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A promising approach to attain long-distance coherent spin propagation is accessing topological spin-polarized edge states in graphene. Achieving this without external magnetic fields necessitates engineering graphene band structure, obtainable through proximity effects in van der Waals heterostructures. In particular, proximity-induced staggered potentials and spin-orbit coupling are expected to form a topological bulk gap in graphene with gapless helical edge states that are robust against disorder. In this work, we detect the spin-polarized helical edge transport in graphene at zero external magnetic field, allowed by the proximity of an interlayer antiferromagnet, CrPS$_4$. We show the coexistence of the quantum spin Hall (QSH) states and magnetism in graphene, where the induced spin-orbit and exchange couplings also give rise to a large anomalous Hall (AH) effect. The detection of the QSH states at zero external magnetic field, together with the AH signal that persists up to room temperature, opens the route for practical applications of magnetic graphene in quantum spintronic circuitries.

Crystallographic anisotropy of the spin-dependent conductivity tensor can be exploited to generate transverse spin-polarized current in a ferromagnetic film. This ferromagnetic spin Hall effect is analogous to the spin-splitting effect in altermagnets and does not require spin-orbit coupling. First-principles screening of 41 non-cubic ferromagnets revealed that many of them, when grown as a single crystal with tilted crystallographic axes, can exhibit large spin Hall angles comparable with the best available spin-orbit-driven spin Hall sources. Macroscopic spin Hall effect is possible for uniformly magnetized ferromagnetic films grown on some low-symmetry substrates with epitaxial relations that prevent cancellation of contributions from different orientation domains. Macroscopic response is also possible for any substrate if magnetocrystalline anisotropy is strong enough to lock the magnetization to the crystallographic axes in different orientation domains., Comment: 10 pages, 2 tables

The efficient generation of spin currents and spin torques via spin-orbit coupling is an important goal of spintronics research. One crucial metric for spin current generation is the spin Hall angle, which is the ratio of the spin Hall current to the transversely flowing charge current. A typical approach to measure the spin Hall angle in nonmagnetic materials is to generate spin currents via spin pumping in an adjacent ferromagnetic layer and measure the transverse voltage from the inverse spin Hall effect in the nonmagnetic layer. However, given that the spin Hall effect also occurs in ferromagnets, single ferromagnetic layers could generate a self-induced transverse voltage during spin pumping as well. Here we show that manganite based La$_{0.67}$Sr$_{0.33}$MnO$_{3}$ (LSMO) films deposited by pulsed laser deposition exhibit a significant self-induced inverse spin Hall voltage while undergoing spin pumping. We observe efficient spin to charge conversion in the LSMO films via the inverse spin Hall effect. A spin pumping voltage of 1.86 $\mu$V is observed in the LSMO (12 nm) film. Using density functional theory and the Kubo formalism, we calculate the intrinsic spin current conductivities of these films and show that they are in reasonable agreement with the experimental measurements.

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir\'e twisted bilayers with time-reversal symmetry and spin $s_z$ conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles, the emergent moir\'e flatbands can be topologically nontrivial due to inversion symmetry breaking. Each of these flatbands for each spin projection admits a lowest-Landau-level description in the chiral limit and at magic twist angle. This allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.

The substantial amount of recent research into spin torques has been accompanied by a revival of interest in the spin-Hall effect. This effect contributes to the spin torque in many materials, including topological insulator/ferromagnet devices, Weyl semimetals, and van der Waals heterostructures. In general the relative sizes of competing spin torque mechanisms remain poorly understood. Whereas a consensus is beginning to emerge on the evaluation of a conserved spin current, the role of extrinsic disorder mechanisms in the spin-Hall effect has not been clarified. In this work we present a comprehensive calculation of the extrinsic spin Hall effect while focussing on the bulk states of topological insulators as a prototype system and employing a fully quantum mechanical formalism to calculate the proper spin current. Our calculation of the proper spin current employs a 4x4 k.p Hamiltonian describing the bulk states of topological insulators. At the same time, we provide a qualitative explanation of the proper spin currents calculated based on an effective $2\times2$ Hamiltonian obtained via a Schrieffer-Wolf transformation. We find that the extrinsic contribution to the proper spin current, driven by side jump, skew scattering and related mechanisms, is of a comparable magnitude to the intrinsic contribution, making it vital to take such disorder effects into account when seeking to understand experiments. Among the scattering effects considered, side jump scattering is the primary contributor to the extrinsic spin Hall effect. The total spin susceptibility calculated here is too small to explain experimentally measured spin torques, hence we expect the spin Hall effect to make a negligible contribution to the spin torque in topological insulator structures.

The spin phenomena observed at a clean metall-insulator interface are typically reduced to Rashba-Edelstein effect, that leads to spin accumulation over a few monolayers. We demonstrate that the presence of interface disorder significantly expands the range of potential phenomena. Specifically, the skew scattering at the metal - insulator boundary gives rise to the "kinetic Rashba-Edelstein effect", where spin accumulation occurs on a much larger length scale comparable to mean free path. Moreover, at higher orders of spin-orbit interaction, skew scattering is accompanied with spin relaxation resulting in the interface spin-Hall effect - a conversion of electrical current to spin current at the metal surface. Unlike the conventional spin-Hall effect, this phenomenon persists even within the Born approximation. These two predicted phenomena can dominate the spin density and spin current in devices of intermediate thickness., Comment: Accepted in Phys. Rev. Research

The search for superconducting systems exhibiting nonreciprocal transport and, specifically, the diode effect, has proliferated in recent years. This trend encompasses a wide variety of systems, including planar hybrid structures, asymmetric SQUIDs, and certain noncentrosymmetric superconductors. A common feature of such systems is a gyrotropic symmetry, realized on different scales and characterized by a polar vector. Alongside time-reversal symmetry breaking, the presence of a polar axis allows for magnetoelectric effects, which, when combined with proximity-induced superconductivity, results in spontaneous non-dissipative currents that underpin the superconducting diode effect. This symmetry established, we present a comprehensive theoretical study of transport in a lateral Josephson junctions composed of a normal metal supporting the spin Hall effect, and attached to a ferromagnetic insulator. Due to the presence of the latter, magnetoelectric effects arise without requiring external magnetic fields. We determine the dependence of the anomalous current on the spin relaxation length and the transport parameters commonly used in spintronics to characterize the interface between the metal and the ferromagnetic insulator. Therefore, our theory naturally unifies nonreciprocal transport in superconducting systems with classical spintronic effects, such as the spin Hall effect, spin galvanic effect, and spin Hall magnetoresistance. We propose an experiment involving measurements of magnetoresistance in the normal state and nonreciprocal transport in the superconducting state. Such experiment, on the one hand, allows for determining the parameters of the model and thus verifying with a greater precision the theories of magnetoelectric effects in normal systems. On the other hand, it contributes to a deeper understanding of the underlying microscopic origins that determine these parameters., Comment: 14 pages, 9 figures

Physical properties such as the conductivity are usually classified according to the symmetry of the underlying system using Neumann's principle, which gives an upper bound for the number of independent components of the corresponding property tensor. However, for a given Hamiltonian, this global approach usually can not give a definite answer on whether a physical effect such as spin Hall effect (SHE) exists or not. It is found that the parity and types of spin-orbit interactions (SOIs) are good indicators that can further reduce the number of independent components of the spin Hall conductivity for a specific system. In terms of the parity as well as various Rashba-like and Dresselhaus-like SOIs, we propose a local approach to classify SHE in two-dimensional (2D) two-band models, where sufficient conditions for identifying the existence or absence of SHE in all 2D magnetic point groups are presented.

Generating a pure spin current using electrons, which have degrees of freedom beyond spin, such as electric charge and valley index, presents challenges. In response, we propose a novel mechanism based on intervalley exciton dynamics in {\em arc-shaped} strained transition metal dichalcogenides (TMDs) to achieve the {\em exciton spin Hall effect} in an electrically insulating regime, without the need for an external electric field. The interplay between strain gradients and strain-induced pseudomagnetic fields results in a net Lorentz force on long-lived intervalley excitons in WSe$_2$, carrying non-zero spin angular momentum. This process generates an exciton-mediated pure spin Hall current, resulting in opposite-sign spin accumulations and local magnetization on the two sides of the single-layer arc-shaped TMD. We demonstrate that the magnetic field induced by spin accumulation, at approximately $\sim {\rm mT}$, can be detected using techniques such as superconducting quantum interference magnetometry or spatially-resolved magneto-optical Faraday and Kerr rotations.

We present a spin-induced none-geodesic effect of Dirac wave packets in a static uniform gravitational field. Our approach is based on the Foldy-Wouthuysen transformation of Dirac equation in a curved spacetime, which predicts the gravitational spin-orbit coupling. Due to this coupling, we find that the dynamics of the free-fall Dirac wave packets with opposite spin polarization will yield the transverse splitting in the direction perpendicular to spin orientation and gravity, which is known as the gravitational spin Hall effect. Even in a static uniform gravitational field, such effect suggests that the weak equivalence principle is violated for quantum particles., Comment: 6 pages, 1 PDF figure

We present a prediction of chiral topological metals with several classes of unconventional quasiparticle fermions in a family of SrGePt-type materials in terms of first-principles calculations. In these materials, fourfold spin-3/2 Rarita-Schwinger-Weyl (RSW) fermion, sixfold excitation, and Weyl fermions coexist around the Fermi level as spin-orbit coupling is considered, and the Chern number for the first two kinds of fermions is the maximal value four. We found that large Fermi arcs from spin-3/2 RSW fermion emerge on the (010)-surface, spanning the whole surface Brillouin zone. Moreover, there exist Fermi arcs originating from Weyl points, which further overlap with trivial bulk bands. In addition, we revealed that the large spin Hall conductivity can be obtained, which attributed to the remarkable spin Berry curvature around the degenerate nodes and band-splitting induced by spin-orbit coupling. Our findings indicate that the SrGePt family of compounds provide an excellent platform for studying on topological electronic states and the intrinsic spin Hall effect., Comment: 10 pages and 7 figures in the main text

The spin-to-charge current interconversion in bilayers composed of ferromagnetic and nonmagnetic layers with strong spin-orbit coupling has garnered considerable attention due to its exceptional potential in advancing spintronics devices for data storage and logic applications. Platinum (Pt) stands out as one of the most effective materials for generating spin current. While the spin conversion efficiency is isotropic in polycrystalline Pt samples, an ongoing debate persists regarding its dependence on the crystalline direction in single crystalline samples. In this study, we aim to comprehensively evaluate the in-plane anisotropy of spin-charge interconversion using an array of complementary Spin Hall and inverse Spin Hall techniques with both incoherent and coherent excitation. Specifically, we investigate the spin-to-charge interconversion in epitaxial, (111)-oriented, Co/Pt bilayers with low surface roughness, as resulted from x-ray experiments. By varying the thickness of the Pt layer, we gain insights into the spin-charge interconversion in epitaxial Pt and highlight the effects of the interfaces. Our results demonstrate an isotropic behavior within the limits of our detection uncertainty. This finding significantly enhances our understanding of spin conversion in one of the most relevant systems in spintronics and paves the way for future research in this field., Comment: Article accepted for publication in Physical Review Materials, DOI not received yet

The spin Hall effect in nonmagnetic materials has been intensively studied and became one of the most crucial spin-charge conversion mechanism in spintronics. However, the spin Hall effect in ferromagnetic metals has been less investigated and remains unclear. In this work, we investigate the spin Hall effect in representative ferromagnetic alloy by using first-principles calculations. We first clarify the spin Hall effect into three different types including conventional (CSHE), spin anomalous (SAHE) and magnetic spin Hall effect (MSHE) and then calculate the corresponding spin Hall conductivity and spin Hall angle for (Fe, Co, Ni)Pt, NiFe and CoFe alloy. We find the above three spin Hall mechanisms do coexist in ferromagnetic metals. Particularly, for Pt-based ferromagnetic alloy, a sizable conventional and magnetic spin Hall angles comparable to that of Pt have been predicted. The remarkable unconventional spin Hall effect in ferromagnetic metal may enrich the spin-charge conversion phenomena. For instance, the spin current generated by remarkable MSHE with out-of-plane spin-polarization should be helpful for field-free switching of perpendicular magnetization through spin-orbit torque effect. This work may stimulate future studies on the spin Hall effect in ferromagnetic metals and pave their promising applications for spin-charge conversion devices in spintronics.

We study the intrinsic spin Hall effect of a Dirac Hamiltonian system with ferromagnetic exchange coupling, a minimal model combining relativistic spin-orbit interaction and ferromagnetism. The energy bands of the Dirac Hamiltonian are split after introducing a Stoner-type ferromagnetic ordering which breaks the spherical symmetry of pristine Dirac model. The totally antisymmetric spin Hall conductivity (SHC) tensor becomes axially anisotropic along the direction of external electric field. Interestingly, the anisotropy does not vanish in the asymptotic limit of zero magnetization. We show that the ferromagnetic ordering breaks the spin degeneracy of the eigenfunctions and modifies the selection rules of the interband transitions for the intrinsic spin Hall effect. The difference in the selection rule between the pristine and the ferromagnetic Dirac phases causes the anisotropy of the SHC, resulting in a discontinuity of the SHC as the magnetization, directed orthogonal to the electric field, is reduced to zero in the ferromagnetic Dirac phase and enters the pristine Dirac phase., Comment: 12 pages, 5 figure

We systematically derive the chiral kinetic theory for chiral fermions with collisions, including the self-energy corrections, from quantum field theories. We find that the Wigner functions and chiral kinetic equations receive both the classical and quantum corrections from the self-energies and their spacetime gradients. We also apply this formalism to study nonequilibrium neutrino transport due to the interaction with thermalized electrons and nucleons, as realized in core-collapse supernovae. We derive neutrino currents along magnetic fields and neutrino spin Hall effect induced by the density gradient at first order in the Fermi constant $G_{\rm F}$ for anisotropic neutrino distributions., Comment: 24 pages, 1 figure, minor errors corrected, published version

The impurity incorporation in host high-spin orbit coupling materials like platinum has shown improved charge-to-spin conversion by modifying the up-spin and down-spin electron trajectories by bending or skewing them in opposite directions. This enables efficient generation, manipulation, and transport of spin currents. In this study, we irradiate the platinum with non-focus dense plasma to incorporate the oxygen ion species. We systematically analyze the spin Hall angle of the oxygen plasma irradiated Pt films using spin torque ferromagnetic resonance. Our results demonstrate a 2.4 times enhancement in the spin Hall effect after plasma treatment of Pt as compared to pristine Pt. This improvement is attributed to the introduction of disorder and defects in the Pt lattice, which enhances the spin-orbit coupling and leads to more efficient charge-to-spin conversion without breaking the spin-orbit torque symmetries. Our findings offer a new method of dense plasma-based modification of material for the development of advanced spintronic devices based on Pt and other heavy metals.

Kagome metals are topological materials with a rich phase diagram featuring various charge density wave orders and even unconventional superconductivity. However, little is still known about possible spin-polarized responses in these non-magnetic compounds. Here, we perform ab-initio calculations of the intrinsic spin Hall effect (SHE) in the kagome metals AV$_3$Sb$_5$ (A=Cs, Rb, K), CsTi$_3$Bi$_5$ and ScV$_6$Sn$_6$. We report large spin Hall conductivities, comparable with the Weyl semimetal TaAs. Additionally, in CsV$_3$Sb$_5$ the SHE is strongly renormalized by the CDW order. We can understand these results based on the topological properties of band structures, demonstrating that the SHE is dominated by the position and shape of the Dirac nodal lines in the kagome sublattice. Our results suggest kagome materials as a promising, tunable platform for future spintronics applications., Comment: 6+2 pages, 7 figures

Driven by various physical origins, the interesting reentrant phenomena in quantum Hall effect (QHE), quantum anomalous Hall effect (QAHE) and non-Hermitian systems have been discussed recently. Here, we present that the reentrant phenomena of quantum spin Hall effect (QSHE) can be achieved by introducing a uniform exchange field into a topological insulator with a four-band model Hamiltonian. Furthermore, it is found that both time-reversal (TR) symmetry broken QSHE and spin-polarized QAHE can simultaneously be generated in the system with proper exchange field strength by inspecting the corresponding edge states. Through analyzing the energy dependent spin-Chern number $\nu_s$ and transmission in the presence of random disorders, we verify the topological protection and the robustness of induced QSHE and QAHE. Finally, the theoretical realization of reentrant QSHE in a topolectrical circuit is demonstrated. Our work not only extends the reentrant phenomena into the QSHE but also stimulates interest in their realization in different systems., Comment: 4 figures

Graphene is a light material for long-distance spin transport due to its low spin-orbit coupling, which at the same time is the main drawback to exhibit a sizeable spin Hall effect. Decoration by light atoms has been predicted to enhance the spin Hall angle in graphene while retaining a long spin diffusion length. Here, we combine a light metal oxide (oxidized Cu) with graphene to induce the spin Hall effect. Its efficiency, given by the product of the spin Hall angle and the spin diffusion length, can be tuned with the Fermi level position, exhibiting a maximum (1.8 $\pm$ 0.6 nm at 100 K) around the charge neutrality point. This all-light-element heterostructure shows a larger efficiency than conventional spin Hall materials. The gate-tunable spin Hall effect is observed up to room temperature. Our experimental demonstration provides an efficient spin-to-charge conversion system free from heavy metals and compatible with large-scale fabrication., Comment: 15 pages, 4 figures, and Supporting Information. Minor typos corrected in this version. Funding information: Marie Sklodowska-Curie Actions, H2020-MSCA-ITN-2020; Project Acronym SPEAR; Grant Agreement No. 955671

The spin Hall effect (SHE) can generate a pure spin current by an electric current, which is promisingly used to electrically control magnetization. To reduce power consumption of this control, a giant spin Hall angle (SHA) in the SHE is desired in low-resistivity systems for practical applications. Here, critical spin fluctuation near the antiferromagnetic (AFM) phase-transition is proved as an effective mechanism to create an additional part of SHE, named as fluctuation spin Hall effect (FSHE). This FSHE enhances the SHA due to the AFM spin fluctuation between conduction electrons and local spins. We detect the FSHE with the inverse and direct spin Hall effect (ISHE and DSHE) set-up and their temperature (T) dependences in the Cr/MgO/Fe magnetic tunnel junctions (MTJs). The SHA is significantly enhanced when temperature is approached to the N\'eel temperature (T_N) and has a peak value of -0.34 at 200 K near T_N. This value is higher than the room-temperature value by 240% and comparable to that of heavy metals Ta and W. Furthermore, the spin Hall resistivity of Cr well fits the modeled T-dependence when T approaches T_N from low temperatures, implying the AFM spin fluctuation nature of strong SHA enhancement. Thus, this study demonstrates the critical spin fluctuation as a prospective way of increasing SHA and enriches the AFM material candidates for spin-orbitronic devices., Comment: 27 pages, 9 figures

Spin Hall effect of spin-texture origin is explored theoretically for antiferromagnetic (AF) metals. It is found that a vector chirality formed by the N\'eel vector gives rise to a topological spin Hall effect. This is topological since it is proportional to the winding number counted by in-plane vector chirality along the sample edge, which can be nonvanishing for AF merons but not for AF skyrmions. The effect is enhanced when the Fermi level lies near the AF gap, and, surprisingly, at weak coupling with small AF gap. These features are confirmed numerically based on the Landauer-B\"uttiker formula. Important roles played by nonadiabatic processes and spin dephasing are pointed out., Comment: 16 pages, 11 figures

Electron hydrodynamics is currently known to emerge only when electron-electron interaction dominates over the momentum-nonconserving scatterings of electrons, where the electron transport is described by a hydrodynamic equation. Here we show that electron transport in electron systems with the spin Hall effect is also given by the hydrodynamic equation, whose kinetic viscosity is determined by the spin diffusion length and the transport lifetime. The electric current vorticity is proportional to the spin accumulation due to the spin Hall effect in two-dimensional systems. We demonstrate by solving the hydrodynamic equation in a two-dimensional system with a cavity, combined with micromagnetic simulation for an attached chiral magnetic insulator, that the spin accumulated near the boundary of the cavity creates a magnetic skyrmion. Our findings and demonstration shed light on a novel aspect of electron hydrodynamics and spin transport., Comment: 6 pages, 4 figures

The spin Hall (SH) effect, the conversion of the electric current to the spin current along the transverse direction, relies on the relativistic spin-orbit coupling (SOC). Here, we develop a microscopic theory on the mechanisms of the SH effect in magnetic metals, where itinerant electrons are coupled with localized magnetic moments via the Hund exchange interaction and the SOC. Both antiferromagnetic metals and ferromagnetic metals are considered. It is shown that the SH conductivity can be significantly enhanced by the spin fluctuation when approaching the magnetic transition temperature of both cases. For antiferromagnetic metals, the pure SH effect appears in the entire temperature range, while for ferromagnetic metals, the pure SH effect is expected to be replaced by the anomalous Hall effect below the transition temperature. We discuss possible experimental realizations and the effect of the quantum criticality when the antiferromagnetic transition temperature is tuned to zero temperature., Comment: Main text 10 pages 7 figures, supplementary material 12 pages 2 figures

Binary neural networks (BNNs) have shown an immense promise for resource-constrained edge artificial intelligence (AI) platforms as their binarized weights and inputs can significantly reduce the compute, storage and communication costs. Several works have explored XNOR-based BNNs using SRAMs and nonvolatile memories (NVMs). However, these designs typically need two bit-cells to encode signed weights leading to an area overhead. In this paper, we address this issue by proposing a compact and low power in-memory computing (IMC) of XNOR-based dot products featuring signed weight encoding in a single bit-cell. Our approach utilizes valley-spin Hall (VSH) effect in monolayer tungsten di-selenide to design an XNOR bit-cell (named 'XNOR-VSH') with differential storage and access-transistor-less topology. We co-optimize the proposed VSH device and a memory array to enable robust in-memory dot product computations between signed binary inputs and signed binary weights with sense margin (SM) > 1 micro-amps. Our results show that the proposed XNOR-VSH array achieves 4.8% ~ 9.0% and 37% ~ 63% lower IMC latency and energy, respectively, with 4 % ~ 64% smaller area compared to spin-transfer-torque (STT)-MRAM and spin-orbit-torque (SOT)-MRAM based XNOR-arrays.

When a spin-splitting field is introduced to a thin film superconductor, the spin currents polarized along the field couples to energy currents that can only decay via inelastic scattering. We study spin and energy injection into such a superconductor where spin-orbit impurity scattering yields inverse spin-Hall and spin-swapping currents. We show that the combined presence of a spin-splitting field, superconductivity, and inelastic scattering gives rise to a strong enhancement of the ordinary inverse spin-Hall effect, as well as unique inverse spin-Hall and spin-swapping signals orders of magnitude stronger than the ordinary inverse spin-Hall signal. These can be completely controlled by the orientation of the spin-splitting field, resulting in a long-range charge and spin accumulations detectable much further from the injector than in the normal-state. While the enhanced inverse spin-Hall signals offer a major improvement in spin detection sensitivity, the unique spin-swap signals can be utilized for designing devices where both the spin and current directions are controlled and altered throughout the geometry., Comment: Main text: 6 pages, 3 figures. Supplemental material: 12 pages, 2 figures

We theoretically study the spin Hall effect in a simple tight-binding model of stacked-kagome Weyl semimetal Co3Sn2S2 with ferromagnetic ordering. We focus on the two types of the spin Hall current: one flowing in the in-plane direction with respect to the kagome lattice (in-plane spin Hall current), and one flowing in the stacking direction (out-of-plane spin Hall current). We show the spin Hall conductivities for those spin currents drastically change depending on the direction of the magnetic moment. Especially, the out-of-plane spin Hall current may induce surface spin accumulation, which are useful for the perpendicular magnetization switching via spin-orbit torque., Comment: 8 pages, 5 figures

The spin Hall effect (SHE), in which electrical current generates transverse spin current, plays an important role in spintronics for the generation and manipulation of spin-polarized electrons. The phenomenon originates from spin-orbit coupling. In general, stronger spin-orbit coupling favors larger SHEs but shorter spin relaxation times and diffusion lengths. To achieve both large SHEs and long-range spin transport in a single material has remained a challenge. Here we demonstrate a giant intrinsic SHE in AB-stacked MoTe2/WSe2 moir\'e bilayers by direct magneto optical imaging. Under moderate electrical currents with density < 1 A/m, we observe spin accumulation on transverse sample edges that nearly saturates the spin density. We also demonstrate long-range spin Hall transport and efficient non-local spin accumulation limited only by the device size (about 10 um). The gate dependence shows that the giant SHE occurs only near the Chern insulating state, and at low temperatures, it emerges after the quantum anomalous Hall breakdown. Our results demonstrate moir\'e engineering of Berry curvature and large SHEs for potential spintronics applications.

We demonstrate a magnetic tunnel junction injected with spin Hall current to exhibit linear rotation of magnetization of the free-ferromagnet using only the spin current. Using the linear resistance change of the MTJ, we devise a circuit for the rectified linear activation (ReLU) function of the artificial neuron. We explore the role of different spin Hall effect (SHE) heavy metal layers on the power consumption of the ReLU circuit. We benchmark the power consumption of the ReLU circuit with different SHE layers by defining a new parameter called the spin Hall power factor. It combines the spin Hall angle, resistivity, and thickness of the heavy metal layer, which translates to the power consumption of the different SHE layers during spin-orbit switching/rotation of the free FM. We employ a hybrid spintronics-CMOS simulation framework that couples Keldysh non-equilibrium Green's function formalism with Landau-Lifshitz-Gilbert-Slonzewski equations and the HSPICE circuit simulator to account for diverse physics of spin-transport and the CMOS elements in our proposed ReLU design. We also demonstrate the robustness of the proposed ReLU circuit against thermal noise and non-trivial power-error trade-off that enables the use of an unstable free-ferromagnet for energy-efficient design. Using the proposed circuit, we evaluate the performance of the convolutional neural network for MNIST datasets and demonstrate comparable classification accuracies to the ideal ReLU with an energy consumption of 75 $pJ$ per sample.