization to larger number of layers is discussed.Comment: 17 pages, including 14 Figures. Higher resolution figures available from the author

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

Andreev conductance of a domain wall

At low temperatures, the transport through a superconductor-ferromagnet tunnel interface is due to tunneling of electrons in pairs. Exchange field of a monodomain ferromagnet aligns electron spins and suppresses the two electron tunneling. The presence of the domain walls at the SF interface strongly enhances the subgap current. The Andreev conductance is proven to be proportional to the total length of domain walls at the SF interface.Comment: 4 pages and 1 figur

Josephson Current in S-FIF-S Junctions: Nonmonotonic Dependence on Misorientation Angle

Spectra and spin structures of Andreev interface states in S-FIF-S junctions are investigated with emphasis on finite transparency and misorientation angle between in-plane magnetizations of ferromagnetic layers in a three-layer interface. It is demonstrated that the Josephson current in S-FIF-S quantum point contacts can exhibit a nonmonotonic dependence on the misorientation angle. The characteristic behavior takes place, if the pi-state is the equilibrium state of the junction in the particular case of parallel magnetizations.Comment: 5 pages, 4 figure

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

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

Proximity effects and characteristic lengths in ferromagnet-superconductor structures

We present an extensive theoretical investigation of the proximity effects that occur in Ferromagnet/Superconductor ($F/S$) systems. We use a numerical method to solve self consistently the Bogoliubov-de Gennes equations in the continuum. We obtain the pair amplitude and the local density of states (DOS), and use these results to extract the relevant lengths characterizing the leakage of superconductivity into the magnet and to study spin splitting into the superconductor. These phenomena are investigated as a function of parameters such as temperature, magnet polarization, interfacial scattering, sample size and Fermi wavevector mismatch, all of which turn out to have important influence on the results. These comprehensive results should help characterize and analyze future data and are shown to be in agreement with existing experiments.Comment: 24 pages, including 26 figure

Layered ferromagnet-superconductor structures: the π\pi state and proximity effects

We investigate clean mutilayered structures of the SFS and SFSFS type, (where the S layer is intrinsically superconducting and the F layer is ferromagnetic) through numerical solution of the self-consistent Bogoliubov-de Gennes equations for these systems. We obtain results for the pair amplitude, the local density of states, and the local magnetic moment. We find that as a function of the thickness $d_F$ of the magnetic layers separating adjacent superconductors, the ground state energy varies periodically between two stable states. The first state is an ordinary "0-state", in which the order parameter has a phase difference of zero between consecutive S layers, and the second is a "$\pi$-state", where the sign alternates, corresponding to a phase difference of $\pi$ between adjacent S layers. This behavior can be understood from simple arguments. The density of states and the local magnetic moment reflect also this periodicity.Comment: 12 pages, 10 Figure

Manifestation of triplet superconductivity in superconductor-ferromagnet structures

We study proximity effects in a multilayered superconductor/ferromagnet (S/F) structure with arbitrary relative directions of the magnetization ${\bf M}$. If the magnetizations of different layers are collinear the superconducting condensate function induced in the F layers has only a singlet component and a triplet one with a zero projection of the total magnetic moment of the Cooper pairs on the ${\bf M}$ direction. In this case the condensate penetrates the F layers over a short length $\xi_J$ determined by the exchange energy $J$. If the magnetizations ${\bf M}$ are not collinear the triplet component has, in addition to the zero projection, the projections $\pm1$. The latter component is even in the momentum, odd in the Matsubara frequency and penetrates the F layers over a long distance that increases with decreasing temperature and does not depend on $J$ (spin-orbit interaction limits this length). If the thickness of the F layers is much larger than $\xi_J$, the Josephson coupling between neighboring S layers is provided only by the triplet component, so that a new type of superconductivity arises in the transverse direction of the structure. The Josephson critical current is positive (negative) for the case of a positive (negative) chirality of the vector ${\bf M}$. We demonstrate that this type of the triplet condensate can be detected also by measuring the density of states in F/S/F structures.Comment: 14 pages; 9 figures. Final version, to be published in Phys. Rev.

Josephson Coupling and Fiske Dynamics in Ferromagnetic Tunnel Junctions

We report on the fabrication of Nb/AlO_x/Pd_{0.82}Ni_{0.18}/Nb superconductor/insulator/ferromagnetic metal/superconductor (SIFS) Josephson junctions with high critical current densities, large normal resistance times area products, high quality factors, and very good spatial uniformity. For these junctions a transition from 0- to \pi-coupling is observed for a thickness d_F ~ 6 nm of the ferromagnetic Pd_{0.82}Ni_{0.18} interlayer. The magnetic field dependence of the \pi-coupled junctions demonstrates good spatial homogeneity of the tunneling barrier and ferromagnetic interlayer. Magnetic characterization shows that the Pd_{0.82}Ni_{0.18} has an out-of-plane anisotropy and large saturation magnetization, indicating negligible dead layers at the interfaces. A careful analysis of Fiske modes provides information on the junction quality factor and the relevant damping mechanisms up to about 400 GHz. Whereas losses due to quasiparticle tunneling dominate at low frequencies, the damping is dominated by the finite surface resistance of the junction electrodes at high frequencies. High quality factors of up to 30 around 200 GHz have been achieved. Our analysis shows that the fabricated junctions are promising for applications in superconducting quantum circuits or quantum tunneling experiments.Comment: 15 pages, 9 figure