Defect-mediated spin relaxation and dephasing in graphene

Emerging Spintronic Materials and Functionalities

The explosive growth of the information era has put forward urgent requirements for ultrahigh-speed and extremely efficient computations. In direct contrary to charge-based computations, spintronics aims to use spins as information carriers for data storage, transmission, and decoding, to help fully realize electronic device miniaturization and high integration for next-generation computing technologies. Currently, many novel spintronic materials have been developed with unique properties and multifunctionalities, including organic semiconductors (OSCs), organic-inorganic hybrid perovskites (OIHPs), and 2D materials (2DMs). These materials are useful to fulfill the demand for developing diverse and advanced spintronic devices. Herein, these promising materials are systematically reviewed for advanced spintronic applications. Due to the distinct chemical and physical structures of OSCs, OIHPs, and 2DMs, their spintronic properties (spin transport and spin manipulation) are discussed separately. In addition, some multifunctionalities due to photoelectric and chiral-induced spin selectivity (CISS) are overviewed, including the spin-filter effect, spin-photovoltaics, spin-light emitting devices, and spin-transistor functions. Subsequently, challenges and future perspectives of using these multifunctional materials for the development of advanced spintronics are presented.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Ultimate Spin Currents in Commercial Chemical Vapor Deposited Graphene

Establishing ultimate spin current efficiency in graphene over industry-standard substrates can facilitate research and development exploration of spin current functions and spin sensing. At the same time, it can resolve core issues in spin relaxation physics while addressing the skepticism of graphene's practicality for planar spintronic applications. In this work, we reveal an exceptionally long spin communication capability of 45 μm and highest to date spin diffusion length of 13.6 μm in graphene on SiO2/Si at room temperature. Employing commercial chemical vapor deposited (CVD) graphene, we show how contact-induced surface charge transfer doping and device doping contributions, as well as spin relaxation, can be quenched in extremely long spin channels and thereby enable unexpectedly long spin diffusion lengths in polycrystalline CVD graphene. Extensive experiments show enhanced spin transport and precession in multiple longest channels (36 and 45 μm) that reveal the highest spin lifetime of ∼2.5-3.5 ns in graphene over SiO2/Si, even under ambient conditions. Such performance, made possible due to our devices approaching the intrinsic spin-orbit coupling of ∼20 μeV in graphene, reveals the role of the D'yakonov-Perel' spin relaxation mechanism in graphene channels as well as contact regions. Our record demonstration, fresh device engineering, and spin relaxation insights unlock the ultimate spin current capabilities of graphene on SiO2/Si, while the robust high performance of commercial CVD graphene can proliferate research and development of innovative spin sensors and spin computing circuits.

Spin Relaxation in s-Wave Superconductors in the Presence of Resonant Spin-Flip Scatterers

Employing analytical methods and quantum transport simulations we investigate the relaxation of quasiparticle spins in graphene proximitized by an s-wave superconductor in the presence of resonant magnetic and spin-orbit active impurities. Off resonance, the relaxation increases with decreasing temperature when electrons scatter off magnetic impurities-the Hebel-Slichter effect-and decreases when impurities have spin-orbit coupling. This distinct temperature dependence (not present in the normal state) uniquely discriminates between the two scattering mechanisms. However, we show that the Hebel-Slichter picture breaks down at resonances. The emergence of Yu-Shiba-Rusinov bound states within the superconducting gap redistributes the spectral weight away from magnetic resonances. The result is opposite to the Hebel-Slichter expectation: the spin relaxation decreases with decreasing temperature. Our findings hold for generic s-wave superconductors with resonant magnetic impurities, but also, as we show, for resonant magnetic Josephson junctions.

Comparisons of magnetic defects and coercive forces for Co/Si(100) and Co/rubrene/Si(100)

Spintronics can add new functionalities to electronic devices by utilizing the spin degree of freedom of electrons. Investigating magnetic defects is crucial for the performance of spintronics devices. However, the effects of magnetic defects that are introduced by the presence of organic materials on their magnetic properties remain unclear. Herein, we report on a novel method using rubrene combined with Kerr microscopy that enables quantitative and direct measurements of magnetic defect density. For Co/Si(100) at a magnetic field near the coercivity value, Kerr microscopy images show a dark image with some magnetic defects. Because of domain wall motion, small patches gradually change the contrast. These magnetic defects are immovable at different magnetic fields and serve as pinning sites for domain wall motion. Experimental evidence shows that coercive force can be reduced by controlling the magnetic defect density by introducing small amounts of rubrene into the films. Furthermore, direct quantitative measurements of magnetic defects show both a one-dimensional bowing of domain walls and strong defect-domain wall interactions in the films. Based on these findings, we propose a viable strategy for reducing the coercive force of Co/Si(100) by controlling the magnetic defect density and this new information promises to be valuable for future applications of spintronics devices.

Observation of spin-polarized Anderson state around charge neutral point in graphene with Fe-clusters

The pristine graphene described with massless Dirac fermion could bear topological insulator state and ferromagnetism via the band structure engineering with various adatoms and proximity effects from heterostructures. In particular, topological Anderson insulator state was theoretically predicted in tight-binding honeycomb lattice with Anderson disorder term. Here, we introduced physi-absorbed Fe-clusters/adatoms on graphene to impose exchange interaction and random lattice disorder, and we observed Anderson insulator state accompanying with Kondo effect and field-induced conducting state upon applying the magnetic field at around a charge neutral point. Furthermore, the emergence of the double peak of resistivity at ν = 0 state indicates spin-splitted edge state with high effective exchange field (>70 T). These phenomena suggest the appearance of topological Anderson insulator state triggered by the induced exchange field and disorder.

Tuning spin-orbit coupling in 2D materials for spintronics: a topical review

Atomically-thin 2D materials have opened up new opportunities in the past decade in realizing novel electronic device concepts, owing to their unusual electronic properties. The recent progress made in the aspect of utilizing additional degrees of freedom of the electrons such as spin and valley suggests that 2D materials have a significant potential in replacing current electronic-charge-based semiconductor technology with spintronics and valleytronics. For spintronics, spin-orbit coupling plays a key role in manipulating the electrons' spin degree of freedom to encode and process information, and there are a host of recent studies exploring this facet of 2D materials. We review the recent advances in tuning spin-orbit coupling of 2D materials which are of notable importance to the progression of spintronics.

Anisotropic conductivity in 2D massive Dirac Fermions: an effect of time reversal symmetry breaking in the surface states of a topological insulator

We calculate the conductivity tensor for massive Dirac Fermions within the semiclassical Boltzmann approach. We consider the effect of two different types of scattering mechanism, namely scalar and magnetic, that act incoherently and use the symmetries of the transition rate to exactly solve the Boltzmann equation. We prove that the conductivity can be anisotropic depending on the strength of the magnetic scatterers in each direction. In the particular situation of magnetic impurities polarised in the x-direction, the conductivity is three times larger in y-direction as compared with the conductivity in the x-direction, for white noise scattering correlation function. We compare the approach we apply with the most commonly used way of dealing with more than one source of scattering, namely with Matthiessen's rule, and show that the approach we applied is more general and suitable for anisotropic scattering.

Sticking of atomic hydrogen on graphene

Recent years have witnessed an ever growing interest in the interactions between hydrogen atoms and a graphene sheet. Largely motivated by the possibility of modulating the electric, optical and magnetic properties of graphene, a huge number of studies have appeared recently that added to and enlarged earlier investigations on graphite and other carbon materials. In this review we give a glimpse of the many facets of this adsorption process, as they emerged from these studies. The focus is on those issues that have been addressed in detail, under carefully controlled conditions, with an emphasis on the interplay between the adatom structures, their formation dynamics and the electric, magnetic and chemical properties of the carbon sheet.

Spin transport in graphene/transition metal dichalcogenide heterostructures

This review summarizes the theoretical and experimental studies of spin transport in graphene interfaced with transition metal dichalcogenides, and assesses its potential for future spintronic applications.

Asymmetric Electron-Hole Decoherence in Ion-Gated Epitaxial Graphene

We report on asymmetric electron-hole decoherence in epitaxial graphene gated by an ionic liquid. The observed negative magnetoresistance near zero magnetic field for different gate voltages, analyzed in the framework of weak localization, gives rise to distinct electron-hole decoherence. The hole decoherence rate increases prominently with decreasing negative gate voltage while the electron decoherence rate does not exhibit any substantial gate dependence. Quantitatively, the hole decoherence rate is as large as the electron decoherence rate by a factor of two. We discuss possible microscopic origins including spin-exchange scattering consistent with our experimental observations.

Spin susceptibilities in armchair graphene nanoribbons with Rashba spin-orbit coupling

Based on linear response theory, we studied the spin susceptibilities of armchair graphene nanoribbons (AGNRs) with Rashba spin-orbit coupling (RSOC) in an oscillating magnetic field. It is shown that by tuning the field frequency, RSOC or ribbon width to satisfy the resonance condition, the spins in AGNRs will be effectively magnetized at room temperature due to the electron transitions between RSOC-induced spin-split subbands. Moreover, in this process the magnitude of spin magnetization can also be flexibly manipulated by selecting different resonant frequency or RSOC. Thus, we provide a promisingly well-controlled scheme for the spin magnetization of AGNRs, which is useful for spintronics applications.

Current-Induced Spin Polarization in Topological Insulator-Graphene Heterostructures

Further development of the field of all-electric spintronics requires the successful integration of spin transport channels with spin injector/generator elements. While with the advent of graphene and related 2D materials high performance spin channel materials are available, the use of nanostructured spin generators remains a major challenge. Especially promising for the latter purpose are 3D topological insulators, whose 2D surface states host massless Dirac Fermions with spin-momentum locking. Here, we demonstrate injection of spin-polarized current from a topological insulator into graphene, enabled by its intimate coupling to an ultrathin Bi2Te2Se nanoplatelet within a van der Waals epitaxial heterostructure. The spin switching signal, whose magnitude scales inversely with temperature, is detectable up to ∼15 K. Our findings establish topological insulators as prospective future components of spintronic devices wherein spin manipulation is achieved by purely electrical means.

Spin Manipulation in Graphene by Chemically Induced Pseudospin Polarization

Spin manipulation is one of the most critical challenges to realize spin-based logic devices and spintronic circuits. Graphene has been heralded as an ideal material to achieve spin manipulation, but so far new paradigms and demonstrators are limited. Here we show that certain impurities such as fluorine adatoms, which locally break sublattice symmetry without the formation of strong magnetic moment, could result in a remarkable variability of spin transport characteristics. The impurity resonance level is found to be associated with a long-range sublattice pseudospin polarization, which by locally decoupling spin and pseudospin dynamics provokes a huge spin lifetime electron-hole asymmetry. In the dilute impurity limit, spin lifetimes could be tuned electrostatically from 100 ps to several nanoseconds, providing a protocol to chemically engineer an unprecedented spin device functionality.

The classical and quantum dynamics of molecular spins on graphene

Controlling the dynamics of spins on surfaces is pivotal to the design of spintronic and quantum computing devices. Proposed schemes involve the interaction of spins with graphene to enable surface-state spintronics and electrical spin manipulation. However, the influence of the graphene environment on the spin systems has yet to be unravelled. Here we explore the spin-graphene interaction by studying the classical and quantum dynamics of molecular magnets on graphene. Whereas the static spin response remains unaltered, the quantum spin dynamics and associated selection rules are profoundly modulated. The couplings to graphene phonons, to other spins, and to Dirac fermions are quantified using a newly developed model. Coupling to Dirac electrons introduces a dominant quantum relaxation channel that, by driving the spins over Villain's threshold, gives rise to fully coherent, resonant spin tunnelling. Our findings provide fundamental insight into the interaction between spins and graphene, establishing the basis for electrical spin manipulation in graphene nanodevices.

Spin phase protection in interference of electron spin waves in lightly hydrogenated graphene

Here, we have realized the extremely light hydrogenation of a graphene surface on SiO₂ by precisely controlling the amount of electron beam (EB) irradiation to a specific EB resist including hydrogen atoms, treated on graphene.

Electronic interference transport and its electron-phonon interaction in the Sb-doped Bi2Se3 nanoplates synthesized by a solvothermal method

Here we synthesized the antimony doped [Formula: see text] nanoplates by the solvothermal method. The angle-dependent magnetoconductance study was carried out and all the [Formula: see text] were found to be normalized to the perpendicular field, indicating a clear 2D electronic state. The features of weak antilocalization and universal conductance fluctuations were clearly identified in the magnetoresistance transport of the 4-probe nanodevices. The dephasing lengths are extracted respectively according to the Hikami-Larkin-Nagaoka theory. It is attributed to the involvement of the dynamic spin centers. The dephasing lengths are found to increase with the decreasing temperature following a [Formula: see text] law with [Formula: see text]. This reveals the additional dephasing source of electron-phonon interaction, which is often absent for pure 2D electronic systems.

Resonant Scattering by Magnetic Impurities as a Model for Spin Relaxation in Bilayer Graphene

We propose that the observed spin relaxation in bilayer graphene is due to resonant scattering by magnetic impurities. We analyze a resonant scattering model due to adatoms on both dimer and nondimer sites, finding that only the former give narrow resonances at the charge neutrality point. Opposite to single-layer graphene, the measured spin-relaxation rate in the graphene bilayer increases with carrier density. Although it has been commonly argued that a different mechanism must be at play for the two structures, our model explains this behavior rather naturally in terms of different broadening scales for the same underlying resonant processes. Not only do our results-using robust and first-principles inspired parameters-agree with experiment, they also predict an experimentally testable sharp decrease of the spin-relaxation rate at high carrier densities.

Influence of Impurity Spin Dynamics on Quantum Transport in Epitaxial Graphene

Experimental evidence from both spin-valve and quantum transport measurements points towards unexpectedly fast spin relaxation in graphene. We report magnetotransport studies of epitaxial graphene on SiC in a vector magnetic field showing that spin relaxation, detected using weak-localization analysis, is suppressed by an in-plane magnetic field B(∥), and thereby proving that it is caused at least in part by spinful scatterers. A nonmonotonic dependence of the effective decoherence rate on B(∥) reveals the intricate role of the scatterers' spin dynamics in forming the interference correction to the conductivity, an effect that has gone unnoticed in earlier weak localization studies.

Tunable Magnetism and Half-Metallicity in Hole-Doped Monolayer GaSe

We find, through first-principles calculations, that hole doping induces a ferromagnetic phase transition in monolayer GaSe. Upon increasing hole density, the average spin magnetic moment per carrier increases and reaches a plateau near 1.0 μB per carrier in a range of 3×10(13)/cm(2)-1×10(14)/cm(2), with the system in a half-metal state before the moment starts to descend abruptly. The predicted itinerant magnetism originates from an exchange splitting of electronic states at the top of the valence band, where the density of states exhibits a sharp van Hove singularity in this quasi-two-dimensional system.

Long distance spin communication in chemical vapour deposited graphene

Graphene is an ideal medium for long-distance spin communication in future spintronic technologies. So far, the prospect is limited by the smaller sizes of exfoliated graphene flakes and lower spin transport properties of large-area chemical vapour-deposited (CVD) graphene. Here we demonstrate a high spintronic performance in CVD graphene on SiO2/Si substrate at room temperature. We show pure spin transport and precession over long channel lengths extending up to 16 μm with a spin lifetime of 1.2 ns and a spin diffusion length ∼6 μm at room temperature. These spin parameters are up to six times higher than previous reports and highest at room temperature for any form of pristine graphene on industrial standard SiO2/Si substrates. Our detailed investigation reinforces the observed performance in CVD graphene over wafer scale and opens up new prospects for the development of lateral spin-based memory and logic applications.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Graphene spintronics

The isolation of graphene has triggered an avalanche of studies into the spin-dependent physical properties of this material and of graphene-based spintronic devices. Here, we review the experimental and theoretical state-of-art concerning spin injection and transport, defect-induced magnetic moments, spin-orbit coupling and spin relaxation in graphene. Future research in graphene spintronics will need to address the development of applications such as spin transistors and spin logic devices, as well as exotic physical properties including topological states and proximity-induced phenomena in graphene and other two-dimensional materials.

Limitations to carrier mobility and phase-coherent transport in bilayer graphene

We present transport measurements on high-mobility bilayer graphene fully encapsulated in hexagonal boron nitride. We show two terminal quantum Hall effect measurements which exhibit full symmetry broken Landau levels at low magnetic fields. From weak localization measurements, we extract gate-tunable phase-coherence times τϕ as well as the inter- and intravalley scattering times τi and τ*, respectively. While τϕ is in qualitative agreement with an electron-electron interaction-mediated dephasing mechanism, electron spin-flip scattering processes are limiting τϕ at low temperatures. The analysis of τi and τ* points to local strain fluctuation as the most probable mechanism for limiting the mobility in high-quality bilayer graphene.

Spin and valley noise in two-dimensional Dirac materials

We develop a theory for optical Faraday rotation noise in two-dimensional Dirac materials. In contrast to spin noise in conventional semiconductors, we find that the Faraday rotation fluctuations are influenced not only by spins but also the valley degrees of freedom attributed to intervalley scattering processes. We illustrate our theory with two-dimensional transition-metal dichalcogenides and discuss signatures of spin and valley noise in the Faraday noise power spectrum. We propose optical Faraday noise spectroscopy as a technique for probing both spin and valley relaxation dynamics in two-dimensional Dirac materials.

Non-invasive transmission electron microscopy of vacancy defects in graphene produced by ion irradiation

Irradiation with high-energy ions has been widely suggested as a tool to engineer properties of graphene. Experiments show that it indeed has a strong effect on graphene's transport, magnetic and mechanical characteristics. However, to use ion irradiation as an engineering tool requires understanding of the type and detailed characteristics of the produced defects which is still lacking, as the use of high-resolution transmission microscopy (HRTEM)--the only technique allowing direct imaging of atomic-scale defects--often modifies or even creates defects during imaging, thus making it impossible to determine the intrinsic atomic structure. Here we show that encapsulating the studied graphene sample between two other (protective) graphene sheets allows non-invasive HRTEM imaging and reliable identification of atomic-scale defects. Using this simple technique, we demonstrate that proton irradiation of graphene produces reconstructed monovacancies, which explains the profound effect that such defects have on graphene's magnetic and transport properties. This finding resolves the existing uncertainty with regard to the effect of ion irradiation on the electronic structure of graphene.

Spin-dependent quantum interference in nonlocal graphene spin valves

Up to date, all spin transport experiments on graphene were done in a semiclassical regime, disregarding quantum transport properties such as phase coherence and interference. Here we show that in a quantum coherent graphene nanostructure the nonlocal voltage is strongly modulated. Using nonlocal measurements, we separate the signal in spin-dependent and spin-independent contributions. We show that the spin-dependent contribution is about 2 orders of magnitude larger than the spin-independent one, when corrected for the finite polarization of the electrodes. The nonlocal spin signal is not only strongly modulated but also changes polarity as a function of the applied gate voltage. By locally tuning the carrier density in the constriction via a side gate electrode we show that the constriction plays a major role in this effect. Our results show the potential of quantum coherent graphene nanostructures for the use in future spintronic devices.

Spin relaxation mechanism in graphene: resonant scattering by magnetic impurities

We propose that the observed small (100 ps) spin relaxation time in graphene is due to resonant scattering by local magnetic moments. At resonances, magnetic moments behave as spin hot spots: the spin-flip scattering rates are as large as the spin-conserving ones, as long as the exchange interaction is greater than the resonance width. Smearing of the resonance peaks by the presence of electron-hole puddles gives quantitative agreement with experiment, for about 1 ppm of local moments. Although magnetic moments can come from a variety of sources, we specifically consider hydrogen adatoms, which are also resonant scatterers. The same mechanism would also work in the presence of a strong local spin-orbit interaction, but this would require heavy adatoms on graphene or a much greater coverage density of light adatoms. To make our mechanism more transparent, we also introduce toy atomic chain models for resonant scattering of electrons in the presence of a local magnetic moment and Rashba spin-orbit interaction.

Extrinsic spin Hall effect induced by resonant skew scattering in graphene

We show that the extrinsic spin Hall effect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spin Hall effect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giant spin Hall currents are within the reach of the current state of the art in device fabrication. The spin Hall effect is robust with respect to thermal fluctuations and disorder averaging.

Spin-orbit coupling in hydrogenated graphene

First-principles calculations of the spin-orbit coupling in graphene with hydrogen adatoms in dense and dilute limits are presented. The chemisorbed hydrogen induces a giant local enhancement of spin-orbit coupling due to sp(3) hybridization which depends strongly on the local lattice distortion. Guided by the reduced symmetry and the local structure of the induced dipole moments, we use group theory to propose realistic minimal Hamiltonians that reproduce the relevant spin-orbit effects for both single-side semihydrogenated graphene (graphone) and for a single hydrogen adatom in a large supercell. The principal linear spin-orbit band splittings are driven by the breaking of the local pseudospin inversion symmetry and the emergence of spin flips on the same sublattice.