Abstract:
We investigate how spins relax in intrinsic graphene. The spin-orbit coupling arises from the band structure and is enhanced by ripples. The orbital motion is influenced by scattering centers and ripple-induced gauge fields. Spin relaxation due to Elliot-Yafet and Dyakonov-Perel mechanisms and gauge fields in combination with spin-orbit coupling are discussed. In intrinsic graphene, the Dyakonov-Perel mechanism and spin flip due to gauge fields dominate and the spin-flip relaxation time is inversely proportional to the elastic scattering time. The spin relaxation anisotropy depends on an intricate competition between these mechanisms. Experimental consequences are discussed.

Abstract:
A continuum model for the effective spin orbit interaction in graphene is derived from a tight-binding model which includes the $\pi$ and $\sigma$ bands. We analyze the combined effects of the intra-atomic spin-orbit coupling, curvature, and applied electric field, using perturbation theory. We recover the effective spin-orbit Hamiltonian derived recently from group theoretical arguments by Kane and Mele. We find, for flat graphene, that the intrinsic spin-orbit coupling $\Hi \propto \Delta^ 2$ and the Rashba coupling due to a perpendicular electric field ${\cal E}$, $\Delta_{\cal E} \propto \Delta$, where $\Delta$ is the intra-atomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term $\Delta_{\rm curv} \propto \Delta$. For the values of $\cal E$ and curvature profile reported in actual samples of graphene, we find that $\Hi < \Delta_{\cal E} \lesssim \Delta_{\rm curv}$. The effect of spin-orbit coupling on derived materials of graphene, like fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only $\Hi$ is important. Both for nanotubes and nanotube caps $\Delta_{\rm curv}$ is in the order of a few Kelvins. We reproduce the known appearance of a gap and spin-splitting in the energy spectrum of nanotubes due to the spin-orbit coupling. For nanotube caps, spin-orbit coupling causes spin-splitting of the localized states at the cap, which could allow spin-dependent field-effect emission.

Abstract:
We derive a closed expression for the finite-temperature conductance of a Coulomb-blockade quantum dot in the presence of an exchange interaction and a parallel magnetic field. Parallel-field dependence of Coulomb-blockade peak position has been used to determine experimentally the ground-state spin of quantum dots. We find that for a realistic value of the exchange interaction, the peak motion can be significantly affected at temperatures as low as kT ~ 0.1 Delta, with Delta being the mean level spacing in the dot. This temperature effect can lead to misidentification of the ground-state spin when a level crossing occurs at low fields. We propose an improved method to determine unambiguously the ground-state spin. This method takes into account level crossings and temperature effects at a finite exchange interaction.

Abstract:
We study the proximity effect in hybrid structures consisting of superconductor and ferromagnetic insulator separated by a normal diffusive metal (S/N/FI structures). These stuctures were proposed to realize the absolute spin-valve effect. We pay special attention to the gaps in the density of states of the normal part. We show that the effect of the ferromagnet is twofold: It not only shifts the density of states but also provides suppression of the gap. The mechanism of this suppression is remarkably similar to that due to magnetic impurities. Our results are obtained from the solution of one-dimensional Usadel equation supplemented with boundary conditions for matrix current at both interfaces.

Abstract:
We study the supercurrent in a superconductor/ferromagnet/superconductor graphene junction. In contrast to its metallic counterpart, the oscillating critical current in our setup decays only weakly upon increasing exchange field and junction width. We find an unusually large residual value of the supercurrent at the oscillatory cusps due to a strong deviation from a sinusoidal current-phase relationship. Our findings suggest a very efficient device for dissipationless supercurrent switching.

Abstract:
Magnetic gates in close proximity to graphene can induce ferromagnetic correlations. We study the effect of such induced magnetization dependent Zeeman splittings on the graphene transport properties. We estimate that induced spin splittings of the order of \Delta ~ 5 meV could be achieved with the use of magnetic insulator gates, e.g. EuO-gates, deposited on top of graphene. We demonstrate that such splittings in proximity induced ferromagnetic graphene could be determined directly from the tunneling resonances in the linear response conductance, as the top gate creates also a tunable barrier in the graphene layer. We show how such splittings could also be determined independently by magnetoresistance measurements in a spin-valve geometry. Because the spin polarization of the current near the Dirac point increases with the length of the barrier, long magnetic gates are desirable for determining \Delta experimentally.

Abstract:
We consider two mechanisms of spin relaxation in disordered graphene. i) Spin relaxation due to curvature spin orbit coupling caused by ripples. ii) Spin relaxation due to the interaction of the electronic spin with localized magnetic moments at the edges. We obtain analytical expressions for the spin relaxation times, tau_SO and tau_J due to both mechanisms and estimate their values for realistic parameters of graphene samples. We obtain that spin relaxation originating from these mechanisms is very weak and spin coherence is expected in disordered graphene up to samples of length L ~ 1 micron.

Abstract:
The circuit theory of mesoscopic transport provides a unified framework to describe spin-dependent or superconductivity-related phenomena. We extend this theory to hybrid systems of normal metals, ferromagnets and superconductors. Our main result is an expression for the current through an arbitrary contact between two general isotropic "nodes", which is suitable to describe the presence of superconducting and ferromagnetic elements in the system, as well as magnetically active interfaces/contacts. In certain cases (weak ferromagnet and magnetic tunnel junction) we derive transparent and simple results for the matrix current.

Abstract:
We investigate spin dependent transport in hybrid superconductor(S)--normal-metal(N)--ferromagnet(F) structures under conditions of proximity effect. We demonstrate the feasibility of the absolute spin-valve effect for a certain interval of voltages in a system consisting of two coupled tri-layer structures. Our results are also valid for non-collinear magnetic configurations of the ferromagnets.