Proximity-induced spin-orbit and exchange coupling in graphene-based heterostructures

The generation of large spin currents, and the associated spin torques, which are at the heart of modern spintronics, has long been achieved by charge-to-spin conversion mechanisms, i.e., the spin Hall effect and/or the Rashba–Edelstein effect, intrinsically linked to strong spin–orbit coupling. Recently, a novel path has been predicted and observed for achieving significant current-induced torques originating from light elements, hence possessing weak spin–orbit interaction. These findings point out to the potential involvement of the orbital counterpart of electrons, namely the orbital Hall and orbital Rashba–Edelstein effects. In this study, we aim at quantifying these orbital-related contributions to the effective torques acting on a thin Co layer in different systems. First, we demonstrate in Pt|Co|Cu|AlOx stacking a comparable torque strength coming from the conversion due to the orbital Rashba–Edelstein effect at the Cu|AlOx interface and the one from the effective spin Hall effect in the bottom Pt|Co system. Second, in order to amplify the orbital-to-spin conversion, we investigate the impact of an intermediate Pt layer in Co|Pt|Cu|CuOx. From the Pt thickness dependence of the effective torques determined by harmonic Hall measurements complemented by spin Hall magneto-resistance and THz spectroscopy experiments, we demonstrate that a large orbital Rashba–Edelstein effect is present at the Cu|CuOx interface, leading to a twofold enhancement of the net torques on Co for the optimal Pt thickness. Our findings not only demonstrate the crucial role that orbital currents can play in low-dimensional systems with weak spin–orbit coupling but also reveal that they enable more energy efficient manipulation of magnetization in spintronic devices.

We develop path-integral Monte Carlo simulations for a parabolic two-dimensional (2D) quantum dot containing $N$ interacting electrons in the presence of Dresselhaus and/or Rashba spin-orbit couplings. Our method solves in a natural way the spin contamination problem and allows for numerically exact finite-temperature results at weak spin-orbit coupling. For $N<10$ electrons, we present data for the addition energy, the particle density, and the total spin $S$ in the Wigner molecule regime of strong Coulomb interactions. We identify magic numbers at N=3 and N=7 via a peak in the addition energy. These magic numbers differ both from weak-interaction and classical predictions, and are stable with respect to (weak) spin-orbit couplings.

Spin pumping has been considered a powerful tool to manipulate the spin current in a ferromagnetic/nonmagnetic (FM/NM) system, where the NM part exhibits large spin-orbit coupling (SOC). In this work, the spin pumping in β-W/Interlayer (IL)/Co2FeAl (CFA) heterostructures grown on Si(100) is systematically investigated with different ILs in which SOC strength ranges from weak to strong. We first measure the spin pumping through the enhancement of effective damping in CFA by varying the thickness of β-W. The damping enhancement in the bilayer of β-W/CFA (without IL) is found to be ∼50% larger than the Gilbert damping in a single CFA layer with a spin diffusion length and spin mixing conductance of 2.12 ± 0.27 nm and 13.17 ± 0.34 nm-2, respectively. Further, the ILs of different SOC strengths such as Al, Mg, Mo, and Ta were inserted at the β-W/CFA interface to probe their impact on damping in β-W/ILs/CFA. The effective damping reduced to 8% and 20% for Al and Mg, respectively, whereas it increased to 66% and 75% with ILs of Mo and Ta, respectively, compared to the β-W/CFA heterostructure. Thus, in the presence of ILs with weak SOC, the spin pumping at the β-W/CFA interface is suppressed, while for the high SOC ILs effective damping increased significantly from its original value of β-W/CFA bilayer using a thin IL. This is further confirmed by performing inverse spin Hall effect measurements. In summary, the transfer of spin angular momentum can be significantly enhanced by choosing a proper ultrathin interface layer. Our study provides a tool to increase the spin current production by inserting an appropriate thin interlayer which is useful in modifying the heterostructure for efficient performance in spintronics devices.

Most of the low-energy effective descriptions of spin-orbit driven Mott insulators consider spin orbit coupling (SOC) as a second order perturbation to electron-electron interactions. However, when SOC is comparable to anisotropic Hund's coupling, such as in Ir, validity of this formally weak-SOC approach is not a priori known. Depending on the relative strength of SOC and anisotropic Hund's coupling, different descriptions of the multiplet structure should be employed in the weak and strong SOC limits, \textit{viz.} \textit{LS} and \textit{jj} coupling schemes, respectively. We investigate the implications of both the coupling schemes on the low-energy effective $t-J$ model and calculate the angle resolved photoemission (ARPES) spectra using self-consistent Born approximation. In particular, we obtain the ARPES spectra of quasi-two-dimensional square-lattice iridate ${\rm Sr_2IrO_4}$ in both weak and strong SOC limits. The differences in the limiting cases are understood in terms of the composition and relative energy splittings of the multiplet structure. Our results indicate that the LS coupling scheme yields better agreement with the experiment, thus providing an indirect evidence for the validity of LS coupling scheme for iridates. We also discuss the implications for other metal ions with strong SOC.

Electronic bound states around charged impurities in two-dimensional systems with structural inversion asymmetry can be described in terms of a two-dimensional hydrogen atom in the presence of a Rashba spin-orbit interaction. Here, the energy levels of the bound electron are evaluated numerically as a function of the spin-orbit interaction, and analytic expressions for the weak and strong spin-orbit coupling limits are compared with the numerical results. It is found that, besides the level splitting due to the lack of inversion symmetry, the energy levels are lowered for sufficiently strong spin-orbit coupling, indicating that the electron gets more tightly bound to the ion as the spin-orbit interaction increases. Similarities and differences with respect to the two-dimensional Fr\"ohlich polaron with the Rashba coupling are discussed.

The two-dimensional electron systems in graphene and in topological insulators are described by massless Dirac equations. Although the two systems have similar Hamiltonians, they are polar opposites in terms of spin-orbit coupling strength. We briefly review the status of efforts to achieve long spin-relaxation times in graphene with its weak spin-orbit coupling, and to achieve large current-induced spin polarizations in topological-insulator surface states that have strong spin-orbit coupling. We also comment on differences between the magnetic responses and dilute-moment coupling properties of the two systems, and on the pseudospin analogue of giant magnetoresistance in bilayer graphene.

Spin-orbit coupling (SOC) is the key to realizing time-reversal-invariant topological phases of matter1,2. SOC was predicted by Kane and Mele3 to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene4-7 has precluded experimental observation in this material. Here we exploit a layer-selective proximity effect-achieved via a van der Waals contact with a semiconducting transition-metal dichalcogenide8-21-to engineer Kane-Mele SOC in ultra clean bilayer graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find that SOC leads to the formation of a distinct, incompressible, gapped phase at charge neutrality. The experimental data agree quantitatively with a simple theoretical model in which the new phase results from SOC-driven band inversion. In contrast to Kane-Mele SOC in monolayer graphene, the inverted phase is not expected to be a time-reversal-invariant topological insulator, despite being separated from conventional band insulators by electric-field-tuned phase transitions where crystal symmetry mandates that the bulk gap must close22. Our electrical transport measurements reveal that the inverted phase has a conductivity of approximately e2/h (where e is the electron charge and h Planck's constant), which is suppressed by exceptionally small in-plane magnetic fields. The high conductivity and anomalous magnetoresistance are consistent with theoretical models that predict helical edge states within the inverted phase that are protected from backscattering by an emergent spin symmetry that remains robust even for large Rashba SOC. Our results pave the way for proximity engineering of strong topological insulators as well as correlated quantum phases in the strong spin-orbit regime in graphene heterostructures.

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 abinitio-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.

The spin Hall effect (SHE) is closely related to the spin-orbit coupling. Therefore, heavy metals are usually considered as materials of choice to obtain large spin Hall angles. Among these materials, some 5d transition metals such as Pt, Ta or W offer the largest spin-charge interconversion efficiency for spin current detections through the inverse spin Hall effect or to obtain efficient current induced magnetization switching in SOT-MRAM devices [1].Despite a weaker spin orbit coupling, spin Hall angles comparable to that of the best 5d materials has also been obtained in 3d ferromagnetic metals such as Co [2] or Ni [3]. More recently nonmagnetic alloys containing Nickel atoms such as NiCu [4] and CoNiB [5] attracted great interest for their large spin Hall angles and their potential for spintronic applications. Using the spin pumping by ferromagnetic resonance technique we could compare the spin to charge current conversion in Ni60Cu40 to the one of Pt. As can be seen in figure 1 a) the normalized spin pumping signal obtained in CFB/NiCu is comparable to that of CFB/Pt. We performed a thickness dependence shown in figure 1 b) to extract the spin Hall angle (θSHE) and spin diffusion length (λs) and obtained results comparable to the one of 5d metals using similar method with λs = 2.4 ± 0.3 nm and θSHE = 4.1 ± 0.5 % [6].Keller and coworkers [4] noticed similarities in the bandstructure of paramagnetic Nickel and Platinum possibly explaining the origin of the effect. The calculated band structure of ferromagnetic Nickel does not resemble that of Platinum and the origin of the large spin Hall effect observed in ferromagnetic Ni [3] could thus be different. The interplay between the spin-orbit coupling and magnetism is known to be at the origin of specific transport properties such as the anomalous magnetoresistance and the anomalous Hall effect. However, the link between the SHE and the magnetic order is complex and still unexplored [7].In order to study the effect of the phase transition we performed spin pumping as a function of temperature in Ni60Cu40 and Ni50Cu50 alloys above and below the Curie temperature. To avoid direct contact between the ferromagnetic spin injector CFB and the magnetic NiCu alloy that would modify CFB resonance properties due to the direct coupling [8] we used a 5 nm thick Cu interlayer. The spin pumping measurements performed in CFB\Cu\ Ni60Cu40 and CFB\Cu\ Ni50Cu50 shown in figure 2 indicate that in NiCu the SHE is insensitive to the magnetic order [6].A large variety of alloys composed of Ni, Co or Fe in the ferromagnetic or paramagnetic phase could be explored as spin current generators and detectors, extending the number of possible light metal systems with a large SHE. In particular, the large spin Hall effect in NiCu shows that it is a promising alternative to obtain large spin orbit torque without heavy metals. **

A hybrid cladding ring-core photonic crystal fiber (PCF) for transmitting orbital angular momentum (OAM) modes is proposed, which breaks the circular symmetry of the fiber structure to suppress the spin–orbit coupling and promotes bending resistance. Through the optimization of fiber structure parameters, the designed fiber can support 22 OAM modes (6 OAM mode groups) over a 200-nm wide bandwidth (covering the whole C + L band) with large effective refractive index separation between adjacent modes (&gt;10−4) and mode groups (&gt;3.6 × 10−3), low confinement losses (&lt;3.5 × 10−9 dB/m), and high mode purity (&gt;98.3%). Meanwhile, the phase of the OAM modes varies periodically and uniformly with an increase in the azimuth angle, and the polarization of OAM modes maintain nearly circular polarization in the designed fiber, which also demonstrates that the fiber has weak spin–orbit coupling. Moreover, the confinement losses of all vector modes are less than 10−7 dB/m when the bending radius is larger than 0.8 mm, indicating strong bending resistance. Furthermore, the fiber also exhibits large differential group delay, relatively low and flat dispersion, and low nonlinear coefficients (&lt;2.0 W−1/km). Therefore, the novel fiber structure has great potential in the application of mode division multiplexing (MDM) based on OAM modes.

Complex oxide heterointerfaces provide a platform to manipulate spin-orbit coupling under the broken inversion symmetry. Moreover, their weak antilocalization (WAL) effect displays quantum coherent behavior due to the strong spin-orbit coupling. Herein, we break through the limitation of lattice mismatch at ReAlO3/STO (Re = La, Pr, Nd, Sm, and Gd) heterointerfaces and obtain their two-dimensional electric gas (2DEG) by spin coating. The effect of different Re elements in the resulting quantum corrections on the conductivity is investigated. It is observed that the conductivity of heterointerfaces is reduced with larger atomic numbers due to the ionization potential of Re elements. Moreover, magnetoresistance (MR) measurements in a perpendicular or a parallel field distinctly uncover strong Rashba spin-orbit coupling (SOC) in ReAO/STO samples besides SAO/STO (Re = Sm) and GAO/STO (Re = Gd), and the effective fields of the SOC (Hso) gradually increase from LAO/STO (Re = La, Hso = 0.82 T) to NAO/STO (Re = Nd, Hso = 1.37 T) at 2 K. The competition between SOC scattering and inelastic scattering is revealed through a temperature-dependence study of MR, and the WAL-weak localization transition is at about 6 K. Furthermore, unambiguous results of the Kondo effect, nonlinear Hall, hysteresis loop, and Rashba SOC suggest the coexistence of WAL at the PAO/STO (Re = Pr) heterointerface with exchange coupling between the localized magnetic moment and the itinerant electron. These results pave a unique route for the exploration of spin-polarized 2DEGs at oxide heterointerfaces.

We explore the possibility of attaining valley-dependent tunnelling and confinement using proximity-induced spin-orbit couplings (SOCs) in graphene-based heterostructures. We consider gate-tunable asymmetric quantum dots (AQDs) on graphene heterostructures and exhibiting a C3v and/or C6v symmetry. By employing a tight-binding model, we explicitly reveal a pure valley confinement and valley signal in AQDs by streaming the valley local density, leading to valley-charge separation in real space. The confinement of the valley quasi-bound states is sensitive to the locally induced SOCs and to the spatial distribution of the induced AQDs; it is also robust against on-site disorder. The adopted process of attaining a pure valley-Hall conductivity and confinement with zero charge currents is expected to provide more options towards valley-dependent electron optics.

Molecular semiconductor (MSC) is a promising candidate for spintronic applications benefiting from its long spin lifetime caused by light elemental-composition essence and thus weak spin-orbit coupling (SOC). According to current knowledge, the SOC effect, normally dominated by the elemental composition, is the main spin-relaxation causation in MSCs, and thus the molecular structure-induced SOC change is one of the most concerned issues. In theoretical study, molecular isomerism, a most prototype phenomenon, has long been considered to possess little difference on spin transport previously, since elemental compositions of isomers are totally the same. However, here in this study, quite different spin-transport performances are demonstrated in ITIC and its structural isomers BDTIC experimentally, for the first time, though the charge transport and molecular stacking of the two films are very similar. By further experiments of electron-paramagnetic resonance and density-functional-theory calculations, it is revealed that noncovalent-conformational locks (NCLs) formed in BDTIC can lead to enhancement of SOC and thus decrease the spin lifetime. Hence, this study suggests the influences from the structural-isomeric effect must be considered for developing highly efficient spin-transport MSCs, which also provides a reliable theoretical basis for solving the great challenge of quantificational measurement of NCLs in films in the future.

Dirac point in two-dimensional (2D) materials has been a fascinating subject of research. Recently, it has been theoretically predicted that Dirac point may also be stabilized in 2D magnetic systems. However, it remains a challenge to identify concrete 2D materials which host such magnetic Dirac point. Here, based on first-principles calculations and theoretical analysis, we propose a stable 2D material, the monolayers TaCoTe$_2$, as an antiferromagnetic (AFM) 2D Dirac material. We show that it has an AFM ground state with an out-of-plane N\'{e}el vector. It hosts a pair of 2D AFM Dirac points on the Fermi level in the absence of spin-orbit coupling (SOC). When the SOC is considered, a small gap is opened at the original Dirac points. Meanwhile, another pair of Dirac points appear on the Brillouin zone boundary below the Fermi level, which are robust under SOC and have a type-II dispersion. Such a type-II AFM Dirac point has not been observed before. We further show that the location of this Dirac point as well as its dispersion type can be controlled by tuning the N\'{e}el vector orientation.

In recent years, spin-based technologies, in which particle spin is utilized for information processing, have become promising for “beyond-CMOS” solid-state devices. Graphene and other layered materials have rapidly established themselves as intriguing building blocks for spintronics applications [1]. Because of the graphene intrinsic low spin-orbit interaction, spins can flow snugly through its crystal lattice over long distances, resulting in an ideal spin communication channel. At the same time, the graphene’s low spin-orbit interaction inhibits spin manipulation, which is the cornerstone for successfully implementing spin-based devices. Nevertheless, this bottleneck can be overcome by combing graphene with other layered materials in artificial van der Waals heterostructures. In this talk, I will present a set of experiments where we study the spin-relaxation in graphene-transition metal dichalcogenides heterostructures [2]. In such engineered van der Waals systems, spin-orbit coupling in graphene is enhanced by proximity-induced effects. As a consequence, the spin dynamics becomes anisotropic [2, 3], with a spin relaxation that depends on the spin orientation. Interestingly, these systems can be also exploited for efficient spin-charge interconversion driven by the spin Hall effect and the inverse spin galvanic effect at room temperature, with conversion efficiencies tailored by electrostatic gating [4].