A continuum model for the effective spin orbit interaction in graphene is derived from a tightbinding model which includes the π and σ bands. We analyze the combined effects of the intraatomic 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 ∆int ∝ ∆ 2 and the Rashba coupling due to an perpendicular electric field E , ∆E ∝ ∆, where ∆ is the intraatomic spin-orbit coupling constant for carbon. Moreover we show that local curvature of the graphene sheet induces an extra spin-orbit coupling term ∆curv ∝ ∆. For the values of E and curvature profile reported in actual samples of graphene, we find that ∆int < ∆E ∆curv. The effect of spin orbit coupling on derived materials of graphene like fullerenes, nanotubes, and nanotube caps, is also studied. For fullerenes, only ∆int is important. Both for nanotubes and nanotube caps ∆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. INTRODUCTION.

We report on fundamental aspects of spin dynamics in heterostructures of graphene and transition metal dichalcogenides (TMDCs). By using realistic models derived from first principles we compute the spin lifetime anisotropy, defined as the ratio of lifetimes for spins pointing out of the graphene plane to those pointing in the plane. We find that the anisotropy can reach values of tens to hundreds, which is unprecedented for typical 2D systems with spin-orbit coupling and indicates a qualitatively new regime of spin relaxation. This behavior is mediated by spin-valley locking, which is strongly imprinted onto graphene by TMDCs. Our results indicate that this giant spin lifetime anisotropy can serve as an experimental signature of materials with strong spin-valley locking, including graphene/TMDC heterostructures and TMDCs themselves. Additionally, materials with giant spin lifetime anisotropy can provide an exciting platform for manipulating the valley and spin degrees of freedom, and for designing novel spintronic devices. PACS numbers: 72.80.Vp, 72.25.Rb, 71.70.Ej Introduction. Following the discovery of graphene in 2004 [1], a host of other two-dimensional (2D) materials have been synthesized and studied, each demonstrating unique properties and showing promise for technological applications [2]. Currently, there is a great deal of interest in layered heterostructures of these materials [3, 4], where the combined system might be engineered for specific applications [5] or might enable the exploration of new phenomena [6, 7]. In the field of spintronics, graphene has exceptional charge transport properties but weak spin-orbit coupling (SOC) on the order of 10 µeV [8], which makes it ideal for long-distance spin transport [9-11] but ineffective for generating or manipulating spin currents. To advance towards spin manipulation, recent work has focused on heterostructures of graphene and magnetic insulators [12-16] or strong SOC materials such as transition metal dichalcogenides (TMDCs) and topo-logical insulators [17-19]. The SOC induced in graphene by a TMDC could enable phenomena such as topological edge states [20] or the spin Hall effect [21-23]. To this end, a variety of recent experiments have explored spin transport in graphene/TMDC heterostruc-tures [21, 24-29]. Magnetotransport measurements revealed that graphene in contact with WS 2 exhibits a large weak antilocalization (WAL) peak, revealing a strong SOC induced by proximity effects [24-26, 30]. Fits to the magnetoconductance yielded spin lifetimes τ s ≈ 5 ps, which is two to three orders of magnitude lower than graphene on traditional substrates [10, 31]. It was later asserted that after the removal of a temperature-independent background, τ s becomes at most only a few hundred femtoseconds [26]. Nonlocal Hanle measurements , meanwhile, have revealed spin lifetimes up to a few tens of picoseconds [27-29] that can be tuned by a back gate [28, 29]. Finally, charge transport measure

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.Graphene can be useful in future advanced applications because of the reduced dimensionality, the long mean free paths and phase coherence lengths, and the control of the number of carriers [1]. Among possible applications, graphene is investigated as a material for spintronic devices [2, 3, 4, 5, 6, 7, 8]. Spintronics aims to inject, detect, and manipulate the electron spin in electronic devices.Spin manipulation via the spin-orbit (SO) coupling has been extensively discussed in semiconductors and metals [9]. The SO coupling enables electric, and not just magnetic, control of the spin [10]. In two dimensional (2D) semiconducting structures, inversion asymmetry results in the Rashba SO coupling [11]. Additionally, bulk inversion asymmetry in A 3 B 5 compounds causes the Dresselhaus SO coupling [12]. Device performance is limited by spin relaxation and understanding its origin enables enhanced spin control. Two mechanisms of spin relaxation discussed in the literature [9,13], the Elliof-Yafet [14,15] and 17] mechanisms, can be relevant in graphene.Elliof-Yafet (EY) spin relaxation is related to how the spin changes its direction during a scattering event [14,15]. This is possible because the SO coupling produces electronic wave functions that are admixtures of spin and orbital angular momentum. Dyakonov-Perel (DP) [16,17] spin relaxation is related to spin precession between scattering events by the effective (Zeeman) magnetic field induced by the SO coupling. This SO induced effective (Zeeman) magnetic field changes direction during scattering. In the EY mechanism, the spin relaxation time is proportional to the elastic scattering time τ el , τ EY so ∝ τ el , whereas the dependence is opposite τ DP so ∝ (τ el ) −1 for the DP mechanism. This qualitative difference allows detection of these two competing mechanisms in disordered samples.Recently, spin transport and spin relaxation were studied in relatively dirty graphene samples [3,18]. A spin relaxation length λ sf ∼ 2µm was measured at room temperature and it was indicated that λ sf is proportional to the elastic mean free path l el , suggesting the EY mechanism to be dominant [3,18]. The measured spin relaxation length is weakly anisotropic, such that spins "outThe SO coupling induces a momentum dependent effective field B which changes direction randomly after scattering events, leading to...

We investigate spin-dependent transport in hybrid superconductor -normal-metal-ferromagnet structures under conditions of the 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 trilayer structures. Our results are also valid for noncollinear magnetic configurations of the ferromagnets. DOI: 10.1103/PhysRevLett.88.047003 PACS numbers: 74.50. +r, 72.10. -d, 74.80.Dm Spin transport in hybrid systems of ferromagnets and normal metals is a very active field of research. This is inspired by prospectives of spin-based electronics or "spintronics" [1]. The feasibility to create and control spin accumulation in such systems by injecting spin polarized current from a ferromagnetic material into a nonmagnetic one is being extensively studied [2]. The theory predicts a variety of novel effects in the case of noncollinear magnetizations [3].The main attention is given to the so-called spin-valve effect, which provides the mechanism for the giant magnetoresistance (GMR) [4]. An idealized ferromagnetic metal would have electrons with only one direction of spin. The current between two such metals would not go if their magnetizations are opposite. This is the absolute spinvalve effect. The absolute effect is impossible to achieve with common ferromagnetic metals, since electron states of both spin directions are present at the Fermi surface. This is why the actual values of GMR are relatively small. There have been substantial efforts to increase these values by exploring various material combinations [4]. Recent attempts to realize the absolute spin-valve effect concentrated on exotic magnetic materials. A spin polarization up to 80% was achieved using the dilute magnetic semiconductor Zn 12x -Mn x Se [5].In this Letter we propose a different approach, in which an absolute spin-valve effect can be achieved without using "exotic" compounds. We suggest to use the proximity effect minigap induced in a normal metal by an adjacent superconductor. This minigap has been predicted long ago [6] and has been intensively investigated in recent years [7]. Features related to the proximity effect can be probed by tunneling spectroscopy measurements. The tunneling current between two superconducting proximity structures exhibits a jump at the voltage eV th ͑D 1 1D 2 ͒,D 1͑2͒ being the minigaps in the structures. This is a consequence of the sharp peak in the density of states at the minigap edge, which mimics a BCS density of states. The current jump at the threshold voltage is well known for tunneling between superconductors [8].We use the minigap to achieve an absolute spin-valve effect for the tunneling current between two hybrid structures. Each structure combines a normal metal part with superconducting and magnetic reservoirs, which induce superconducting and magnetic correlations in the normal metal part. The presence of a normal part is essential to provide a physical separation between the sources of superconducting and ferr...

The electrical resistance of ferromagnetic/normal-metal (F/N) heterostructures depends on the nature of the junctions that may be tunnel barriers, point contacts, or intermetallic interfaces. For all junction types, the resistance of disordered F/N/F perpendicular spin valves as a function of the angle between magnetization vectors is shown to obey a simple universal law. The spin-current induced magnetization torque can be measured by the angular magnetoresistance of these spin valves. The results are generalized to arbitrary magnetoelectronic circuits.