Two complementary effects modify the GHz magnetization dynamics of nanoscale heterostructures of ferromagnetic and normal materials relative to those of the isolated magnetic constituents. On the one hand, a time-dependent ferromagnetic magnetization pumps a spin angular-momentum flow into adjacent materials and, on the other hand, spin angular momentum is transferred between ferromagnets by an applied bias, causing mutual torques on the magnetizations. These phenomena are manifestly nonlocal: they are governed by the entire spin-coherent region that is limited in size by spin-flip relaxation processes. This review presents recent progress in understanding the magnetization dynamics in ferromagnetic heterostructures from first principles, focusing on the role of spin pumping in layered structures. The main body of the theory is semiclassical and based on a mean-field Stoner or spin-density-functional picture, but quantum-size effects and the role of electron-electron correlations are also discussed. A growing number of experiments support the theoretical predictions. The formalism should be useful for understanding the physics and for engineering the characteristics of small devices such as magnetic random-access memory elements. CONTENTS

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.

The electron transport properties of hybrid ferromagnetic|normal metal structures such as multilayers and spin valves depend on the relative orientation of the magnetization direction of the ferromagnetic elements. Whereas the contrast in the resistance for parallel and antiparallel magnetizations, the so-called Giant Magnetoresistance, is relatively well understood for quite some time, a coherent picture for non-collinear magnetoelectronic circuits and devices has evolved only recently. We review here such a theory for electron charge and spin transport with general magnetization directions that is based on the semiclassical concept of a vector spin accumulation. In conjunction with first-principles calculations of scattering matrices many phenomena, e.g. the currentinduced spin-transfer torque, can be understood and predicted quantitatively for different material combinations.

Spintronics relies on the transport of spins, the intrinsic angular momentum of electrons, as an alternative to the transport of electron charge as in conventional electronics. The long-term goal of spintronics research is to develop spin-based, low-dissipation computing-technology devices. Recently, long-distance transport of a spin current was demonstrated across ferromagnetic insulators. However, antiferromagnetically ordered materials, the most common class of magnetic materials, have several crucial advantages over ferromagnetic systems for spintronics applications: antiferromagnets have no net magnetic moment, making them stable and impervious to external fields, and can be operated at terahertz-scale frequencies. Although the properties of antiferromagnets are desirable for spin transport, indirect observations of such transport indicate that spin transmission through antiferromagnets is limited to only a few nanometres. Here we demonstrate long-distance propagation of spin currents through a single crystal of the antiferromagnetic insulator haematite (α-FeO), the most common antiferromagnetic iron oxide, by exploiting the spin Hall effect for spin injection. We control the flow of spin current across a haematite-platinum interface-at which spins accumulate, generating the spin current-by tuning the antiferromagnetic resonance frequency using an external magnetic field. We find that this simple antiferromagnetic insulator conveys spin information parallel to the antiferromagnetic Néel order over distances of more than tens of micrometres. This mechanism transports spins as efficiently as the most promising complex ferromagnets. Our results pave the way to electrically tunable, ultrafast, low-power, antiferromagnetic-insulator-based spin-logic devices that operate without magnetic fields at room temperature.

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

The interface-induced magnetization damping of thin ferromagnetic films in contact with normal-metal layers is calculated from first principles for clean and disordered Fe/Au and Co/Cu interfaces. Interference effects arising from coherent scattering turn out to be very small, consistent with a very small magnetic coherence length. Because the mixing conductances which govern the spin transfer are to a good approximation real-valued, the spin pumping can be described by an increased Gilbert damping factor but an unmodified gyromagnetic ratio. The results also confirm that the spin-current-induced magnetization torque is an interface effect.

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...

Current-driven magnetization dynamics in ferromagnetic metals is studied in a self-consistent adiabatic local-density approximation in the presence of spin-conserving and spin-dephasing impurity scattering. Based on a quantum kinetic equation, we derive Gilbert damping and spin-transfer torques entering the LandauLifshitz equation to linear order in frequency and wave vector. Gilbert damping and a current-driven dissipative torque scale identically and compete, with the result that a steady current-driven domain-wall motion is insensitive to spin dephasing in the limit of weak ferromagnetism. A uniform magnetization is found to be much more stable against spin torques in the itinerant than in the s-d model for ferromagnetism. A dynamic spin-transfer torque reminiscent of the spin pumping in multilayers is identified and shown to govern the current-induced domain-wall distortion.