Emergent Correlated Phases in Rhombohedral Trilayer Graphene Induced by Proximity Spin-Orbit and Exchange Coupling.

The impact of proximity-induced spin-orbit and exchange coupling on the correlated phase diagram of rhombohedral trilayer graphene (RTG) is investigated theoretically. By employing ab initio-fitted effective models of RTG encapsulated by transition metal dichalcogenides (spin-orbit proximity effect) and ferromagnetic Cr_{2}Ge_{2}Te_{6} (exchange proximity effect), we incorporate the Coulomb interactions within the random-phase approximation to explore potential correlated phases at different displacement fields and doping. We find a rich spectrum of spin-valley resolved Stoner and intervalley coherence instabilities induced by the spin-orbit proximity effects, such as the emergence of a spin-valley-coherent phase due to the presence of valley-Zeeman coupling. Similarly, proximity exchange removes the phase degeneracies by biasing the spin direction, enabling a magnetocorrelation effect-strong sensitivity of the correlated phases to the relative magnetization orientations (parallel or antiparallel) of the encapsulating ferromagnetic layers.

Charge Transfer and Asymmetric Coupling of MoSe2 Valleys to the Magnetic Order of CrSBr.

van der Waals heterostructures composed of two-dimensional (2D) transition metal dichalcogenides and vdW magnetic materials offer an intriguing platform to functionalize valley and excitonic properties in nonmagnetic TMDs. Here, we report magneto photoluminescence (PL) investigations of monolayer (ML) MoSe2 on the layered A-type antiferromagnetic (AFM) semiconductor CrSBr under different magnetic field orientations. Our results reveal a clear influence of the CrSBr magnetic order on the optical properties of MoSe2, such as an anomalous linear-polarization dependence, changes of the exciton/trion energies, a magnetic-field dependence of the PL intensities, and a valley g-factor with signatures of an asymmetric magnetic proximity interaction. Furthermore, first-principles calculations suggest that MoSe2/CrSBr forms a broken-gap (type-III) band alignment, facilitating charge transfer processes. The work establishes that antiferromagnetic-nonmagnetic interfaces can be used to control the valley and excitonic properties of TMDs, relevant for the development of opto-spintronics devices.

Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in Graphene/Cr_{2}Ge_{2}Te_{6}.

We investigate the twist-angle and gate dependence of the proximity exchange coupling in twisted graphene on monolayer Cr_{2}Ge_{2}Te_{6} from first principles. The proximitized Dirac band dispersions of graphene are fitted to a model Hamiltonian, yielding effective sublattice-resolved proximity-induced exchange parameters (λ_{ex}^{A} and λ_{ex}^{B}) for a series of twist angles between 0° and 30°. For aligned layers (0° twist angle), the exchange coupling of graphene is the same on both sublattices, λ_{ex}^{A}≈λ_{ex}^{B}≈4 meV, while the coupling is reversed at 30° (with λ_{ex}^{A}≈λ_{ex}^{B}≈-4 meV). Remarkably, at 19.1° the induced exchange coupling becomes antiferromagnetic: λ_{ex}^{A}<0, λ_{ex}^{B}>0. Further tuning is provided by a transverse electric field and the interlayer distance. The predicted proximity magnetization reversal and emergence of an antiferromagnetic Dirac dispersion make twisted graphene/Cr_{2}Ge_{2}Te_{6} bilayers a versatile platform for realizing topological phases and for spintronics applications.

Strain-Induced Exciton Hybridization in WS_{2} Monolayers Unveiled by Zeeman-Splitting Measurements.

Mechanical deformations and ensuing strain are routinely exploited to tune the band gap energy and to enhance the functionalities of two-dimensional crystals. In this Letter, we show that strain leads also to a strong modification of the exciton magnetic moment in WS_{2} monolayers. Zeeman-splitting measurements under magnetic fields up to 28.5 T were performed on single, one-layer-thick WS_{2} microbubbles. The strain of the bubbles causes a hybridization of k-space direct and indirect excitons resulting in a sizable decrease in the modulus of the g factor of the ground-state exciton. These findings indicate that strain may have major effects on the way the valley number of excitons can be used to process binary information in two-dimensional crystals.

Electrical Control of Valley-Zeeman Spin-Orbit-Coupling-Induced Spin Precession at Room Temperature.

The ultimate goal of spintronics is achieving electrically controlled coherent manipulation of the electron spin at room temperature to enable devices such as spin field-effect transistors. With conventional materials, coherent spin precession has been observed in the ballistic regime and at low temperatures only. However, the strong spin anisotropy and the valley character of the electronic states in 2D materials provide unique control knobs to manipulate spin precession. Here, by manipulating the anisotropic spin-orbit coupling in bilayer graphene by the proximity effect to WSe_{2}, we achieve coherent spin precession in the absence of an external magnetic field, even in the diffusive regime. Remarkably, the sign of the precessing spin polarization can be tuned by a back gate voltage and by a drift current. Our realization of a spin field-effect transistor at room temperature is a cornerstone for the implementation of energy efficient spin-based logic.

Proximity Spin-Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3.

The recently discovered two-dimensional magnetic insulator CrI3 is an intriguing case for basic research and spintronic applications since it is a ferromagnet in the bulk but an antiferromagnet in bilayer form, with its magnetic ordering amenable to external manipulations. Using the first-principles quantum transport approach, we predict that injecting unpolarized charge current parallel to the interface of the bilayer-CrI3/monolayer-TaSe2 van der Waals (vdW) heterostructure will induce spin-orbit torque and thereby drive the dynamics of magnetization on the first monolayer of CrI3 in direct contact with TaSe2. By combining the calculated complex angular dependence of spin-orbit torque with the Landau-Lifshitz-Gilbert equation for classical dynamics of magnetization, we demonstrate that current pulses can switch the direction of magnetization on the first monolayer to become parallel to that of the second monolayer, thereby converting CrI3 from antiferromagnet to ferromagnet while not requiring any external magnetic field. We explain the mechanism of this reversible current-driven nonequilibrium phase transition by showing that first monolayer of CrI3 carries current due to evanescent wave functions injected by metallic transition metal dichalcogenide TaSe2, while concurrently acquiring strong spin-orbit coupling via such a proximity effect, whereas the second monolayer of CrI3 remains insulating. The transition can be detected by passing vertical read current through the vdW heterostructure, encapsulated by a bilayer of hexagonal boron nitride and sandwiched between graphite electrodes, where we find a tunneling magnetoresistance of ≃240%.

Swapping Exchange and Spin-Orbit Coupling in 2D van der Waals Heterostructures.

The concept of swapping the two most important spin interactions-exchange and spin-orbit coupling-is proposed based on two-dimensional multilayer van der Waals heterostructures. Specifically, we show by performing realistic ab initio simulations, that a single device consisting of a bilayer graphene sandwiched by a 2D ferromagnet Cr_{2}Ge_{2}Te_{6} (CGT) and a monolayer WS_{2}, is able not only to generate, but also to swap the two interactions. The highly efficient swapping is enabled by the interplay of gate-dependent layer polarization in bilayer graphene and short-range spin-orbit and exchange proximity effects affecting only the layers in contact with the sandwiching materials. We call these structures ex-so-tic, for supplying either exchange (ex) or spin-orbit (so) coupling in a single device, by gating. Such bifunctional devices demonstrate the potential of van der Waals spintronics engineering using 2D crystal multilayers.

Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling.

We investigate an effective model of proximity modified graphene (or symmetrylike materials) with broken time-reversal symmetry. We predict the appearance of quantum anomalous Hall phases by computing bulk band gap and Chern numbers for benchmark combinations of system parameters. Allowing for staggered exchange field enables quantum anomalous Hall effect in flat graphene with Chern number C=1. We explicitly show edge states in zigzag and armchair nanoribbons and explore their localization behavior. Remarkably, the combination of staggered intrinsic spin-orbit and uniform exchange coupling gives topologically protected (unlike in time-reversal systems) pseudohelical states, whose spin is opposite in opposite zigzag edges. Rotating the magnetization from out of plane to in plane makes the system trivial, allowing us to control topological phase transitions. We also propose, using density functional theory, a material platform-graphene on Ising antiferromagnet MnPSe_{3}-to realize staggered exchange (pseudospin Zeeman) coupling.

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.

Protected Pseudohelical Edge States in Z_{2}-Trivial Proximitized Graphene.

We investigate topological properties of models that describe graphene on realistic substrates which induce proximity spin-orbit coupling in graphene. A Z_{2} phase diagram is calculated for the parameter space of (generally different) intrinsic spin-orbit coupling on the two graphene sublattices, in the presence of Rashba coupling. The most fascinating case is that of staggered intrinsic spin-orbit coupling which, despite being topologically trivial, Z_{2}=0, does exhibit edge states protected by time-reversal symmetry for zigzag ribbons as wide as micrometers. We call these states pseudohelical as their helicity is locked to the sublattice. The spin character and robustness of the pseudohelical modes is best exhibited on a finite flake, which shows that the edge states have zero g factor, carry a pure spin current in the cross section of the flake, and exhibit spin-flip reflectionless tunneling at the armchair edges.

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.

Transport Spectroscopy of Sublattice-Resolved Resonant Scattering in Hydrogen-Doped Bilayer Graphene.

We report the experimental observation of sublattice-resolved resonant scattering in bilayer graphene by performing simultaneous cryogenic atomic hydrogen doping and electron transport measurements in an ultrahigh vacuum. This allows us to monitor the hydrogen adsorption on the different sublattices of bilayer graphene without atomic-scale microscopy. Specifically, we detect two distinct resonant scattering peaks in the gate-dependent resistance, which evolve as a function of the atomic hydrogen dosage. Theoretical calculations show that one of the peaks originates from resonant scattering by hydrogen adatoms on the α sublattice (dimer site) while the other originates from hydrogen adatoms on the ß sublattice (nondimer site), thereby enabling a method for characterizing the relative sublattice occupancy via transport measurements. Utilizing this new capability, we investigate the adsorption and thermal desorption of hydrogen adatoms via controlled annealing and conclude that hydrogen adsorption on the ß sublattice is energetically favored. Through site-selective desorption from the α sublattice, we realize hydrogen doping with adatoms primarily on a single sublattice, which is highly desired for generating ferromagnetism.

Proximity Effects in Bilayer Graphene on Monolayer WSe_{2}: Field-Effect Spin Valley Locking, Spin-Orbit Valve, and Spin Transistor.

Proximity orbital and spin-orbit effects of bilayer graphene on monolayer WSe_{2} are investigated from first principles. We find that the built-in electric field induces an orbital band gap of about 10 meV in bilayer graphene. Remarkably, the proximity spin-orbit splitting for holes is 2 orders of magnitude-the spin-orbit splitting of the valence band at K is about 2 meV-more than for electrons. Effectively, holes experience spin valley locking due to the strong proximity of the lower graphene layer to WSe_{2}. However, applying an external transverse electric field of some 1 V/nm, countering the built-in field of the heterostructure, completely reverses this effect and allows, instead of holes, electrons to be spin valley locked with 2 meV spin-orbit splitting. Such a behavior constitutes a highly efficient field-effect spin-orbit valve, making bilayer graphene on WSe_{2} a potential platform for a field-effect spin transistor.

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.

Excitonic Valley Effects in Monolayer WS2 under High Magnetic Fields.

Transition-metal dichalcogenides can be easily produced as atomically thin sheets, exhibiting the possibility to optically polarize and read out the valley pseudospin of extremely stable excitonic quasiparticles present in these 2D semiconductors. Here, we investigate a monolayer of tungsten disulfide in high magnetic fields up to 30 T via photoluminescence spectroscopy at low temperatures. The valley degeneracy is lifted for all optical features, particularly for excitons, singlet and triplet trions, for which we determine the g factor separately. While the observation of a diamagnetic shift of the exciton and trion resonances gives us insight into the real-space extension of these quasiparticles, magnetic field-induced valley polarization effects shed light onto the exciton and trion dispersion relations in reciprocal space. The field dependence of the trion valley polarizations is in line with the predicted trion splitting into singlet and triplet configurations.

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.

Magnetoanisotropic Andreev reflection in ferromagnet-superconductor junctions.

Andreev reflection spectroscopy of ferromagnet-superconductor (FS) junctions [corrected] is an important probe of spin polarization. We theoretically investigate spin-polarized transport in FS junctions in the presence of Rashba and Dresselhaus interfacial spin-orbit fields and show that Andreev reflection can be controlled by changing the magnetization orientation. We predict a giant in- and out-of-plane magnetoanisotropy of the junction conductance. If the ferromagnet is highly spin polarized-in the half-metal limit-the magnetoanisotropic Andreev reflection depends universally on the spin-orbit fields only. Our results show that Andreev reflection spectroscopy can be used for sensitive probing of interfacial spin-orbit fields in a FS junction.

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.

Excitonic signatures of ferroelectric order in parallel-stacked MoS2.

Interfacial ferroelectricity, prevalent in various parallel-stacked layered materials, allows switching of out-of-plane ferroelectric order by in-plane sliding of adjacent layers. Its resilience against doping potentially enables next-generation storage and logic devices. However, studies have been limited to indirect sensing or visualization of ferroelectricity. For transition metal dichalcogenides, there is little knowledge about the influence of ferroelectric order on their intrinsic valley and excitonic properties. Here, we report direct probing of ferroelectricity in few-layer 3R-MoS2 using reflectance contrast spectroscopy. Contrary to a simple electrostatic perception, layer-hybridized excitons with out-of-plane electric dipole moment remain decoupled from ferroelectric ordering, while intralayer excitons with in-plane dipole orientation are sensitive to it. Ab initio calculations identify stacking-specific interlayer hybridization leading to this asymmetric response. Exploiting this sensitivity, we demonstrate optical readout and control of multi-state polarization with hysteretic switching in a field-effect device. Time-resolved Kerr ellipticity reveals direct correspondence between spin-valley dynamics and stacking order.

Ultraviolet interlayer excitons in bilayer WSe2.

Interlayer excitons in van der Waals heterostructures are fascinating for applications like exciton condensation, excitonic devices and moiré-induced quantum emitters. The study of these charge-transfer states has almost exclusively focused on band edges, limiting the spectral region to the near-infrared regime. Here we explore the above-gap analogues of interlayer excitons in bilayer WSe2 and identify both neutral and charged species emitting in the ultraviolet. Even though the transitions occur far above the band edge, the states remain metastable, exhibiting linewidths as narrow as 1.8 meV. These interlayer high-lying excitations have switchable dipole orientations and hence show prominent Stark splitting. The positive and negative interlayer high-lying trions exhibit significant binding energies of 20-30 meV, allowing for a broad tunability of transitions via electric fields and electrostatic doping. The Stark splitting of these trions serves as a highly accurate, built-in sensor for measuring interlayer electric field strengths, which are exceedingly difficult to quantify otherwise. Such excitonic complexes are further sensitive to the interlayer twist angle and offer opportunities to explore emergent moiré physics under electrical control. Our findings more than double the accessible energy range for applications based on interlayer excitons.