We study proximity effects at ferromagnet superconductor interfaces by self-consistent numerical solution of the Bogoliubov-de Gennes equations for the continuum, without any approximations. Our procedures allow us to study systems with long superconducting coherence lengths. We obtain results for the pair potential, the pair amplitude, and the local density of states. We use these results to extract the relevant proximity lengths. We find that the superconducting correlations in the ferromagnet exhibit a damped oscillatory behavior that is reflected in both the pair amplitude and the local density of states. The characteristic length scale of these oscillations is approximately inversely proportional to the exchange field, and is independent of the superconducting coherence length in the range studied. We find the superconducting coherence length to be nearly independent of the ferromagnetic polarization. 74.50.+r, 74.25.Fy, 74.80.Fp

We study triplet pairing correlations in clean Ferromagnet (F)/Superconductor (S) nanojunctions, via fully self consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle α between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and α. The triplet amplitudes are largest at times on the order of the inverse "Debye" frequency, and at that time scale they are long ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.PACS numbers: 74.45.+c, 74.25.Bt, 74.78.Fk The proximity effects in superconductor/ferromagnet (SF) heterostructures lead to the coexistence of ferromagnetic and superconducting ordering and to novel transport phenomena [1,2]. Interesting effects that arise from the interplay between these orderings have potential technological applications in fields such as spintronics [3]. For example, the relative orientation of the magnetizations in the F layers in FSF trilayers can have a strong influence on the conductivity [4,5,6,7,8], making them good spin valve candidates. Such trilayers were first proposed[9] for insulating F layers and later for metallic [10,11] ones. This interplay also results in fundamental new physics. An outstanding example is the existence of "odd" triplet superconductivity. This is an s-wave pairing triplet state that is even in momentum, and therefore not destroyed by nonmagnetic impurities, but with the triplet correlations being odd in frequency, so that the equal time triplet amplitudes vanish as required by the Pauli principle. This exotic pairing state with total spin one was proposed long ago [12] as a possible state in superfluid 3 He. Although this type of pairing does not occur there, it is possible in certain FSF systems [1,2,13,14] with ordinary singlet pairing in S. This arrangement can induce, via proximity effects, triplet correlations with m = 0 and m = ±1 projections of the total spin. If the magnetization orientations in both F layers are unidirectional and along the quantization axis, symmetry arguments show that only the m = 0 projection along that axis can exist.Odd triplet pairing in F/S structures has been studied in the dirty limit through linearized Usadel-type quasiclassical equations [2,13,14,15]. In this case, it was found that m = 0 triplet pairs always exist. They are suppressed in F over short length scales, just as the singlet pairs. The m = ±1 components, for which the exchange field is not pair-breaking, can be long ranged, and were found to exist for nonhomogeneous magnetization. For FSF trilayers [2,16,17], the quasiclassical methods predict that the structure contains a superposition of all three spin triplet projections except when the magnetizations of the F layers are collinear, in wh...

We study induced triplet pairing correlations in clean ferromagnet/superconductor/ferromagnet heterostructures. The pairing state in the superconductor is the conventional singlet s-wave, and the angle α between the magnetizations of the two ferromagnetic layers is arbitrary. We use a numerical fully self-consistent solution of the microscopic equations and obtain the time-dependent triplet correlations via the Heisenberg equations of motion. We find that in addition to the usual singlet correlations, triplet correlations, odd in time as required by the Pauli principle, are induced in both the ferromagnets and the superconductor. These time-dependent correlations are largest at times of order of the inverse of the Debye cutoff frequency, ωD, and we find that within that time scale they are often spatially very long ranged. We discuss the behavior of the characteristic penetration lengths that describe these triplet correlations. We also find that the ferromagnets can locally magnetize the superconductor near the interface, and that the local magnetization then undergoes strongly damped oscillations. The local density of states exhibits a variety of energy signatures, which we discuss, as a function of ferromagnetic strength and α.

In tunneling spectroscopy studies of ferromagnet/superconductor (F/S) junctions, the effects of spin polarization, Fermi wavevector mismatch (FWM) between the F and S regions, and interfacial resistance play a crucial role. We study the low bias conductance spectrum of these junctions, governed by Andreev reflection at the F/S interface. We consider both d-and s-wave superconductors as well as mixed states of the d + is form. We present results for a range of values of the relevant parameters and find that a rich variety of features appears, depending on pairing state and other conditions. We show that in the presence of FWM, spin polarization can enhance Andreev reflection and give rise to a zero bias conductance peak for an s-wave superconductor.74.80. Fp, 74.50+r,

The superconducting transition temperature T(c) of a ferromagnet (F)-superconductor (S)-ferromagnet trilayer depends on the mutual orientation of the magnetic moments of the F layers. This effect has been previously observed in F/S/F systems as a T(c) difference between parallel and antiparallel configurations of the F layers. Here we report measurements of T(c) in CuNi/Nb/CuNi trilayers as a function of the angle between the magnetic moments of the CuNi ferromagnets. The observed angular dependence of T(c) is in qualitative agreement with a F/S proximity theory that accounts for the odd triplet component of the condensate predicted to arise for noncollinear orientation of the magnetic moments of the F layers.