Using selection rules imposed by the Pauli principle, we classify pairing correlations according to their symmetry properties with respect to spin, momentum, and energy. We observe that inhomogeneity always leads to mixing of even-and odd-energy pairing components. We investigate the superconducting pairing correlations present near interfaces between superconductors and ferromagnets, with focus on clean systems consisting of singlet superconductors and either weak or half-metallic ferromagnets. Spin-active scattering in the interface region induces all of the possible symmetry components. In particular, the long-range equal-spin pairing correlations have odd-frequency s-wave and even-frequency p-wave components of comparable magnitudes. We also analyze the Josephson current through a half-metal. We find analytic expressions and a universality in the temperature dependence of the critical current in the tunneling limit.

An analytical form of the quantum magnetization oscillations (de Haas-van Alphen effect) is derived for two-and quasi two-dimensional metals in normal and superconducting mixed states. The theory is developed under condition µ/ωc ≫ 1 (µ is the chemical potential and ωc the cyclotron frequency), which is proved to be valid for using grand canonical ensemble in the systems of low dimensionality. Effects of impurity, temperature, spin-splitting and vortex lattice -in the case of superconductors of type II -, are taken into account. Contrary to the three dimensional case, the oscillations in sufficiently pure systems of low dimensionality and at sufficiently low temperatures are characterized by a saw-tooth wave form, which smoothened with temperature and concentration of impurities growth. In the normal quasi two-dimensional systems, the expression for the magnetization oscillations includes an extra factor expressed through the transfer integral between the layers. The additional damping effect due to the vortex lattice is found. The criterion of proximity to the upper critical field for the observation of de Haas-van Alphen effect in the superconducting mixed state is established.

We report complementary studies of the critical temperature and the critical current in ferromagnet (Ni) -superconductor (Nb) multilayers. The observed oscillatory behavior of both quantities upon variation of the thickness of the ferromagnetic layer is found to be in good agreement with theory. The length scale of oscillations is identical for both quantities and is set by the magnetic length corresponding to an exchange field of 200 meV in Ni. The consistency between the behavior of the two quantities provides strong evidence for periodic π phase shifts in these devices.

We present theoretical results on the interplay of magnetic and superconducting orders in diffusive ferromagnet-superconductor-ferromagnet trilayers. The induced triplet superconducting correlations throughout the trilayer lead to an induced spin magnetization. We include self-consistency of the order parameter in the superconducting layer at arbitrary temperatures, arbitrary interface transparency, and any relative orientation of the exchange fields in the two ferromagnets. We propose to use the torque on the trilayer in an external magnetic field as a probe of the presence of triplet correlations in the superconducting phase.The importance of triplet pairing correlations in the interface region between a singlet superconductor and a ferromagnet recently became the focus of research in the field of spintronics [1,2,3,4]. In contrast to clean triplet p-wave superconductors and superfluids, for diffusive materials p-wave correlations are suppressed and triplet correlations have s-wave orbital symmetry, but are odd in frequency [1]. In the case of a homogeneous magnetization of the ferromagnet, the spin projection of the triplet correlations on the quantization axis of the exchange field is zero. If, on the other hand, the distribution of the exchange field in the ferromagnet is inhomogeneous in space, then under suitable conditions [5] also triplet correlations with non-zero spin projection (equal spin pairs) are induced [1,2,3]. Triplet pairing correlations induce in turn a spin magnetization both in the ferromagnet and in the superconductor [6,7].An important question is how to experimentally find good fingerprints of the triplet superconducting correlations. Theoretical work has been focused on calculations of T c [5,8,9], the local density of states (LDOS) [4, 10, 11], or to search for unconventional Josephson couplings [3,12]. Experimentally, no smoking gun has been found although recently magnetization changes were observed through neutron reflectometry on multilayers of YBa 2 Cu 3 O 7 and La 2/3 Ca 1/3 MnO 3 [13]. Various other properties of FS heterostructures that could be influenced by triplet superconducting correlations have been measured, as for example a negative Josephson coupling (π junctions) [14], and LDOS modulations [15].In the following we present results for the induced triplet correlations and corresponding changes of the magnetization in a ferromagnet-superconductorferromagnet (FSF) trilayer with arbitrary misalignment of the exchange fields in the two F layers. We put forward signatures of triplet correlations that can be measured experimentally.The FSF trilayer we consider is sketched in Fig. 1. We denote the layer thicknesses by d F 1 , d S , and d F 2 respectively. The x-axis is directed perpendicular to the layer interfaces with the origin at the center of the superconductor. The z-axis is aligned with the exchange field J 1 in the left ferromagnet. The angle between the exchange fields J 1 and J 2 is denoted θ J . We also assume translational invariance in the y-z-plane.We use the qu...