Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Gigantic Anisotropy of Self-Induced Spin-Orbit Torque in Weyl Ferromagnet Co2MnGa

Spin-orbit torque (SOT) is receiving tremendous attention from both fundamental and application-oriented aspects. Co2MnGa, a Weyl ferromagnet that is in a class of topological quantum materials, possesses cubic-based high structural symmetry, the L21 crystal ordering, which should be incapable of hosting anisotropic SOT in conventional understanding. Here we show the discovery of a gigantic anisotropy of self-induced SOT in Co2MnGa. The magnitude of the SOT is comparable to that of heavy metal/ferromagnet bilayer systems, despite the high inversion symmetry of the Co2MnGa structure. More surprisingly, a sign inversion of the self-induced SOT is observed for different crystal axes. This finding stems from the interplay of the topological nature of the electronic states and their strong modulation by external strain. Our research enriches the understanding of the physics of self-induced SOT and demonstrates a versatile method for tuning SOT efficiencies in a wide range of materials for topological and spintronic devices.

Giant Orbital-to-Spin Conversion for Efficient Current-Induced Magnetization Switching of Ferrimagnetic Insulator

It has long been believed that the attachment of two heavy metals such as Ta and Pt with opposite spin Hall angles results in a weakened net torque generation efficiency in magnetization switching devices. Here, we report a giant orbital-to-spin conversion in Ta/Pt/Tm3Fe5O12 (TmIG) heterostructures. We show that the torque generation efficiency is enhanced by an order of magnitude in the Ta/Pt/TmIG trilayer compared to that in the Pt/TmIG bilayer. This enhancement is further evidenced by the fact that the critical current density for the magnetization switching of the Ta/Pt/TmIG is an order of magnitude smaller than that of the Pt/TmIG. It is found that the orbital current generated from Ta through the orbital Hall effect (OHE) is converted to the spin current in the interior of Pt. Our discovery offers an extraordinary approach to enhance the torque generation for magnetization switching of insulators and provides an important piece of information for orbitronics.

High temperature stability in few atomic layer MoS2 based thin film heterostructures: structural, static and dynamic magnetization properties

Layered transition metal dichalcogenides (TMDs) have shown commendable properties for spintronic applications. From the device perspective, the structural quality of the TMD as well as its interface with the adjacent ferromagnetic (FM) layer is of paramount importance. Here, we present the spin-dynamic behaviour in the widely studied TMDs, i.e., MoS₂ using Co₆₀Fe₂₀B₂₀ (CoFeB), i.e., in MoS₂(1-4 layers)/CoFeB(4-15 nm) heterostructures, both in the as-grown state and in the in situ annealed state (400 °C in a vacuum). Raman spectroscopy revealed systematic variation in the separation (δ) between the characteristic Raman shifts corresponding to the E_2g and A_1gvis-à-vis the number of layers (n_L) of MoS₂. The analysis of the ferromagnetic resonance (FMR) spectroscopy measurements performed on these heterostructures revealed the spin pumping from CoFeB to the MoS₂ layer as evidenced by the ∼49% (∼51%) enhancement in the effective damping parameter with respect to the damping parameter of bare as-deposited (annealed) CoFeB films. This enhancement is attributed to the spin-pumping owing to the high spin-orbit coupling of monolayer MoS₂. The latter is also confirmed by density functional theory calculations. By finding the effective spin mixing conductance of the MoS₂/CoFeB interface, the effective spin current density in the MoS₂ layer is estimated to increase from ∼0.3 to 0.7 MA m^-2 with CoFeB thickness for both the as-deposited and annealed heterostructures. Furthermore, the δ vs. n_L curve of the as-deposited heterostructure did not show any significant change upon annealing, which demonstrated that the spin transport and magnetic properties of these heterostructures remained unaffected even after annealing at a high temperature of 400 °C. Hence, this establishes the high thermal stability of the sputter grown MoS₂/CoFeB heterostructures. Thus, this study highlights the important role of MoS₂ as an efficient spin current-generating source for spin-orbit torque based magnetic memory applications, given the high-temperature stability and high-quality monolayers of MoS₂ and its excellent performance with CoFeB thin films.

Intrinsic Magnetic Proximity Effect at the Atomically Sharp Interface of CoxFe3-xO4/Pt Grown by Molecular Beam Epitaxy

Co_xFe_3-xO₄(CFO)/Pt bilayers prepared by molecular beam epitaxy were investigated for the anomalous Hall effect and X-ray magnetic circular dichroism (XMCD). We found that the anomalous Hall effect originates from a magnetic proximity effect at the CFO/Pt interface. The XMCD signal in the Pt L-edge was obtained only for the sample deposited at 600 °C, indicating that the magnetic proximity effect is sensitive to the interface structure. Transmission electron microscopy images of the CFO/Pt interface and XMCD measurements of Co and Fe L-edges do not provide direct evidence for interfacial atomic diffusion or alloying. In summary, these results suggest that the magnetic proximity effect is robust for transport properties, such as the anomalous Hall effect, while the induced magnetic moment depends on slight differences in the interfacial structure, such as the presence or absence of interfacial oxygen ions.

Field-free spin-orbit torque switching assisted by in-plane unconventional spin torque in ultrathin [Pt/Co]N

Electrical manipulation of magnetization without an external magnetic field is critical for the development of advanced non-volatile magnetic-memory technology that can achieve high memory density and low energy consumption. Several recent studies have revealed efficient out-of-plane spin-orbit torques (SOTs) in a variety of materials for field-free type-z SOT switching. Here, we report on the corresponding type-x configuration, showing significant in-plane unconventional spin polarizations from sputtered ultrathin [Pt/Co]_N, which are either highly textured on single crystalline MgO substrates or randomly textured on SiO₂ coated Si substrates. The unconventional spin currents generated in the low-dimensional Co films result from the strong orbital magnetic moment, which has been observed by X-ray magnetic circular dichroism (XMCD) measurement. The x-polarized spin torque efficiency reaches up to -0.083 and favors complete field-free switching of CoFeB magnetized along the in-plane charge current direction. Micromagnetic simulations additionally demonstrate its lower switching current than type-y switching, especially in narrow current pulses. Our work provides additional pathways for electrical manipulation of spintronic devices in the pursuit of high-speed, high-density, and low-energy non-volatile memory.

Observation of the orbital Hall effect in a light metal Ti

The orbital Hall effect¹ refers to the generation of electron orbital angular momentum flow transverse to an external electric field. Contrary to the common belief that the orbital angular momentum is quenched in solids, theoretical studies^2,3 predict that the orbital Hall effect can be strong and is a fundamental origin of the spin Hall effect^4-7 in many transition metals. Despite the growing circumstantial evidence^8-11, its direct detection remains elusive. Here we report the magneto-optical observation of the orbital Hall effect in the light metal titanium (Ti). The Kerr rotation by the orbital magnetic moment accumulated at Ti surfaces owing to the orbital Hall current is measured, and the result agrees with theoretical calculations semi-quantitatively and is supported by the orbital torque¹² measurement in Ti-based magnetic heterostructures. This result confirms the orbital Hall effect and indicates that the orbital angular momentum is an important dynamic degree of freedom in solids. Moreover, this calls for renewed studies of the orbital effect on other degrees of freedom such as spin^2,3,13,14, valley^15,16, phonon^17-19 and magnon^20,21 dynamics.

Deterministic Magnetization Switching via Tunable Noncollinear Spin Configurations in Canted Magnets

Spin obit torque (SOT) driven magnetization switching has been used widely for encoding consumption-efficient memory and logic. However, symmetry breaking under a magnetic field is required to realize the deterministic switching in synthetic antiferromagnets with perpendicular magnetic anisotropy (PMA), which limits their potential applications. Herein, we report all electric-controlled magnetization switching in the antiferromagnetic Co/Ir/Co trilayers with vertical magnetic imbalance. Besides, the switching polarity could be reversed by optimizing the Ir thickness. By using the polarized neutron reflection (PNR) measurements, the canted noncollinear spin configuration was observed in Co/Ir/Co trilayers, which results from the competition of magnetic inhomogeneity. In addition, the asymmetric domain walls demonstrated by micromagnetic simulations result from introducing imbalance magnetism, leading to the deterministic magnetization switching in Co/Ir/Co trilayers. Our findings highlight a promising route to electric-controlled magnetism via tunable spin configuration, improve our understanding of physical mechanisms, and significantly promote industrial applications in spintronic devices.

Anatomy of nanomagnetic switching at a 3D topological insulator PN junction

A P-N junction engineered within a Dirac cone system acts as a gate tunable angular filter based on Klein tunneling. For a 3D topological insulator with a substantial bandgap, such a filter can produce a charge-to-spin conversion due to the dual effects of spin-momentum locking and momentum filtering. We analyze how spins filtered at an in-plane topological insulator PN junction (TIPNJ) interact with a nanomagnet, and argue that the intrinsic charge-to-spin conversion does not translate to an external gain if the nanomagnet also acts as the source contact. Regardless of the nanomagnet's position, the spin torque generated on the TIPNJ is limited by its surface current density, which in turn is limited by the bulk bandgap. Using quantum kinetic models, we calculated the spatially varying spin potential and quantified the localization of the current versus the applied bias. Additionally, with the magnetodynamic simulation of a soft magnet, we show that the PN junction can offer a critical gate tunability in the switching probability of the nanomagnet, with potential applications in probabilistic neuromorphic computing.

Spin-orbit torque flash analog-to-digital converter

Although analog-to-digital converters (ADCs) are critical components in mixed-signal integrated circuits (IC), their performance has not been improved significantly over the last decade. To achieve a radical improvement (compact, low power and reliable ADCs), spintronics can be considered as a proper candidate due to its compatibility with CMOS and wide applications in storage, neuromorphic computing, and so on. In this paper, a proof-of-concept of a 3-bit spin-CMOS Flash ADC using in-plane-anisotropy magnetic tunnel junctions (i-MTJs) with spin-orbit torque (SOT) switching mechanism is designed, fabricated and characterized. In this ADC, each MTJ plays the role of a comparator whose threshold is set by the engineering of the heavy metal (HM) width. Such an approach can reduce the ADC footprint. Monte-Carlo simulations based on the experimental measurements show the process variations/mismatch limits the accuracy of the proposed ADC to 2 bits. Moreover, the maximum differential nonlinearity (DNL) and integral nonlinearity (INL) are 0.739 LSB (least significant bit) and 0.7319 LSB, respectively.

Coherent antiferromagnetic spintronics

Antiferromagnets have attracted extensive interest as a material platform in spintronics. So far, antiferromagnet-enabled spin-orbitronics, spin-transfer electronics and spin caloritronics have formed the bases of antiferromagnetic spintronics. Spin transport and manipulation based on coherent antiferromagnetic dynamics have recently emerged, pushing the developing field of antiferromagnetic spintronics towards a new stage distinguished by the features of spin coherence. In this Review, we categorize and analyse the critical effects that harness the coherence of antiferromagnets for spintronic applications, including spin pumping from monochromatic antiferromagnetic magnons, spin transmission via phase-correlated antiferromagnetic magnons, electrically induced spin rotation and ultrafast spin-orbit effects in antiferromagnets. We also discuss future opportunities in research and applications stimulated by the principles, materials and phenomena of coherent antiferromagnetic spintronics.

Graphene Spin Valves for Spin Logic Devices

An alternative to charge-based electronics identifies the spin degree of freedom for information communication and processing. The long spin-diffusion length in graphene at room temperature demonstrates its ability for highly scalable spintronics. The development of the graphene spin valve (SV) has inspired spin devices in graphene including spin field-effect transistors and spin majority logic gates. A comprehensive picture of spin transport in graphene SVs is required for further development of spin logic. This review examines the advances in graphene SVs and their role in the development of spin logic devices. Different transport and scattering mechanisms in charge and spin are discussed. Furthermore, the on/off switching energy between graphene SVs and charge-based FETs is compared to highlight their prospects for low-power devices. The challenges and perspectives that need to be addressed for the future development of spin logic devices are then outlined.

Non-volatile electric control of spin-orbit torques in an oxide two-dimensional electron gas

Spin-orbit torques (SOTs) have opened a novel way to manipulate the magnetization using in-plane current, with a great potential for the development of fast and low power information technologies. It has been recently shown that two-dimensional electron gases (2DEGs) appearing at oxide interfaces provide a highly efficient spin-to-charge current interconversion. The ability to manipulate 2DEGs using gate voltages could offer a degree of freedom lacking in the classical ferromagnetic/spin Hall effect bilayers for spin-orbitronics, in which the sign and amplitude of SOTs at a given current are fixed by the stack structure. Here, we report the non-volatile electric-field control of SOTs in an oxide-based Rashba-Edelstein 2DEG. We demonstrate that the 2DEG is controlled using a back-gate electric-field, providing two remanent and switchable states, with a large resistance contrast of 1064%. The SOTs can then be controlled electrically in a non-volatile way, both in amplitude and in sign. This achievement in a 2DEG-CoFeB/MgO heterostructures with large perpendicular magnetization further validates the compatibility of oxide 2DEGs for magnetic tunnel junction integration, paving the way to the advent of electrically reconfigurable SOT MRAMS circuits, SOT oscillators, skyrmion and domain-wall-based devices, and magnonic circuits.

Manipulation of the Topological Ferromagnetic State in a Weyl Semimetal by Spin-Orbit Torque

Magnetic Weyl semimetals (MWSMs) exhibit unconventional transport phenomena, such as large anomalous Hall (and Nernst) effects, which are absent in spatial inversion asymmetry WSMs. Compared with its nonmagnetic counterpart, the magnetic state of a MWSM provides an alternative way for the modulation of topology. Spin-orbit torque (SOT), as an effective means of electrically controlling the magnetic states of ferromagnets, may be used to manipulate the topological magnetic states of MWSMs. Here we confirm the MWSM state of high-quality Co₂MnGa film by systematically investigating the transport measurements and demonstrating that the magnetization and topology of Co₂MnGa can be electrically manipulated. The electrical and magnetic optical measurements further reveal that the current-induced SOT switches the topological magnetic state in a 180-degree manner by applying positive/negative current pulses and in a 90-degree manner by alternately applying two orthogonal current pulses. This work opens up more opportunities for spintronic applications based on topological materials.

Spin-Momentum Locking and Ultrafast Spin-Charge Conversion in Ultrathin Epitaxial Bi1 - x Sbx Topological Insulator

The helicity of three-dimensional (3D) topological insulator surface states has drawn significant attention in spintronics owing to spin-momentum locking where the carriers' spin is oriented perpendicular to their momentum. This property can provide an efficient method to convert charge currents into spin currents, and vice-versa, through the Rashba-Edelstein effect. However, experimental signatures of these surface states to the spin-charge conversion are extremely difficult to disentangle from bulk state contributions. Here, spin- and angle-resolved photo-emission spectroscopy, and time-resolved THz emission spectroscopy are combined to categorically demonstrate that spin-charge conversion arises mainly from the surface state in Bi_{1 - x} Sb_x ultrathin films, down to few nanometers where confinement effects emerge. This large conversion efficiency is correlated, typically at the level of the bulk spin Hall effect from heavy metals, to the complex Fermi surface obtained from theoretical calculations of the inverse Rashba-Edelstein response. Both surface state robustness and sizeable conversion efficiency in epitaxial Bi_{1 - x} Sb_x thin films bring new perspectives for ultra-low power magnetic random-access memories and broadband THz generation.

Time-Reversal-Even Nonlinear Current Induced Spin Polarization

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe_{2}, and in ferromagnetic monolayer MnSe_{2}, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems.

Spin pumping through nanocrystalline topological insulators

The topological surface states (TSSs) in topological insulators (TIs) offer exciting prospects for dissipationless spin transport. Common spin-based devices, such as spin valves, rely on trilayer structures in which a non-magnetic layer is sandwiched between two ferromagnetic (FM) layers. The major disadvantage of using high-quality single-crystalline TI films in this context is that a single pair of spin-momentum locked channels spans across the entire film, meaning that only a very small spin current can be pumped from one FM to the other, along the side walls of the film. On the other hand, using nanocrystalline TI films, in which the grains are large enough to avoid hybridization of the TSSs, will effectively increase the number of spin channels available for spin pumping. Here, we used an element-selective, x-ray based ferromagnetic resonance technique to demonstrate spin pumping from a FM layer at resonance through the TI layer and into the FM spin sink.

Efficient Spin-Orbit Torque Switching in a Perpendicularly Magnetized Heusler Alloy MnPtGe Single Layer

Electrically manipulating magnetic moments by spin-orbit torque (SOT) has great potential applications in magnetic memories and logic devices. Although there have been rich SOT studies on magnetic heterostructures, low interfacial thermal stability and high switching current density still remain an issue. Here, highly textured, polycrystalline Heusler alloy Mn_xPt_yGe (MPG) films with various thicknesses are directly deposited onto thermally oxidized silicon wafers. The perpendicular magnetization of the MPG single layer can be reversibly switched by electrical current pulses with a magnitude as low as 4.1 × 10¹⁰Am^-2, as evidenced by both the electrical transport and the magnetic optical measurements. The switching is shown to arise from inversion symmetry breaking due to the vertical composition gradient of the films after sample annealing. The SOT effective fields of the samples are analyzed systematically. It is found that the SOT efficiency increases with the film thickness, suggesting a robust bulk-like behavior in the single magnetic layer. Furthermore, a memristive characteristic has been observed due to a multidomain switching property in the single-layer MPG device. Additionally, deterministic field-free switching of magnetization is observed when the electric current flows orthogonal to the direction of the in-plane compositional gradient due to the in-plane symmetry breaking. This work proves that the MPG is a good candidate to be utilized in high-density and efficient magnetoresistive random access memory devices and other spintronic applications.

Bulk Rashba-Type Spin Splitting in Non-Centrosymmetric Artificial Superlattices

Spin current, converted from charge current via spin Hall or Rashba effects, can transfer its angular momentum to local moments in a ferromagnetic layer. In this regard, the high charge-to-spin conversion efficiency is required for magnetization manipulation for developing future memory or logic devices including magnetic random-access memory. Here, the bulk Rashba-type charge-to-spin conversion is demonstrated in an artificial superlattice without centrosymmetry. The charge-to-spin conversion in [Pt/Co/W] superlattice with sub-nm scale thickness shows strong W thickness dependence. When the W thickness becomes 0.6 nm, the observed field-like torque efficiency is about 0.6, which is an order larger than other metallic heterostructures. First-principles calculation suggests that such large field-like torque arises from bulk-type Rashba effect due to the vertically broken inversion symmetry inherent from W layers. The result implies that the spin splitting in a band of such an ABC-type artificial SL can be an additional degree of freedom for the large charge-to-spin conversion.

Enhanced Spin Current in Ni81 Fe19 /Cu-CuOx Bilayer with Top and Sideways Oxidization

Generation and manipulation of spin current are the cores of spintronic devices, which are intensely pursued. Heavy metals with strong spin-orbit coupling are commonly used for the generation of spin current, but are incompatible with the mass production of devices, and the polarization of spin current is limited to be in-plane. Here, it is shown that the spin current with strong out-of-plane polarization component can be generated and transmitted in Ni₈₁ Fe₁₉ /Cu-CuO_x bilayer with sideways and top oxidizations. The charge-to-spin current conversion efficiency can be enhanced through the spin currents consisting of both out-of-plane polarization (σ_z ) and in-plane polarization (σ_y ) induced by spin-vorticity coupling. Such a spin current is demonstrated to be closely related to the lateral oxidization gradient and can be controlled by changing the temperatures and times of annealing. The finding here provides a novel degree of freedom to produce and control the spin current in spintronic devices.

Strong variation of spin-orbit torques with relative spin relaxation rates in ferrimagnets

Spin-orbit torques (SOTs) have been widely understood as an interfacial transfer of spin that is independent of the bulk properties of the magnetic layer. Here, we report that SOTs acting on ferrimagnetic FexTb1-x layers decrease and vanish upon approaching the magnetic compensation point because the rate of spin transfer to the magnetization becomes much slower than the rate of spin relaxation into the crystal lattice due to spin-orbit scattering. These results indicate that the relative rates of competing spin relaxation processes within magnetic layers play a critical role in determining the strength of SOTs, which provides a unified understanding for the diverse and even seemingly puzzling SOT phenomena in ferromagnetic and compensated systems. Our work indicates that spin-orbit scattering within the magnet should be minimized for efficient SOT devices. We also find that the interfacial spin-mixing conductance of interfaces of ferrimagnetic alloys (such as FexTb1-x) is as large as that of 3d ferromagnets and insensitive to the degree of magnetic compensation.

Observation of large spin conversion anisotropy in bismuth

While the effective g-factor can be anisotropic due to the spin-orbit interaction (SOI), its existence in solids cannot be simply asserted from a band structure, which hinders progress on studies from such viewpoints. The effective g-factor in bismuth (Bi) is largely anisotropic; especially for holes at T-point, the effective g-factor perpendicular to the trigonal axis is negligibly small (<0.112), whereas the effective g-factor along the trigonal axis is very large (62.7). We clarified in this work that the large anisotropy of effective g-factor gives rise to the large spin conversion anisotropy in Bi from experimental and theoretical approaches. Spin-torque ferromagnetic resonance was applied to estimate the spin conversion efficiency in rhombohedral (110) Bi to be 17 to 27%, which is unlike the negligibly small efficiency in Bi(111). Harmonic Hall measurements support the large spin conversion efficiency in Bi(110). A large spin conversion anisotropy as the clear manifestation of the anisotropy of the effective g-factor is observed. Beyond the emblematic case of Bi, our study unveiled the significance of the effective g-factor anisotropy in condensed-matter physics and can pave a pathway toward establishing novel spin physics under g-factor control.

Skyrmion based majority logic gate by voltage controlled magnetic anisotropy in a nanomagnetic device

Magnetic skyrmions are topologically protected spin textures and they are suitable for future logic-in-memory applications for energy-efficient, high-speed information processing and computing technologies. In this work, we have demonstrated skyrmion-based 3 bit majority logic gate using micromagnetic simulations. The skyrmion motion is controlled by introducing agatethat works on voltage controlled magnetic anisotropy. Here, the inhomogeneous magnetic anisotropy behaves as a tunable potential barrier/well that modulates the skyrmion trajectory in the structure for the successful implementation of the majority logic gate. In addition, several other effects such as skyrmion-skyrmion topological repulsion, skyrmion-edge repulsion, spin-orbit torque and skyrmion Hall effect have been shown to govern the logic functionalities. We have systematically presented the robust logic operations by varying the current density, magnetic anisotropy, voltage-controlled gate dimension and geometrical parameters of the logic device. The skyrmion Hall angle is monitored to understand the trajectory and stability of the skyrmion as a function of time in the logic device. The results demonstrate a novel method to achieve majority logic by using voltage controlled magnetic anisotropy which further opens up a new route for skyrmion-based low-power and high-speed computing devices.

Resistive Switching Crossbar Arrays Based on Layered Materials

Resistive switching (RS) devices are metal/insulator/metal cells that can change their electrical resistance when electrical stimuli are applied between the electrodes, and they can be used to store and compute data. Planar crossbar arrays of RS devices can offer a high integration density (>10⁸  devices mm^{- 2} ) and this can be further enhanced by stacking them three-dimensionally. The advantage of using layered materials (LMs) in RS devices compared to traditional phase-change materials and metal oxides is that their electrical properties can be adjusted with a higher precision. Here, the key figures-of-merit and procedures to implement LM-based RS devices are defined. LM-based RS devices fabricated using methods compatible with industry are identified and discussed. The focus is on small devices (size < 9 µm² ) arranged in crossbar structures, since larger devices may be affected by artifacts, such as grain boundaries and flake junctions. How to enhance device performance, so to accelerate the development of this technology, is also discussed.

Engineering Pt/Co/AlOxheterostructures to enhance the Dzyaloshinskii-Moriya interaction

The study of interfacial Dzyaloshinskii-Moriya interaction (DMI) in perpendicularly magnetized structurally asymmetric heavy metal/ferromagnet multilayer systems is of high importance due to the formation of chiral magnetic textures in the presence of DMI. Here, we report the impact of cobalt oxidation at the Co/AlO_xinterface in Pt/Co/AlO_xtrilayer structures on the DMI by varying the post-growth annealing time, Al thickness and substrate. To quantify DMI we employed magneto-optical imaging of the asymmetric domain wall expansion, hysteresis loop shift, and spin-wave spectroscopy techniques. We further correlated the Co oxidation with low-temperature Hall effect measurements and x-ray photoelectron spectroscopy. Our results emphasize the importance of full characterization of the magnetic films that could be used for magnetic random access memory technologies when subjected to the semiconductor temperature processing conditions, as the magnetic interactions are critical for device performance and can be highly sensitive to oxidation and other effects.

Enhanced spin-orbit torque and field-free switching in Au/TMDs/Ni hybrid structures

Spin-orbit torque (SOT) plays a significant role in spintronic logic and memory devices. However, due to the limited spin Hall angle and SOT symmetry in a heavy-metal-ferromagnet bilayer, further improving SOT efficiency and all-electric magnetization manipulation remain a challenge. Here we report enhanced SOT efficiency and all-electric switching in Au based magnetic structures, by inserting two-dimensional transition metal dichalcogenides (2D TMDs) with large spin-orbit coupling. With the TMD spacer insert, both damping-like and field-like SOTs are improved, and an unconventional out-of-plane damping-like SOT is induced, due to the interface orbital hybridization, modified spin-mixing conductance and orbital current. Moreover, current induced field-free magnetization switching is demonstrated in Au/WTe₂/Ni and Au/MoS₂/Ni devices, and it shows multiple intermediate states and can be efficiently controlled by an electric current. Our results open a path for increasing torques and expand the application of 2D TMDs in spintronic devices for neuromorphic computing.

Electric field manipulation of spin chirality and skyrmion dynamic

The Dzyaloshinskii-Moriya interaction (DMI) is an antisymmetric exchange interaction that stabilizes spin chirality. One scientific and technological challenge is understanding and controlling the interaction between spin chirality and electric field. In this study, we investigate an unconventional electric field effect on interfacial DMI, skyrmion helicity, and skyrmion dynamics in a system with broken inversion symmetry. We design heterostructures with a 3d-5d atomic orbital interface to demonstrate the gate bias control of the DMI energy and thus transform the DMI between opposite chiralities. Furthermore, we use this voltage-controlled DMI (VCDMI) to manipulate the skyrmion spin texture. As a result, a type of intermediate skyrmion with a unique helicity is created, and its motion can be controlled and made to go straight. Our work shows the effective control of spin chirality, skyrmion helicity, and skyrmion dynamics by VCDMI. It promotes the emerging field of voltage-controlled chiral interactions and voltage-controlled skyrmionics.

Voltage-Controlled Dzyaloshinskii-Moriya Interaction Torque Switching of Perpendicular Magnetization

Magnetization switching is the most important operation in spintronic devices. In modern nonvolatile magnetic random-access memory (MRAM), it is usually realized by spin-transfer torque (STT) or spin-orbit torque (SOT). However, both STT and SOT MRAM require current to drive magnetization switching, which will cause Joule heating. Here, we report an alternative mechanism, Dzyaloshinskii-Moriya interaction (DMI) torque, that can realize magnetization switching fully controlled by voltage pulses. We find that a consequential voltage-controlled reversal of DMI chirality in multiferroics can lead to continued expansion of a skyrmion thanks to the DMI torque. Enough DMI torque will eventually make the skyrmion burst into a quasiuniform ferromagnetic state with reversed magnetization, thus realizing the switching of a perpendicular magnet. The discovery is demonstrated in two-dimensional multiferroics, CuCrP_{2}Se_{6} and CrN, using first-principles calculations and micromagnetic simulations. As an example, we applied the DMI torque for simulating leaky-integrate-fire functionality of biological neurons. Our discovery of DMI torque switching of perpendicular magnetization provides tremendous potential toward magnetic-field-free and current-free spintronic devices, and neuromorphic computing as well.

Sizable spin-to-charge conversion in PLD-grown amorphous (Mo, W)Te2-xfilms

We report on the spin-to-charge conversion (SCC) in Mo_0.25W_0.75Te_2-x(MWT)/Y₃Fe₅O₁₂(YIG) heterostructures at room temperature. The centimeter-scale amorphous MWT films are deposited on liquid-phase-epitaxial YIG by pulsed laser deposition technique. The significant SCC voltage is measured in the MWT layer with a sizable spin Hall angle of ∼0.021 by spin pumping experiments. The control experiments by inserting MgO or Ag layer between MWT and YIG show that the SCC is mainly attributed to the inverse spin Hall effect rather than the thermal or interfacial Rashba effect. Our work provides a novel spin-source material for energy-efficient topological spintronic devices.

Octupole-driven magnetoresistance in an antiferromagnetic tunnel junction

The tunnelling electric current passing through a magnetic tunnel junction (MTJ) is strongly dependent on the relative orientation of magnetizations in ferromagnetic electrodes sandwiching an insulating barrier, rendering efficient readout of spintronics devices^1-5. Thus, tunnelling magnetoresistance (TMR) is considered to be proportional to spin polarization at the interface¹ and, to date, has been studied primarily in ferromagnets. Here we report observation of TMR in an all-antiferromagnetic tunnel junction consisting of Mn₃Sn/MgO/Mn₃Sn (ref. ⁶). We measured a TMR ratio of around 2% at room temperature, which arises between the parallel and antiparallel configurations of the cluster magnetic octupoles in the chiral antiferromagnetic state. Moreover, we carried out measurements using a Fe/MgO/Mn₃Sn MTJ and show that the sign and direction of anisotropic longitudinal spin-polarized current in the antiferromagnet⁷ can be controlled by octupole direction. Strikingly, the TMR ratio (about 2%) of the all-antiferromagnetic MTJ is much larger than that estimated using the observed spin polarization. Theoretically, we found that the chiral antiferromagnetic MTJ may produce a substantially large TMR ratio as a result of the time-reversal, symmetry-breaking polarization characteristic of cluster magnetic octupoles. Our work lays the foundation for the development of ultrafast and efficient spintronic devices using antiferromagnets^8-10.

A Noble-Metal-Free Spintronic System with Proximity-Enhanced Ferromagnetic Topological Surface State of FeSi above Room Temperature

Strongly spin-orbit coupled states at metal interfaces, topological insulators, and 2D materials enable efficient electric control of spin states, offering great potential for spintronics. However, there are still materials challenges to overcome, including the integration into advanced silicon electronics and the scarce resources of constituent heavy elements of those materials. Through magneto-transport measurements and first-principles calculations, here robust spin-orbit coupling (SOC)-induced properties of a ferromagnetic topological surface state in FeSi and their controllability via hybridization with adjacent materials are demonstrated. In comparison to the case of its naturally oxidized surface, the ferromagnetic transition temperature is greatly increased beyond room temperature and the effective SOC strength is almost doubled at the surface in proximity to a wide-bandgap fluoride insulator. Those enhanced magnetic properties enable room-temperature magnetization switching, being applicable to spin-orbit torque based spintronic devices. Realization of strong SOC in the noble-metal-free silicon-based compound will accelerate spintronic applications.

Significant Role of Interfacial Spin-Orbit Coupling in the Spin-to-Charge Conversion in Pt/NiFe Heterostructure

For the spin-to-charge conversion (SCC) in heavy metal/ferromagnet (HM/FM) heterostructure, the contribution of interfacial spin-orbit coupling (SOC) remains controversial. Here, we investigate the SCC process of the Pt/NiFe heterostructure by the spin pumping in YIG/Pt/NiFe/IrMn multilayers. Due to the exchange bias of NiFe/IrMn structure, the NiFe magnetization can be switched between magnetically unsaturated and saturated states by opposite resonance fields of YIG layer. The spin-pumping signal is found to decrease significantly when the NiFe magnetization is changed from the saturated state to the unsaturated state. Theoretical analysis indicates that the interfacial spin absorption is enhanced for the above-mentioned NiFe magnetic state change, which results in the increased and decreased spin flow in the Pt layer and across the Pt/NiFe interface, respectively. These results demonstrate that in our case the interfacial SOC effect at the Pt/NiFe interface is dominant over the bulk inverse spin Hall effect in the Pt layer. Our work reveals a significant role of interfacial SOC in the SCC in HM/FM heterostructure, which can promote the development of high-efficiency spintronic devices through interfacial engineering.

Heavy metal deposition temperature tuned spin pumping efficiency control in permalloy/tantalum bilayers

Spin pumping is a key property for spintronic application that can be realized in heavy metal/ferromagnet bilayers. Here we demonstrate the possibility of improving spin pumping in permalloy (Py)/tantalum (Ta) bilayers through control of Ta heavy metal deposition temperature. Through a combination of structural and ferromagnetic resonance based magnetization dynamics study, we reveal the role of Ta deposition temperature in improving spin mixing conductance which is a key parameter for spin pumping across the Py/Ta interface. The results show that by depositing Ta above room temperature, a high spin mixing conductance of 7.7 ×10¹⁸m^-2is obtained withα-Ta layer. The results present an understanding of the correlation between heavy metal deposition temperature and interface structure improvement and consequent control of spin pumping in Py/Ta bilayers.

Ultrashort spin-orbit torque generated by femtosecond laser pulses

To realize the very objective of spintronics, namely the development of ultra-high frequency and energy-efficient electronic devices, an ultrafast and scalable approach to switch magnetic bits is required. Magnetization switching with spin currents generated by the spin-orbit interaction at ferromagnetic/non-magnetic interfaces is one of such scalable approaches, where the ultimate switching speed is limited by the Larmor precession frequency. Understanding the magnetization precession dynamics induced by spin-orbit torques (SOTs) is therefore of great importance. Here we demonstrate generation of ultrashort SOT pulses that excite Larmor precession at an epitaxial Fe/GaAs interface by converting femtosecond laser pulses into high-amplitude current pulses in an electrically biased p-i-n photodiode. We control the polarity, amplitude, and duration of the current pulses and, most importantly, also their propagation direction with respect to the crystal orientation. The SOT origin of the excited Larmor precession was revealed by a detailed analysis of the precession phase and amplitude at different experimental conditions.

Cascadable in-memory computing based on symmetric writing and readout

The building block of in-memory computing with spintronic devices is mainly based on the magnetic tunnel junction with perpendicular interfacial anisotropy (p-MTJ). The resulting asymmetric write and readout operations impose challenges in downscaling and direct cascadability of p-MTJ devices. Here, we propose that a previously unimplemented symmetric write and readout mechanism can be realized in perpendicular-anisotropy spin-orbit (PASO) quantum materials based on Fe3GeTe2 and WTe2. We demonstrate that field-free and deterministic reversal of the perpendicular magnetization can be achieved using unconventional charge-to-z-spin conversion. The resulting magnetic state can be readily probed with its intrinsic inverse process, i.e., z-spin-to-charge conversion. Using the PASO quantum material as a fundamental building block, we implement the functionally complete set of logic-in-memory operations and a more complex nonvolatile half-adder logic function. Our work highlights the potential of PASO quantum materials for the development of scalable energy-efficient and ultrafast spintronic computing.

Spin-pumping investigations in as-deposited and 400 °C annealed Co60Fe20B20/Mo heterostructures

The spin-pumping behavior in the as-deposited and post-deposition annealed (at 400 °C) Co60Fe20B20/Molybdenum (CoFeB/Mo) heterostructures is investigated. It is found that while in both the as-deposited and annealed CoFeB/Mo heterostructures, Mo crystallizes in the form of mixed phases, i.e., body centered cubic (bcc) and face centered cubic (fcc), the dominance, however, changes from fcc to bcc on annealing. The ferromagnetic resonance measurements reveal that despite relatively low spin orbit coupling of Mo, the spin-pumping efficiency and magnetic properties in both the as-deposited as well as in the annealed heterostructures was comparable with those reported in similar CoFeB based heterostructures comprising of other nonmagnetic metals such as W and Ta. The spin efficiency parameters are, however, slightly better when the Mo film is predominantly in the fcc phase as compared to the case when the Mo film dominantly comprises of the bcc phase. The different spin-pumping efficiencies in the two different combinations of phases of Mo are attributed to the different band structures and the density of states in different phases of Mo, as confirmed by density functional theory calculations. The slight changes observed in the spin-pumping response are possibly attributed to the structural manifestations that result at the interface that the two phases of Mo share with CoFeB. Importantly, despite the weak spin–orbit interaction, the 4d transition metal Mo could be a suitable choice of non-magnetic material for spin pumping when the thermal stability of different layers in the CoFeB based spintronic devices is of paramount concern.

Spintronic Physical Unclonable Functions Based on Field-Free Spin-Orbit-Torque Switching

Physical unclonable function (PUFs) utilize inherent random physical variations of solid-state devices and are a core ingredient of hardware security primitives. PUFs promise more robust information security than that provided by the conventional software-based approaches. While silicon- and memristor-based PUFs are advancing, their reliability and scalability require further improvements. These are currently limited by output fluctuations and associated additional peripherals. Here, highly reliable spintronic PUFs that exploit field-free spin-orbit-torque switching in IrMn/CoFeB/Ta/CoFeB structures are demonstrated. It is shown that the stochastic switching polarity of the perpendicular magnetization of the top CoFeB can be achieved by manipulating the exchange bias directions of the bottom IrMn/CoFeB. This serves as an entropy source for the spintronic PUF, which is characterized by high entropy, uniqueness, reconfigurability, and digital output. Furthermore, the device ensures a zero bit-error-rate under repetitive operations and robustness against external magnetic fields, and offers scalable and energy-efficient device implementations.

Local and global energy barriers for chiral domain walls in synthetic antiferromagnet-ferromagnet lateral junctions

Of great promise are synthetic antiferromagnet-based racetrack devices in which chiral composite domain walls can be efficiently moved by current. However, overcoming the trade-off between energy efficiency and thermal stability remains a major challenge. Here we show that chiral domain walls in a synthetic antiferromagnet-ferromagnet lateral junction are highly stable against large magnetic fields, while the domain walls can be efficiently moved across the junction by current. Our approach takes advantage of field-induced global energy barriers in the unique energy landscape of the junction that are added to the local energy barrier. We demonstrate that thermal fluctuations are equivalent to the magnetic field effect, thereby, surprisingly, increasing the energy barrier and further stabilizing the domain wall in the junction at higher temperatures, which is in sharp contrast to ferromagnets or synthetic antiferromagnets. We find that the threshold current density can be further decreased by tilting the junction without affecting the high domain wall stability. Furthermore, we demonstrate that chiral domain walls can be robustly confined within a ferromagnet region sandwiched on both sides by synthetic antiferromagnets and yet can be readily injected into the synthetic antiferromagnet regions by current. Our findings break the aforementioned trade-off, thereby allowing for versatile domain-wall-based memory, and logic, and beyond.

Electrical Control of Spin Hall Effect in Pt by Hydrogen Ion Adsorption and Desorption

The manipulation of charge-to-spin current conversion and spin-orbit torque (SOT) is of great interest due to its profound physics and potential applications. Controlling the spin current through the electric field provides a perspective for highly efficient SOT devices. Here, we use H₂O-doped ionic liquid gating to realize the reversible and nonvolatile manipulation of the spin Hall effect of Pt, and the spin Hall angle can be modulated by 48% within an accessible gate voltage range. The increase in the spin Hall angle is demonstrated to be caused by the adsorption of hydrogen ions on the Pt surface and the consequent enhancement of the spin Hall conductivity under positive voltage. Furthermore, the enhancement of the spin Hall angle is beneficial to reduce the critical current density for driving the domain wall motion. These results supply a method for the dynamic control of the charge-to-spin current conversion, which will promote the development of spintronic devices driven by electric fields.

A comparative study of the domain wall motion in ferrimagnets (Fe,Co)1-x(Gd,Tb)x

Magnetic domain walls (DWs) in rare-earth-transition-metal (RE-TM) ferrimagnetic alloys can be used as information carriers in nonvolatile spintronic devices. Due to the rich combinations of RE-TM elements (such as CoGd, FeGd, CoTb, and FeTb in our case), it is intriguing to reveal the characteristics of DW dynamics in these wide choices of RE-TM compounds. Through a systematic study of the DW motion in thin films with different compositions of stacking order Pt(3 nm)/(Fe,Co)_1-x(Gd,Tb)_x(∼8 nm)/Ta(3 nm), we show that the partially compensated ferrimagnets CoGd and FeGd can exhibit a faster DW motion under various (in-plane and out-of-plane) magnetic fields driven by current-induced spin-orbit torques. In stark contrast with the fast motion of domain walls in Gd-based ferrimagnets, we find that the CoTb system exhibits much slower DW dynamics, and the FeTb system shows no motion, but evolved into a multi-domain state upon applying current pulses. Our results demonstrate that ferrimagnets CoGd and FeGd are more suitable candidates for achieving ultrafast DW motion, which could be useful for developing spintronic memory and logic devices.

Spin homojunction with high interfacial transparency for efficient spin-charge conversion

High interfacial transparency is vital to achieve efficient spin-charge conversion for ideal spintronic devices with low energy consumption. However, in traditional ferromagnetic/nonmagnetic heterojunctions, the interfacial Rashba spin-orbit coupling brings about spin memory loss (SML) and two-magnon scattering (TMS), quenching spin current crossing the heterointerfaces. To address the intrinsic deficiency of heterointerface, we design a ferromagnetic FeRh/antiferromagnetic FeRh spin homojunction for efficient spin-charge conversion, verified by a high interfacial transparency of 0.75 and a high spin torque efficiency of 0.34 from spin pumping measurements. First-principles calculations demonstrate that the interfacial electric field of homojunction is two orders of magnitude smaller than that of traditional heterojunction, producing negligible interfacial spin-orbit coupling to drastically reduce SML and TMS. Our spin homojunction exhibits potential and enlightenment for future energy-efficient spintronic devices.

Large Spin-To-Charge Conversion at the Two-Dimensional Interface of Transition-Metal Dichalcogenides and Permalloy

Spin-to-charge conversion is an essential requirement for the implementation of spintronic devices. Recently, monolayers (MLs) of semiconducting transition-metal dichalcogenides (TMDs) have attracted considerable interest for spin-to-charge conversion due to their high spin-orbit coupling and lack of inversion symmetry in their crystal structure. However, reports of direct measurement of spin-to-charge conversion at TMD-based interfaces are very much limited. Here, we report on the room-temperature observation of a large spin-to-charge conversion arising from the interface of Ni₈₀Fe₂₀ (Py) and four distinct large-area (∼5 × 2 mm²) ML TMDs, namely, MoS₂, MoSe₂, WS₂, and WSe₂. We show that both spin mixing conductance and the Rashba efficiency parameter (λ_IREE) scale with the spin-orbit coupling strength of the ML TMD layers. The λ_IREE parameter is found to range between -0.54 and -0.76 nm for the four ML TMDs, demonstrating a large spin-to-charge conversion. Our findings reveal that the TMD/ferromagnet interface can be used for efficient generation and detection of spin current, opening new opportunities for novel spintronic devices.

Field-Free Spin-Orbit Torque Switching Enabled by the Interlayer Dzyaloshinskii-Moriya Interaction

Perpendicularly magnetized structures that are switchable using a spin current under field-free conditions can potentially be applied in spin-orbit torque magnetic random-access memory (SOT-MRAM). Several structures have been developed; however, new structures with a simple stack structure and MRAM compatibility are urgently needed. Herein, a typical structure in a perpendicular spin-transfer torque MRAM, the Pt/Co multilayer and its synthetic antiferromagnetic counterpart with perpendicular magnetic anisotropy, was observed to possess an intrinsic interlayer chiral interaction between neighboring magnetic layers, namely, the interlayer Dzyaloshinskii-Moriya interaction (DMI) effect. Furthermore, using a current parallel to the eigenvector of the interlayer DMI, we switched the perpendicular magnetization of both structures without a magnetic field, owing to the additional symmetry breaking introduced by the interlayer DMI. This SOT switching scheme realized in the Pt/Co multilayer and its synthetic antiferromagnet structure may open a new avenue toward practical perpendicular SOT-MRAM and other SOT devices.

Gate-controlled skyrmion and domain wall chirality

Magnetic skyrmions are localized chiral spin textures, which offer great promise to store and process information at the nanoscale. In the presence of asymmetric exchange interactions, their chirality, which governs their dynamics, is generally considered as an intrinsic parameter set during the sample deposition. In this work, we experimentally demonstrate that a gate voltage can control this key parameter. We probe the chirality of skyrmions and chiral domain walls by observing the direction of their current-induced motion and show that a gate voltage can reverse it. This local and dynamical reversal of the chirality is due to a sign inversion of the interfacial Dzyaloshinskii-Moriya interaction that we attribute to ionic migration of oxygen under gate voltage. Micromagnetic simulations show that the chirality reversal is a continuous transformation, in which the skyrmion is conserved. This control of chirality with 2-3 V gate voltage can be used for skyrmion-based logic devices, yielding new functionalities.

Deterministic switching of a perpendicularly polarized magnet using unconventional spin-orbit torques in WTe2

Spin-orbit torque (SOT)-driven deterministic control of the magnetic state of a ferromagnet with perpendicular magnetic anisotropy is key to next-generation spintronic applications including non-volatile, ultrafast and energy-efficient data-storage devices. However, field-free deterministic switching of perpendicular magnetization remains a challenge because it requires an out-of-plane antidamping torque, which is not allowed in conventional spin-source materials such as heavy metals and topological insulators due to the system's symmetry. The exploitation of low-crystal symmetries in emergent quantum materials offers a unique approach to achieve SOTs with unconventional forms. Here we report an experimental realization of field-free deterministic magnetic switching of a perpendicularly polarized van der Waals magnet employing an out-of-plane antidamping SOT generated in layered WTe₂, a quantum material with a low-symmetry crystal structure. Our numerical simulations suggest that the out-of-plane antidamping torque in WTe₂ is essential to explain the observed magnetization switching.

Coherent Picture on the Pure Spin Transport between Ag/Bi and Ferromagnets

In a joint effort of both experiments and first-principles calculations, we resolve a hotly debated controversy and provide a coherent picture on the pure spin transport between Ag/Bi and ferromagnets. We demonstrate a strong inverse Rashba-Edelstein effect (IREE) at the interface in between Ag/Bi with a ferromagnetic metal (FM) but not with a ferromagnetic insulator. This is in sharp contrast to the previously claimed IREE at Ag/Bi interface or inverse spin Hall effect dominated spin transport. A more than one order of magnitude modulation of IREE signal is realized for different Ag/Bi-FM interfaces, casting strong tunability and a new direction for searching efficient spintronics materials.

Efficient Tuning of the Spin-Orbit Torque via the Magnetic Phase Transition of FeRh

The understanding and control of the spin-orbit torque (SOT) are central to antiferromagnetic spintronics. Despite the fact that a giant SOT efficiency has been achieved in numerous materials, its efficient tuning in a given material has not been established. Materials with magnetic phase transitions (MPTs) offer a new perspective, as the SOT efficiency may vary significantly for the different magnetic orderings across the transition, and the transition itself can be readily tuned by various control parameters. This work reports that the SOT efficiency of a FeRh-based perpendicular magnetized heterostructure can be significantly tuned by varying the temperature across the MPT. The SOT efficiency exhibits a temperature hysteresis associated with the first-order nature of the MPT, and its value in the ferromagnetic phase is seen to be enhanced by ∼450%, simply by a lowering of temperature to drive FeRh into the antiferromagnetic phase. Furthermore, current-induced magnetization switching can be achieved without an assistant magnetic field for both ferromagnetic and antiferromagnetic FeRh, with a low critical switching current density for the latter. These results not only directly establish FeRh as an efficient spin generator but also present a strategy to dynamically tune SOT via varying the temperature across MPTs.

Enhancing the Spin-Orbit Torque Efficiency by the Insertion of a Sub-nanometer β-W Layer

Spin-orbit torque (SOT) efficiency is one of the key issues of spintronics. However, enhancing the SOT efficiency is usually limited by the positive correlation between resistivity and the spin Hall ratio, where a high resistivity often accompanies a large spin Hall ratio. Here, we demonstrate that sub-nanometer β-W intercalation has a considerable impact on the SOT efficiency in α-W (6 nm)/Co (8 nm)/Pt (3 nm) samples. The damping-like SOT efficiency per unit current density, ξ_DL^j, of α-W (5.7 nm)/β-W (0.3 nm)/Co (8 nm)/Pt (3 nm) shows a ∼ 296% enhancement compared to that of the α-W/Co/Pt system. Meanwhile, a resistivity similar to that of α-W and the spin Hall ratio larger than β-W induce a giant damping-like SOT efficiency per applied electric field, ξ_DL^E, which is about 12.1 times larger than that of β-W. Our findings will benefit the SOT devices by reducing energy consumption.