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We unveil novel spin-orbit torque mechanisms driven by topological edge states in magnetic graphene-based devices. Within the energy gap, a damping-like torque plateau emerges within the quantum anomalous Hall phase upon breaking particle-hole symmetry, while for energies at the spin-split Dirac points located within the bands, a large damping-like torque develops as a result of a vanishing Fermi contour. Such torques are tunable by the degree of spin-pseudospin entanglement dictated by proximity-induced spin-orbit coupling terms. This additionally allows to reach the upper limit of charge-to-spin conversion in non-magnetic devices.

We report a very large spin-orbit torque (SOT) capability of chromium-based transition metal dichalcogenides (TMD) in their Janus forms CrXTe, with X=S,Se. The structural inversion symmetry breaking, inherent to Janus structures is responsible for a large SOT response generated by giant Rashba splitting, equivalent to that obtained by applying a transverse electric field of $\sim 100 \,\text{V} \,\text{nm}^{-1}$ in non-Janus CrTe\textsubscript{2}, completely out of experimental reach. By performing transport simulations on custom-made Wannier tight-binding models, Janus systems are found to exhibit a SOT performance comparable to the most efficient two-dimensional materials, while allowing for field-free perpendicular magnetization switching owing to their reduced in-plane symmetry. Altogether, our findings evidence that magnetic Janus TMDs stand as suitable candidates for ultimate SOT-MRAM devices., Comment: 6 pages

We report an efficient numerical approach to compute the different components of the orbital Hall responses in disordered topological materials from the Berry phase theory of magnetization. The theoretical framework is based on the Chebyshev expansion of Green's functions and the off-diagonal elements of the position operator for systems under arbitrary boundary conditions. The capability of this scheme is shown by computing the orbital Hall conductivity for gapped graphene and the Haldane model in the presence of nonperturbative disorder effects. This methodology enables realistic simulations of orbital Hall responses in highly complex models of disordered materials.

We investigate a generalized multi-orbital tight-binding model on a triangular lattice, a system prevalent in a wide range of two-dimensional materials, and particularly relevant for simulating transition metal dichalcogenide monolayers. We show that the interplay between spin-orbit coupling and different symmetry-breaking mechanisms leads to the emergence of four distinct topological phases [Eck, P., \textit{et al.}, Phys. Rev. B, 107 (11), 115130 (2023)]. Remarkably, this interplay also triggers the orbital Hall effect with distinguished characteristics. Furthermore, by employing the Landauer-B\"uttiker formula, we establish that in the orbital Hall insulating phase, the orbital angular momentum is carried by edge states present in nanoribbons with specific terminations. We also show that, as expected, they do not have topological protection against the disorder of the edge states belonging to a first-order topological insulator.

We report a theoretical description of novel spin-orbit torque components emerging in two-dimensional Dirac materials with broken inversion symmetry. In contrast to usual metallic interfaces where field-like and damping-like torque components are competing, we find that an intrinsic damping-like torque which derives from all Fermi-sea electrons can be simultaneously enhanced along with the field-like component. Additionally, hitherto overlooked torque components unique to Dirac materials, emerge from the coupling between spin and pseudospin degrees of freedom. These torques are found to be resilient to disorder and could enhance the magnetic switching performance of nearby magnets.

We unveil a hitherto concealed spin-orbit torque mechanism driven by orbital degrees of freedom in centrosymmetric two-dimensional transition metal dichalcogenides (focusing on PtSe${}_2$ ). Using first-principles simulations, tight-binding models and large-scale quantum transport calculations, we show that such a mechanism fundamentally stems from a spatial localization of orbital textures at opposite sides of the material, which imprints their symmetries onto spin-orbit coupling effects, further producing efficient and tunable spin-orbit torque. Our study suggests that orbital-spin entanglement at play in centrosymmetric materials can be harnessed as a resource for outperforming conventional spin-orbit torques generated by the Rashba-type effects.

We evidence the possibility for coherent electrical manipulation of the spin orientation of topologically protected edge states in a low-symmetry quantum spin Hall insulator. By using a combination of ab-initio simulations, symmetry-based modeling, and large-scale calculations of the spin Hall conductivity, it is shown that small electric fields can efficiently vary the spin textures of edge currents in monolayer 1T'-WTe2 by up to a 90-degree spin rotation, without jeopardizing their topological character. These findings suggest a new kind of gate-controllable spin-based device, topologically protected against disorder and of relevance for the development of topological spintronics.

We reveal giant proximity-induced magnetism and valley-polarization effects in Janus Pt dichalcogenides (such as SPtSe), when bound to the Europium oxide (EuO) substrate. Using first-principles simulations, it is surprisingly found that the charge redistribution, resulting from proximity with EuO, leads to the formation of two K and K$^{'}$valleys in the conduction bands. Each of these valleys displays its own spin polarization and a specific spin-texture dictated by broken inversion and time-reversal symmetries, and valley-exchange and Rashba splittings as large as hundreds of meV. This provides a platform for exploring novel spin-valley physics in low-dimensional semiconductors, with potential spin transport mechanisms such as spin-orbit torques much more resilient to disorder and temperature effects., Comment: 6 pages, 4 figures

The discovery of an ever increasing family of atomic layered magnetic materials, together with the already established vast catalogue of strong spin-orbit coupling (SOC) and topological systems, calls for some guiding principles to tailor and optimize novel spin transport and optical properties at their interfaces. Here we focus on the latest developments in both fields that have brought them closer together and make them ripe for future fruitful synergy. After outlining fundamentals on van der Waals (vdW) magnetism and SOC effects, we discuss how their coexistence, manipulation and competition could ultimately establish new ways to engineer robust spin textures and drive the generation and dynamics of spin current and magnetization switching in 2D materials-based vdW heterostructures. Grounding our analysis on existing experimental results and theoretical considerations, we draw a prospective analysis about how intertwined magnetism and spin-orbit torque (SOT) phenomena combine at interfaces with well-defined symmetries, and how this dictates the nature and figures-of-merit of SOT and angular momentum transfer. This will serve as a guiding role in designing future non-volatile memory devices that utilize the unique properties of 2D materials with the spin degree of freedom., Comment: 26 pages, 5 figures, 1 table and 1 textbox

Realizations of some topological phases in two-dimensional systems rely on the challenge of jointly incorporating spin-orbit and magnetic exchange interactions. Here, we predict the formation and control of a fully valley-polarized quantum anomalous Hall effect in bilayer graphene, by separately imprinting spin-orbit and magnetic proximity effects in different layers. This results in varying spin splittings for the conduction and valence bands, which gives rise to a topological gap at a single Dirac cone. The topological phase can be controlled by a gate voltage and switched between valleys by reversing the sign of the exchange interaction. By performing quantum transport calculations in disordered systems, the chirality and resilience of the valley-polarized edge state are demonstrated. Our findings provide a promising route to engineer a topological phase that could enable low-power electronic devices and valleytronic applications., Comment: Final published version. PRB letter: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.L161113

Proximity effects are one of the pillars of exotic phenomena and technological applications of two dimensional materials. However, the interactions nature depends strongly on the materials involved, their crystalline symmetries, and interfacial properties. Here we used large-scale first-principle calculations to demonstrate that strain and twist-angle are efficient knobs to tailor the spin-orbit coupling in graphene transition metal dichalcogenide heterobilayers. We found that by choosing a twist-angle of 30 degrees, the spin relaxation times increase by two orders of magnitude, opening a path to improve these heterostructures spin transport capability. Moreover, we demonstrate that strain and twist angle will modify the relative values of valley-Zeeman and Rashba spin-orbit coupling, allowing to tune the system into an ideal Dirac-Rashba regime. These results enable us to envision an answer for the variability of spin-orbit coupling found in different experiments and have significant consequences for applications that depend on polycrystallinity, where grains form at different orientations.

We theoretically predict that vanadium-based Janus dichalcogenide monolayers constitute an ideal platform for spin-orbit-torque memories. Using first principles calculations, we demonstrate that magnetic exchange and magnetic anisotropy energies are higher for heavier chalcogen atoms, while the broken inversion symmetry in the Janus form leads to the emergence of Rashba-like spin-orbit coupling. The spin-orbit torque efficiency is evaluated using optimized quantum transport methodology and found to be comparable to heavy nonmagnetic metals. The coexistence of magnetism and spin-orbit coupling in such materials with tunable Fermi-level opens new possibilities for monitoring magnetization dynamics in the perspective of non-volatile magnetic random access memories., Comment: 5 pages, 4 figures

We report an unconventional quantum spin Hall phase in the monolayer T$_\text{d}$-WTe$_2$, which exhibits hitherto unknown features in other topological materials. The low-symmetry of the structure induces a canted spin texture in the $yz$ plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized ($2e^2/h$) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multi-probe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials., Comment: For comments please contact josehugo.garcia@icn2.cat

The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted on the specific symmetries of traditionally studied systems, not in a fundamental constraint. Recently, experiments on few-layer ${\rm MoTe}_2$ and ${\rm WTe}_2$ showed that the reduced symmetry of these strong spin-orbit coupling materials enables a new form of {\it canted} spin Hall effect, characterized by concurrent in-plane and out-of-plane spin polarizations. Here, through quantum transport calculations on realistic device geometries, including disorder, we predict a very large gate-tunable SHE figure of merit $\lambda_s\theta_{xy}\sim 1\text{--}50$ nm in ${\rm MoTe}_2$ and ${\rm WTe}_2$ monolayers that significantly exceeds values of conventional SHE materials. This stems from a concurrent long spin diffusion length ($\lambda_s$) and charge-to-spin interconversion efficiency as large as $\theta_{xy} \approx 80$\%, originating from momentum-invariant (persistent) spin textures together with large spin Berry curvature along the Fermi contour, respectively. Generalization to other materials and specific guidelines for unambiguous experimental confirmation are proposed, paving the way towards exploiting such phenomena in spintronic devices. These findings vividly emphasize how crystal symmetry and electronic topology can govern the intrinsic SHE and spin relaxation, and how they may be exploited to broaden the range and efficiency of spintronic materials and functionalities., Comment: Published version, Phys. Rev. Reserach

Improved fabrication techniques have enabled the possibility of ballistic transport and unprecedented spin manipulation in ultraclean graphene devices. Spin transport in graphene is typically probed in a nonlocal spin valve and is analyzed using spin diffusion theory, but this theory is not necessarily applicable when charge transport becomes ballistic or when the spin diffusion length is exceptionally long. Here, we study these regimes by performing quantum simulations of graphene nonlocal spin valves. We find that conventional spin diffusion theory fails to capture the crossover to the ballistic regime as well as the limit of long spin diffusion length. We show that the latter can be described by an extension of the current theoretical framework. Finally, by covering the whole range of spin dynamics, our study opens a new perspective to predict and scrutinize spin transport in graphene and other two-dimensional material-based ultraclean devices., Comment: 6 pages, 4 figures. Physical Review Letters

We report on the emergence of bulk, valley-polarized currents in graphene-based devices, driven by spatially varying regions of broken sublattice symmetry, and revealed by non-local resistance ($R_\mathrm{NL}$) fingerprints. By using a combination of quantum transport formalisms, giving access to bulk properties as well as multi-terminal device responses, the presence of a non-uniform local bandgap is shown to give rise to valley-dependent scattering and a finite Fermi surface contribution to the valley Hall conductivity, related to characteristics of $R_\mathrm{NL}$. These features are robust against disorder and provide a plausible interpretation of controversial experiments in graphene/hBN superlattices. Our findings suggest both an alternative mechanism for the generation of valley Hall effect in graphene, and a route towards valley-dependent electron optics, by materials and device engineering., Comment: 6 pages, 4 figures

Spin-orbit coupling stands as a powerful tool to interconvert charge and spin currents and to manipulate the magnetization of magnetic materials through the spin torque phenomena. However, despite the diversity of existing bulk materials and the recent advent of interfacial and low-dimensional effects, control of the interconvertion at room-temperature remains elusive. Here, we unequivocally demonstrate strongly enhanced room-temperature spin-to-charge (StC) conversion in graphene driven by the proximity of a semiconducting transition metal dichalcogenide(WS2). By performing spin precession experiments in properly designed Hall bars, we separate the contributions of the spin Hall and the spin galvanic effects. Remarkably, their corresponding conversion effiencies can be tailored by electrostatic gating in magnitude and sign, peaking nearby the charge neutrality point with a magnitude that is comparable to the largest efficiencies reported to date. Such an unprecedented electric-field tunability provides a new building block for spin generation free from magnetic materials and for ultra-compact magnetic memory technologies., Comment: 13 pages, 4 figures

Anisotropic electronic transport is a possible route towards nanoscale circuitry design, particularly in two-dimensional materials. Proposals to introduce such a feature in patterned graphene have to date relied on large-scale structural inhomogeneities. Here we theoretically explore how a random, yet homogeneous, distribution of zigzag-edged triangular perforations can generate spatial anisotropies in both charge and spin transport. Anisotropic electronic transport is found to persist under considerable disordering of the perforation edges, suggesting its viability under realistic experimental conditions. Furthermore, controlling the relative orientation of perforations enables spin filtering of the transmitted electrons, resulting in a half-metallic anisotropic transport regime. Our findings point towards a co-integration of charge and spin control in a two-dimensional platform of relevance for nanocircuit design. We further highlight how geometrical effects allow finite samples to display finite transverse resistances, reminiscent of Spin Hall effects, in the absence of any bulk fingerprints of such mechanisms, and explore the underlying symmetries behind this behaviour., Comment: 11 pages, 6 figures

Graphene is an excellent material for long distance spin transport but allows little spin manipulation. Transition metal dichalcogenides imprint their strong spin-orbit coupling into graphene via proximity effect, and it has been predicted that efficient spin-to-charge conversion due to spin Hall and Rashba-Edelstein effects could be achieved. Here, by combining Hall probes with ferromagnetic electrodes, we unambiguously demonstrate experimentally spin Hall effect in graphene induced by MoS$_2$ proximity and for varying temperature up to room temperature. The fact that spin transport and spin Hall effect occur in different parts of the same material gives rise to a hitherto unreported efficiency for the spin-to-charge voltage output. Remarkably for a single graphene/MoS$_2$ heterostructure-based device, we evidence a superimposed spin-to-charge current conversion that can be indistinguishably associated with either the proximity-induced Rashba-Edelstein effect in graphene or the spin Hall effect in MoS$_2$. By comparing our results to theoretical calculations, the latter scenario is found the most plausible one. Our findings pave the way towards the combination of spin information transport and spin-to-charge conversion in two-dimensional materials, opening exciting opportunities in a variety of future spintronic applications., Comment: 15 pages, 4 figures and Supporting Information

The Haldane model on a honeycomb lattice is a paradigmatic example of a system featuring quantized Hall conductivity in the absence of an external magnetic field, that is, a quantum anomalous Hall effect. Recent theoretical work predicted that the anomalous Hall conductivity of massive Dirac fermions can display Shubnikov-de Haas (SdH) oscillations, which could be observed in topological insulators and honeycomb layers with strong spin--orbit coupling. Here, we investigate the electronic transport properties of Chern insulators subject to high magnetic fields by means of accurate spectral expansions of lattice Green's functions. We find that the anomalous component of the Hall conductivity displays visible SdH oscillations at low temperature. \textcolor{black}{The effect is shown to result from the modulation of the next-nearest neighbour flux accumulation due to the Haldane term,} which removes the electron--hole symmetry from the Landau spectrum. To support our numerical findings, we derive a long-wavelength description beyond the linear ('Dirac cone') approximation. Finally, we discuss the dependence of the energy spectra shift for reversed magnetic fields with the topological gap and the lattice bandwidth.

Since its discovery, graphene has been a promising material for spintronics: its low spin-orbit coupling, negligible hyperfine interaction, and high electron mobility are obvious advantages for transporting spin information over long distances. However, such outstanding transport properties also limit the capability to engineer active spintronics, where strong spin-orbit coupling is crucial for creating and manipulating spin currents. To this end, transition metal dichalcogenides, which have larger spin-orbit coupling and good interface matching, appear to be highly complementary materials for enhancing the spin-dependent features of graphene while maintaining its superior charge transport properties. In this review, we present the theoretical framework and the experiments performed to detect and characterize the spin-orbit coupling and spin currents in graphene/transition metal dichalcogenide heterostructures. Specifically, we will concentrate on recent measurements of Hanle precession, weak antilocalization and the spin Hall effect, and provide a comprehensive theoretical description of the interconnection between these phenomena., Comment: 21 pages, 11 figures. This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright\c{opyright}American Chemical Society after peer review. To access the final edited and published work see http://pubs.rsc.org/en/Content/ArticleLanding/2018/CS/C7CS00864C

Large spin-orbital proximity effects have been predicted in graphene interfaced with a transition metal dichalcogenide layer. Whereas clear evidence for an enhanced spin-orbit coupling has been found at large carrier densities, the type of spin-orbit coupling and its relaxation mechanism remained unknown. We show for the first time an increased spin-orbit coupling close to the charge neutrality point in graphene, where topological states are expected to appear. Single layer graphene encapsulated between the transition metal dichalcogenide WSe$_2$ and hBN is found to exhibit exceptional quality with mobilities as high as 100000 cm^2/V/s. At the same time clear weak anti-localization indicates strong spin-orbit coupling and a large spin relaxation anisotropy due to the presence of a dominating symmetric spin-orbit coupling is found. Doping dependent measurements show that the spin relaxation of the in-plane spins is largely dominated by a valley-Zeeman spin-orbit coupling and that the intrinsic spin-orbit coupling plays a minor role in spin relaxation. The strong spin-valley coupling opens new possibilities in exploring spin and valley degree of freedom in graphene with the realization of new concepts in spin manipulation.

We consider an effective model for graphene with interface-induced spin-orbit coupling and calculate the quantum Hall effect in the low-energy limit. We perform a systematic analysis of the contribution of the different terms of the effective Hamiltonian to the quantum Hall effect (QHE). By analysing the spin-splitting of the quantum Hall states as a function of magnetic field and gate-voltage, we obtain different scaling laws that can be used to characterise the spin-orbit coupling in experiments. Furthermore, we employ a real-space quantum transport approach to calculate the quantum Hall conductivity and investigate the robustness of the QHE to disorder introduced by hydrogen impurities. For that purpose, we combine first-principles calculations and a genetic algorithm strategy to obtain a graphene-only Hamiltonian that models the impurity.

We report on a theoretical study of the spin Hall Effect (SHE) and weak antilocal-ization (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/WS 2 system is found to maximize spin proximity effects compared to graphene on MoS 2 , WSe 2 , or MoSe 2 , 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., Comment: This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright\c{opyright}American Chemical Society after peer review. To access the final edited and published work see http://pubs.acs.org/articlesonrequest/AOR-c2pZ8WnmG7pcF4MIivjz

We report on fundamental aspects of spin dynamics in graphene interfaced with 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. In the presence of strong intervalley scattering the anisotropy can reach unprecedented values of tens to hundreds, while it reduces to 1/2 for weak disorder. This behavior is mediated by spin-valley locking, which is strong in TMDCs and is imprinted onto graphene. Such giant spin transport anisotropy, driven by proximity effects, provides an exciting paradigm for designing novel spin device functionalities., Comment: 5 pages

Theoretical predictions and recent experimental results suggest one can engineer spin Hall effect in graphene by enhancing the spin-orbit coupling in the vicinity of an impurity. We use a Chebyshev expansion of the Kubo-Bastin formula to compute the spin conductivity tensor for a tight-binding model of graphene with randomly distributed impurities absorbed on top of carbon atoms. We model the impurity-induced spin-orbit coupling with a graphene-only Hamiltonian that takes into account three different contributions~\cite{Gmitra2013} and show how the spin Hall and longitudinal conductivities depend on the strength of each spin-orbit coupling and the concentration of impurities. Additionally, we calculate the real-space projection of the density of states in the vicinity of the Dirac point for single and multiple impurities and correlate these results with the conductivity calculations., Comment: 8 pages, 8 figures

We consider resonant scatterers with large scattering cross-sections in graphene that are produced by a gated disk or a vacancy, and show that a gated ring can be engineered to produce an efficient electron cloak. We also demonstrate that this same scheme can be applied to tune the direction of electron flow. Our analysis is based on a partial-wave expansion of the electronic wave-functions in the continuum approximation, described by the Dirac equation. Using a symmetrized version of the massless Dirac equation, we derive a general condition for the cloaking of a scatterer by a potential with radial symmetry. We also perform tight-binding calculations to show that our findings are robust against the presence of disorder in the gate potential., Comment: 11 pages

We describe an efficient numerical approach to calculate the longitudinal and transverse Kubo conductivities of large systems using Bastin's formulation. We expand the Green's functions in terms of Chebyshev polynomials and compute the conductivity tensor for any temperature and chemical potential in a single step. To illustrate the power and generality of the approach, we calculate the conductivity tensor for the quantum Hall effect in disordered graphene and analyze the effect of the disorder in a Chern insulator in Haldane's model on a honeycomb lattice., Comment: 5 pages, 3 figures and a supplementary material (3 pages)

We address the nature of the disordered state that results from the adsorption of adatoms in graphene. For adatoms that sit at the center of the honeycomb plaquette, as in the case of most transition metals, we show that the ones that form a zero-energy resonant state lead to Anderson localization in the vicinity of the Dirac point. Among those, we show that there is a symmetry class of adatoms where Anderson localization is suppressed, leading to an exotic metallic state with large and rare charge droplets, that localizes only at the Dirac point. We identify the experimental conditions for the observation of the Anderson transition for adatoms in graphene., Comment: 8 pages, 5 figures, 2 appendixes, Final version