Determination of the spin-lifetime anisotropy in graphene using oblique spin precession

Magnetic clusters as efficient EY-like spin-scattering centres in graphene

The spin scattering induced by magnetic adsorbates on graphene was studied using a combination of transport measurements on a graphene field effect transistor decorated with atomically precise nickel clusters and first principles calculations. A comparative study before and after deposition of Ni4 clusters unambiguously corroborated the contribution of the added scatterers. An investigation of the spin scattering parameters as a function of the applied voltage indicated a cluster-induced Elliot-Yafet like spin scattering mechanism. Density functional theory calculations were used in combination with a tight-binding model to quantify the strength of the spin-orbit coupling terms induced by the adsorbed clusters.

Highly anisotropic spin transport in ultrathin black phosphorus

In anisotropic crystals, the direction-dependent effective mass of carriers can have a profound impact on spin transport dynamics. The puckered crystal structure of black phosphorus leads to direction-dependent charge transport and optical response, suggesting that it is an ideal system for studying anisotropic spin transport. To this end, we fabricate and characterize high-mobility encapsulated ultrathin black-phosphorus-based spin valves in a four-terminal geometry. Our measurements show that in-plane spin lifetimes are strongly gate tunable and exceed one nanosecond. Through high out-of-plane magnetic fields, we observe a fivefold enhancement in the out-of-plane spin signal case compared to in-plane and estimate a colossal spin-lifetime anisotropy of ∼6. This finding is further confirmed by oblique Hanle measurements. Additionally, we estimate an in-plane spin-lifetime anisotropy ratio of up to 1.8. Our observation of strongly anisotropic spin transport along three orthogonal axes in this pristine material could be exploited to realize directionally tunable spin transport.

Ab Initio Predictions of Spin Relaxation, Dephasing, and Diffusion in Solids

Spin relaxation, dephasing, and diffusion are at the heart of spin-based information technology. Accurate theoretical approaches to simulate spin lifetimes (τs), determining how fast the spin polarization and phase information will be lost, are important to the understanding of the underlying mechanism of these spin processes, and invaluable in searching for promising candidates of spintronic materials. Recently, we develop a first-principles real-time density-matrix (FPDM) approach to simulate spin dynamics for general solid-state systems. Through the complete first-principles descriptions of light-matter interaction and scattering processes including electron-phonon, electron-impurity, and electron-electron scatterings with self-consistent spin-orbit coupling, as well as ab initio Landé g-factor, our method can predict τs at various conditions as a function of carrier density and temperature, under electric and magnetic fields. By employing this method, we successfully reproduce experimental results of disparate materials and identify the key factors affecting spin relaxation, dephasing, and diffusion in different materials. Specifically, we predict that germanene has long τs (∼100 ns at 50 K), a giant spin lifetime anisotropy, and spin-valley locking effect under electric fields, making it advantageous for spin-valleytronic applications. Based on our theoretical derivations and ab initio simulations, we propose a new useful electronic quantity, named spin-flip angle θ↑↓, for the understanding of spin relaxation through intervalley spin-flip scattering processes. Our method can be further applied to other emerging materials and extended to simulate exciton spin dynamics and steady-state photocurrents due to photogalvanic effect.

Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2

Van der Waals interactions with transition metal dichalcogenides were shown to induce strong spin-orbit coupling (SOC) in graphene, offering great promises to combine large experimental flexibility of graphene with unique tuning capabilities of the SOC. Here, we probe SOC-driven band splitting and electron dynamics in graphene on WSe2 by measuring ballistic transverse magnetic focusing. We found a clear splitting in the first focusing peak whose evolution in charge density and magnetic field is well reproduced by calculations using the SOC strength of ~ 13 meV, and no splitting in the second peak that indicates stronger Rashba SOC. Possible suppression of electron-electron scatterings was found in temperature dependence measurement. Further, we found that Shubnikov-de Haas oscillations exhibit a weaker band splitting, suggesting that it probes different electron dynamics, calling for a new theory. Our study demonstrates an interesting possibility to exploit ballistic electron motion pronounced in graphene for emerging spin-orbitronics.

Ultralong 100 ns spin relaxation time in graphite at room temperature

Graphite has been intensively studied, yet its electron spins dynamics remains an unresolved problem even 70 years after the first experiments. The central quantities, the longitudinal (T₁) and transverse (T₂) relaxation times were postulated to be equal, mirroring standard metals, but T₁ has never been measured for graphite. Here, based on a detailed band structure calculation including spin-orbit coupling, we predict an unexpected behavior of the relaxation times. We find, based on saturation ESR measurements, that T₁ is markedly different from T₂. Spins injected with perpendicular polarization with respect to the graphene plane have an extraordinarily long lifetime of 100 ns at room temperature. This is ten times more than in the best graphene samples. The spin diffusion length across graphite planes is thus expected to be ultralong, on the scale of ~ 70 μm, suggesting that thin films of graphite - or multilayer AB graphene stacks - can be excellent platforms for spintronics applications compatible with 2D van der Waals technologies. Finally, we provide a qualitative account of the observed spin relaxation based on the anisotropic spin admixture of the Bloch states in graphite obtained from density functional theory calculations.

Synthetic Rashba spin-orbit system using a silicon metal-oxide semiconductor

The spin-orbit interaction (SOI), mainly manifesting itself in heavy elements and compound materials, has been attracting much attention as a means of manipulating and/or converting a spin degree of freedom. Here, we show that a Si metal-oxide- semiconductor (MOS) heterostructure possesses Rashba-type SOI, although Si is a light element and has lattice inversion symmetry resulting in inherently negligible SOI in bulk form. When a strong gate electric field is applied to the Si MOS, we observe spin lifetime anisotropy of propagating spins in the Si through the formation of an emergent effective magnetic field due to the SOI. Furthermore, the Rashba parameter α in the system increases linearly up to 9.8 × 10^-16 eV m for a gate electric field of 0.5 V nm^-1; that is, it is gate tuneable and the spin splitting of 0.6 μeV is relatively large. Our finding establishes a family of spin-orbit systems.

Van der Waals heterostructures for spintronics and opto-spintronics

The large variety of 2D materials and their co-integration in van der Waals heterostructures enable innovative device engineering. In addition, their atomically thin nature promotes the design of artificial materials by proximity effects that originate from short-range interactions. Such a designer approach is particularly compelling for spintronics, which typically harnesses functionalities from thin layers of magnetic and non-magnetic materials and the interfaces between them. Here we provide an overview of recent progress in 2D spintronics and opto-spintronics using van der Waals heterostructures. After an introduction to the forefront of spin transport research, we highlight the unique spin-related phenomena arising from spin-orbit and magnetic proximity effects. We further describe the ability to create multifunctional hybrid heterostructures based on van der Waals materials, combining spin, valley and excitonic degrees of freedom. We end with an outlook on perspectives and challenges for the design and production of ultracompact all-2D spin devices and their potential applications in conventional and quantum technologies.

Robust Spin Interconnect with Isotropic Spin Dynamics in Chemical Vapor Deposited Graphene Layers and Boundaries

The utilization of large-area graphene grown by chemical vapor deposition (CVD) is crucial for the development of scalable spin interconnects in all-spin-based memory and logic circuits. However, the fundamental influence of the presence of multilayer graphene patches and their boundaries on spin dynamics has not been addressed yet, which is necessary for basic understanding and application of robust spin interconnects. Here, we report universal spin transport and dynamic properties in specially devised single layer, bilayer, and trilayer graphene channels and their layer boundaries and folds that are usually present in CVD graphene samples. We observe uniform spin lifetime with isotropic spin relaxation for spins with different orientations in graphene layers and their boundaries at room temperature. In all of the inhomogeneous graphene channels, the spin lifetime anisotropy ratios for spins polarized out-of-plane and in-plane are measured to be close to unity. Our analysis shows the importance of both Elliott-Yafet and D'yakonov-Perel' mechanisms with an increasing role of the latter mechanism in multilayer channels. These results of universal and isotropic spin transport on large-area inhomogeneous CVD graphene with multilayer patches and their boundaries and folds at room temperature prove its outstanding spin interconnect functionality, which is beneficial for the development of scalable spintronic 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.

Proposal for Unambiguous Electrical Detection of Spin-Charge Conversion in Lateral Spin Valves

Efficient detection of spin-charge conversion is crucial for advancing our understanding of emergent phenomena in spin-orbit-coupled nanostructures. Here, we provide a proof of principle of an electrical detection scheme of spin-charge conversion that enables full disentanglement of competing spin-orbit coupling (SOC) transport phenomena in diffusive lateral channels, i.e., the inverse spin Hall effect and the spin galvanic effect. A suitable geometry in an applied oblique magnetic field is shown to provide direct access to SOC transport coefficients through a symmetry analysis of the output nonlocal resistance. The scheme is robust against tilting of the spin-injector magnetization, disorder, and spurious non-spin-related contributions to the nonlocal signal and can be used to probe spin-charge conversion effects in both spin-valve and hybrid optospintronic devices.

Tunable room-temperature spin galvanic and spin Hall effects in van der Waals heterostructures

Spin-orbit coupling stands as a powerful tool to interconvert charge and spin currents and to manipulate the magnetization of magnetic materials through spin-torque phenomena. However, despite the diversity of existing bulk materials and the recent advent of interfacial and low-dimensional effects, control of this interconversion at room temperature remains elusive. Here, we demonstrate strongly enhanced room-temperature spin-to-charge interconversion in graphene driven by the proximity of WS₂. By performing spin precession experiments in appropriately designed Hall bars, we separate the contributions of the spin Hall and the spin galvanic effects. Remarkably, their corresponding conversion efficiencies can be tailored by electrostatic gating in magnitude and sign, peaking near the charge neutrality point with an equivalent magnitude that is comparable to the largest efficiencies reported to date. Such electric-field tunability provides a building block for spin generation free from magnetic materials and for ultra-compact magnetic memory technologies.

Two-Dimensional Flexible High Diffusive Spin Circuits

Owing to their unprecedented electronic properties, graphene and two-dimensional (2D) crystals have brought fresh opportunities for advances in planar spintronic devices. Graphene is an ideal medium for spin transport while being an exceptionally resilient material for flexible nanoelectronics. However, these extraordinary traits have never been combined to create flexible graphene spin circuits. Realizing such circuits could lead to bendable strain-spin sensors, as well as a unique platform to explore pure spin current based operations and low-power 2D flexible nanoelectronics. Here, we demonstrate graphene spin circuits on flexible substrates for the first time. Despite the rough topography of the flexible substrates, these circuits prepared with chemical vapor deposited monolayer graphene reveal an efficient room temperature spin transport with distinctively large spin diffusion coefficients ∼0.2 m² s^-1. Compared to earlier graphene devices on Si/SiO₂ substrates, such values are up to 20 times larger, leading to one order higher spin signals and an enhanced spin diffusion length ∼10 μm in graphene-based nonlocal spin valves fabricated using industry standard systems. This high performance arising out of a characteristic substrate terrain shows promise of a scalable and flexible platform towards flexible 2D spintronics. Our innovation is a key step for the exploration of strain-dependent 2D spin phenomena and paves the way for flexible graphene spin memory-logic units and planar spin sensors.

Observation of Spin-Valley-Coupling-Induced Large Spin-Lifetime Anisotropy in Bilayer Graphene

We report the first observation of a large spin-lifetime anisotropy in bilayer graphene (BLG) fully encapsulated between hexagonal boron nitride. We characterize the out-of-plane (τ_{⊥}) and in-plane (τ_{∥}) spin lifetimes by oblique Hanle spin precession. At 75 K and the charge neutrality point (CNP), we observe a strong anisotropy of τ_{⊥}/τ_{∥}=8±2. This value is comparable to graphene-transition-metal-dichalcogenide heterostructures, whereas our high-quality BLG provides with τ_{⊥} up to 9 ns, a spin lifetime more than 2 orders of magnitude larger. The anisotropy decreases to 3.5±1 at a carrier density of n=6×10^{11}  cm^{-2}. Temperature-dependent measurements show above 75 K a decrease of τ_{⊥}/τ_{∥} with increasing temperature, reaching the isotropic case close to room temperature. We explain our findings with electric-field-induced spin-valley coupling arising from the small intrinsic spin-orbit fields in BLG of 12  μeV at the CNP.

Strong and Tunable Spin-Lifetime Anisotropy in Dual-Gated Bilayer Graphene

We report the discovery of a strong and tunable spin-lifetime anisotropy with excellent out-of-plane spin lifetimes up to 7.8 ns at 100 K in dual-gated bilayer graphene. Remarkably, this realizes the manipulation of spins in graphene by electrically controlled spin-orbit fields, which is unexpected due to graphene's weak intrinsic spin-orbit coupling (∼12  μeV). We utilize both the in-plane magnetic field Hanle precession and oblique Hanle precession measurements to directly compare the lifetimes of out-of-plane vs in-plane spins. We find that near the charge neutrality point, the application of a perpendicular electric field opens a band gap and generates an out-of-plane spin-orbit field that stabilizes out-of-plane spins against spin relaxation, leading to a large spin-lifetime anisotropy (defined as the ratio between out-of-plane and in-plane spin lifetime) up to ∼12 at 100 K. This intriguing behavior occurs because of the unique spin-valley coupled band structure of bilayer graphene. Our results demonstrate the potential for highly tunable spintronic devices based on dual-gated 2D materials.

Spin inversion in graphene spin valves by gate-tunable magnetic proximity effect at one-dimensional contacts

Graphene has remarkable opportunities for spintronics due to its high mobility and long spin diffusion length, especially when encapsulated in hexagonal boron nitride (h-BN). Here, we demonstrate gate-tunable spin transport in such encapsulated graphene-based spin valves with one-dimensional (1D) ferromagnetic edge contacts. An electrostatic backgate tunes the Fermi level of graphene to probe different energy levels of the spin-polarized density of states (DOS) of the 1D ferromagnetic contact, which interact through a magnetic proximity effect (MPE) that induces ferromagnetism in graphene. In contrast to conventional spin valves, where switching between high- and low-resistance configuration requires magnetization reversal by an applied magnetic field or a high-density spin-polarized current, we provide an alternative path with the gate-controlled spin inversion in graphene.

Spin Proximity Effects in Graphene/Topological Insulator Heterostructures

Enhancing the spin-orbit interaction in graphene, via proximity effects with topological insulators, could create a novel 2D system that combines nontrivial spin textures with high electron mobility. To engineer practical spintronics applications with such graphene/topological insulator (Gr/TI) heterostructures, an understanding of the hybrid spin-dependent properties is essential. However, to date, despite the large number of experimental studies on Gr/TI heterostructures reporting a great variety of remarkable (spin) transport phenomena, little is known about the true nature of the spin texture of the interface states as well as their role on the measured properties. Here, we use ab initio simulations and tight-binding models to determine the precise spin texture of electronic states in graphene interfaced with a Bi₂Se₃ topological insulator. Our calculations predict the emergence of a giant spin lifetime anisotropy in the graphene layer, which should be a measurable hallmark of spin transport in Gr/TI heterostructures and suggest novel types of spin devices.

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.

Large Proximity-Induced Spin Lifetime Anisotropy in Transition-Metal Dichalcogenide/Graphene Heterostructures

Van der Waals heterostructures have become a paradigm for designing new materials and devices in which specific functionalities can be tailored by combining the properties of the individual 2D layers. A single layer of transition-metal dichalcogenide (TMD) is an excellent complement to graphene (Gr) because the high quality of charge and spin transport in Gr is enriched with the large spin-orbit coupling of the TMD via the proximity effect. The controllable spin-valley coupling makes these heterostructures particularly attractive for spintronic and opto-valleytronic applications. In this work, we study spin precession in a monolayer MoSe₂/Gr heterostructure and observe an unconventional, dramatic modulation of the spin signal, showing 1 order of magnitude longer lifetime of out-of-plane spins compared to that of in-plane spins (τ_⊥ ≈ 40 ps and τ_∥ ≈ 3.5 ps). This demonstration of a large spin lifetime anisotropy in TMD/Gr heterostructures, is a direct evidence of induced spin-valley coupling in Gr and provides an accessible route for manipulation of spin dynamics in Gr, interfaced with TMDs.

Giant Spin Lifetime Anisotropy in Graphene Induced by Proximity Effects

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.

Probing optical anisotropy of nanometer-thin van der waals microcrystals by near-field imaging

Most van der Waals crystals present highly anisotropic optical responses due to their strong in-plane covalent bonding and weak out-of-plane interactions. However, the determination of the polarization-dependent dielectric constants of van der Waals crystals remains a nontrivial task, since the size and dimension of the samples are often below or close to the diffraction limit of the probe light. In this work, we apply an optical nano-imaging technique to determine the anisotropic dielectric constants in representative van der Waals crystals. Through the study of both ordinary and extraordinary waveguide modes in real space, we are able to quantitatively determine the full dielectric tensors of nanometer-thin molybdenum disulfide and hexagonal boron nitride microcrystals, the most-promising van der Waals semiconductor and dielectric. Unlike traditional reflection-based methods, our measurements are reliable below the length scale of the free-space wavelength and reveal a universal route for characterizing low-dimensional crystals with high anisotropies.

The optical response of van der Waals layered crystals is strongly anisotropic. Here, the authors develop a nano-imaging technique to determine the in-plane and out-of-plane components of the anisotropic dielectric tensors in MoS₂ and hBN, two representative van der Waals crystals.

Large room temperature spin-to-charge conversion signals in a few-layer graphene/Pt lateral heterostructure

Electrical generation and detection of pure spin currents without the need of magnetic materials are key elements for the realization of full electrically controlled spintronic devices. In this framework, achieving a large spin-to-charge conversion signal is crucial, as considerable outputs are needed for plausible applications. Unfortunately, the values obtained so far have been rather low. Here we exploit the spin Hall effect by using Pt, a non-magnetic metal with strong spin-orbit coupling, to generate and detect pure spin currents in a few-layer graphene channel. Furthermore, the outstanding properties of graphene, with long-distance spin transport and higher electrical resistivity than metals, allow us to achieve in our graphene/Pt lateral heterostructures the largest spin-to-charge output voltage at room temperature reported so far in the literature. Our approach opens up exciting opportunities towards the implementation of spin-orbit-based logic circuits and all electrical control of spin information without magnetic field.

Spintronic devices with full electrical control rely on electrical generation and detection of spin currents in the absence of magnetic materials. Here, the authors use Pt, a non-magnetic metal, to generate and detect pure spin currents in a few-layer graphene channel, achieving a remarkable spin-to-charge voltage signal at room temperature.

Spin Hall Effect and Weak Antilocalization in Graphene/Transition Metal Dichalcogenide Heterostructures

We report on a theoretical study of the spin Hall Effect (SHE) and weak antilocalization (WAL) in graphene/transition metal dichalcogenide (TMDC) heterostructures, computed through efficient real-space quantum transport methods, and using realistic tight-binding models parametrized from ab initio calculations. The graphene/WS₂ system is found to maximize spin proximity effects compared to graphene on MoS₂, WSe₂, or MoSe₂ with a crucial role played by disorder, given the disappearance of SHE signals in the presence of strong intervalley scattering. Notably, we found that stronger WAL effects are concomitant with weaker charge-to-spin conversion efficiency. For further experimental studies of graphene/TMDC heterostructures, our findings provide guidelines for reaching the upper limit of spin current formation and for fully harvesting the potential of two-dimensional materials for spintronic applications.

Electrical gate control of spin current in van der Waals heterostructures at room temperature

Two-dimensional (2D) crystals offer a unique platform due to their remarkable and contrasting spintronic properties, such as weak spin–orbit coupling (SOC) in graphene and strong SOC in molybdenum disulfide (MoS₂). Here we combine graphene and MoS₂ in a van der Waals heterostructure (vdWh) to demonstrate the electric gate control of the spin current and spin lifetime at room temperature. By performing non-local spin valve and Hanle measurements, we unambiguously prove the gate tunability of the spin current and spin lifetime in graphene/MoS₂ vdWhs at 300 K. This unprecedented control over the spin parameters by orders of magnitude stems from the gate tuning of the Schottky barrier at the MoS₂/graphene interface and MoS₂ channel conductivity leading to spin dephasing in high-SOC material. Our findings demonstrate an all-electrical spintronic device at room temperature with the creation, transport and control of the spin in 2D materials heterostructures, which can be key building blocks in future device architectures.

Two-dimensional materials are unique to build heterostructures with contrasting spintronic properties. Here, Dankert and Dash utilize a van der Waals heterostructure with graphene and MoS₂ to demonstrate an all-electrical device for creation, transport and control of the spin current up to room temperature.

Strong Modulation of Spin Currents in Bilayer Graphene by Static and Fluctuating Proximity Exchange Fields

Two-dimensional materials provide a unique platform to explore the full potential of magnetic proximity-driven phenomena, which can be further used for applications in next-generation spintronic devices. Of particular interest is to understand and control spin currents in graphene by the magnetic exchange field of a nearby ferromagnetic material in graphene-ferromagnetic-insulator (FMI) heterostructures. Here, we present the experimental study showing the strong modulation of spin currents in graphene layers by controlling the direction of the exchange field due to FMI magnetization. Owing to clean interfaces, a strong magnetic exchange coupling leads to the experimental observation of complete spin modulation at low externally applied magnetic fields in short graphene channels. Additionally, we discover that the graphene spin current can be fully dephased by randomly fluctuating exchange fields. This is manifested as an unusually strong temperature dependence of the nonlocal spin signals in graphene, which is due to spin relaxation by thermally induced transverse fluctuations of the FMI magnetization.

Spin Hall Effect and Origins of Nonlocal Resistance in Adatom-Decorated Graphene

Recent experiments reporting an unexpectedly large spin Hall effect (SHE) in graphene decorated with adatoms have raised a fierce controversy. We apply numerically exact Kubo and Landauer-Büttiker formulas to realistic models of gold-decorated disordered graphene (including adatom clustering) to obtain the spin Hall conductivity and spin Hall angle, as well as the nonlocal resistance as a quantity accessible to experiments. Large spin Hall angles of ∼0.1 are obtained at zero temperature, but their dependence on adatom clustering differs from the predictions of semiclassical transport theories. Furthermore, we find multiple background contributions to the nonlocal resistance, some of which are unrelated to the SHE or any other spin-dependent origin, as well as a strong suppression of the SHE at room temperature. This motivates us to design a multiterminal graphene geometry which suppresses these background contributions and could, therefore, quantify the upper limit for spin-current generation in two-dimensional materials.