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Two-Dimensional van der Waals Materials and Heterostructures for Spin-Orbit Torque Applications

Towhidur Rahaman

https://orcid.org/0009-0001-3318-4446

Department of Physics, Indian Institute of Technology Patna, Patna, Bihar 801106, India

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Abhishek Kumar

Department of Physics, Indian Institute of Technology Ropar, Rupnagar 140001, India

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Soumya Jyoti Ray

Department of Physics, Indian Institute of Technology Patna, Patna, Bihar 801106, India

E-mail Address: ray@iitp.ac.in

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, and

Debangsu Roy

Department of Physics, Indian Institute of Technology Ropar, Rupnagar 140001, India

E-mail Address: debangsu@iitrpr.ac.in

Corresponding author.

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https://doi.org/10.1142/S201032472340026XCited by:1 (Source: Crossref)

This article is part of the issue:

Special Issue: Spin Pumping and Spin-Orbit Torques in Magnetic Heterostructures
Guest Editors: Akash Kumar (University of Gothenburg, Sweden and Tohoku University, Japan), Shunsuke Fukami (Tohoku University, Japan) and Johan Åkerman (University of Gothenburg, Sweden and Tohoku University, Japan)

Abstract

Spin-orbit torque (SOT) plays an efficient and versatile role in electrical manipulation in spintronic devices at the nanoscale, which shows great promise for ultrafast and energy-efficient magnetic random-access memory (MRAM). To get high-performance SOT devices, their charge-to-spin conversion ratio must be sufficiently high and low current consumption is the desired one. Two-dimensional van der Waals (2D-vdW) materials possess strong tunability and spin-orbit coupling compared to conventional metals, which can efficiently achieve both things. This review covers a generalized introduction to SOT and its origin, their measurement techniques, SOTs observed in various 2D material-based heterostructures made of topological insulators (TIs), transition metal dichalcogenides (TMDs), and van der Waals (vdW) materials as they have excellent electronic properties down to their monolayer limit and ease of integration. Further, it covers the recent progress of SOT devices in each category, highlighting their potential for achieving high-performance and energy-efficient spintronic devices and their potential applications.

Keywords:

1. Introduction

The search for efficient means to process and store information coupled with negligible dissipation has been a perpetual effort in modern-day electronics. In this regard, the field “Spintronics” has become important which exploits the electron spin degree of freedom.¹ The present-day commercial memory and storage device is based on one type of magnetic order, i.e., ferromagnetism and utilizes a fundamental principle that the opposite spin orientation represents the 0 and 1 state. Recently, the need for higher data storage densities with reduced access time and device power consumption has become the focus of research.^1,2 Recent years have witnessed a renewed interest in developing spin-based logic and memory devices capable of operating at high frequency with low energy consumption.^2,3,4 However, spin-transfer torque (STT) based magnetic random-access memory (MRAM) devices experience low endurance issues due to the flow of high current density through the tunnel barrier during writing operation.⁵ In this regard, MRAM utilizing spin-orbit torque (SOT) mechanism for magnetization switching becomes of paramount importance owing to better endurance, faster access time and lower energy consumption in comparison to STT-MRAM. In SOT-MRAM, the lateral current flowing through the heavy metal (HM) layer generates spin current due to the bulk spin-Hall effect (SHE)^4,6 or/and the interfacial Rashba–Edelstein effect (REE).⁷ The spin current, in turn, induces a torque in the adjacent ferromagnetic (FM) layer, leading to the magnetization reversal in the FM layer in HM/FM heterostructures. Here, the spin torques are generally comprised of two orthogonal components, namely anti-damping-like torque (AD-SOT) and field-like torque (FL-SOT).^3,7 The in-plane AD-SOT is utilized for field-free current-induced deterministic switching of the FM layer during the writing process in the MRAM. Notably, in SOT-MRAM, a perpendicularly magnetized (PMA) FM layer is preferred due to high endurance against the writing current, better thermal stability and low current requirement for magnetization switching. It has to be noted that AD-SOT generated by the HM layer lies in the film plane as a consequence of the global two-fold rotational symmetry.^2,3 Thus, to achieve deterministic switching of the HM/FM (PMA) bilayer, out-of-plane AD-SOT is desired. This is achieved in SOT-MRAM by applying an additional in-plane magnetic field to induce field-free magnetization switching. Moreover, various mechanisms have been proposed to achieve magnetization switching without the application of any external symmetry-breaking magnetic field, such as the use of a wedge layer (either FM,^8,9,10 HM),^11,12 exchange bias field of antiferromagnets¹³ and so on thus complicating the realization of the SOT-MRAM with HM layer. In addition, the usual HM layer, including Ta, W and Pt, finds its application in SOT-MRAM restricted due to its lower SOT efficiencies, which lie in the range of 0.1–0.3, and the inability to produce the out-of-plant AD-SOT. In this regard, two-dimensional transition metal dichalcogenides (2D-TMDs) offer a better alternative as a source of the SOC layer than HM.

In 2D-TMDs, the atoms are arranged in a hexagonally packed structure. Here, the weak van der Waals (vdW) force holds the atomic layers together, and its layered structure leads to its anisotropic nature, which is revealed through its directional-dependent electrical and magnetic properties. Generally, an isolated monolayer of 2D-TMDs exhibits mirror reflection symmetry, which is destroyed when deposited on a substrate. In addition, inversion symmetry is broken (preserved) in stacks of TMD, which comprise an odd (even) number of monolayers. Generally, the broken mirror/inversion symmetry leads to the in-plane confinement of the motion of the electron, thus leading to large SOCs.¹⁴ In addition, when the TMDs have been subjected to gating, a REE SOC arises, which further pins the electron spin in the in-plane direction.¹⁵ Thus, the absence of inversion symmetries coupled with gate-induced REE leads to the large effective mass of the electrons yielding large SOCs. Moreover, it is expected in TMDs that due to the breaking of the symmetries, the out-of-plane AD-SOT arises, which could eventually lead to the deterministic switching of the adjacent PMA FM layer.¹⁶ This scenario is not feasible for the HM/FM bilayer as HM is an isotropic system. When coupled with the FM layer, it gives rise to inversion symmetry breaking along the z-axis, leading to in-plane AD-SOT. Thus, in this project, we intend to investigate the SOT in all metallic TMD/FM bilayers to realize field-free deterministic switching in the FM layer. Very recently, atomically thin 2D vdW magnets like Cr₂Ge₂Te₆, Fe₃GeTe₂ and CrI₃ are known to exhibit long-range magnetism^17,18 that offers excellent magnetism and high SOT efficiency due to the presence of intrinsic PMA. This intrinsic PMA remains preserved down to its monolayer limit, making it attractive for application as ultra-thin magnetic layers in SOT devices.

This review aims to present a thorough overview of the latest developments in the realm of 2D vdW materials and heterostructures for SOT applications. Initially, we delve into the concept of SOT, its historical origins and significance in spintronics, followed by its measurement techniques and an in-depth examination of the synthesis methods employed for 2D vdW materials. Subsequently, the focus shifts toward SOT based on TIs and TMDs, particularly emphasizing their properties and potential applications. Furthermore, we explore the fascinating world of atomically thin vdW magnets and monochalcogenides examining their unique properties and possibilities in the world of SOT devices. Finally, the review concludes by highlighting the promising applications of SOT devices and offering valuable insights into the future prospects of this exciting field.

2. Origin of SOT

SOT emerged as an efficient and promising technique for the electrical manipulation of magnetization in spintronic devices.^4,19,20 The origin of the SOT is based on the spin accumulation at the HM/FM interface (Fig. 1(a)). It was first achieved in magnetic semiconductor GaMnAs.²¹ The spin accumulation arises from two different SOC phenomena: Spin Hall Effect (SHE)^22,23,24 and Rashba–Edelstein Effect (REE).^25,26 SHE is a bulk SOC phenomenon, whereas REE is an interfacial SOC phenomenon.²⁷ Both effects are responsible for the spin accumulation at the interface of HM/FM heterostructure. Figure 1(b) describes the behavior of flowing charge current in a nonmagnetic (NM) layer that produces a spin current due to the asymmetric spin deflection caused by SOC. The accumulated spins then diffuse into the adjacent FM layer transferring the angular momentum from the spin current to the magnetization of the FM and exerting torque on it, causing switching of the magnetization (Fig. 1(d)). A spin current carrying spin polarization vector ( $σ$ $σ$ ) produces two types of SOTs on the magnetization (m): damping-like SOT $τ_{DL} - m \times (m \times σ)$ $τ_{DL} - m \times (m \times σ)$ and field-like SOT ( $τ_{FL} - m \times σ)$ $τ_{FL} - m \times σ)$ . The DL-SOT is due to the absorption of the spin current components perpendicular to the m, whereas the FL-SOT is due to the spin current reflection with spin rotation.^28,29

Fig. 1. Schematic diagram of SOC and SOT phenomenon: (a) A three-dimensional representation of SOT, (b) Schematic diagram of spin Hall effect, (c) Rashba–Edelstein effect with an internal electric field E_R perpendicular to the film plane, (d) SOT effect. $T_{FL}$ $T_{FL}$ and $T_{DL}$ $T_{DL}$ represent the field-like and damping-like torque.

2.1. Spin hall effect (SHE)

The idea was first predicted theoretically by D’Yakonov and Parel in 1971.²² They reported that the polarization of the spin current is directed perpendicular to both the direction of the charge and spin currents. Hirsch²³ and Zhang²⁴ revisited this idea and renamed this phenomenon as the spin Hall effect. SHE is a bulk phenomenon. The first experimental verification of SHE was observed in 2004 by Koto et al.³⁰ using the magneto-optical Kerr method in GaAs semiconductors and Al or Pt metals. It was reported that magnetization switching in Ga $_{1 - x}$ $_{1 - x}$ Mn_xAs by the spin current from the bulk SOC.

The mechanism of the SHE is based on the generation of the transverse spin current ( $J_{s})$ $J_{s})$ when an unpolarized charge current ( J $_{c})$ $_{c})$ flows into the high SOC spin source layer, the deflection of the spin-up and spin-down electrons in opposite directions leads to a net spin polarization and is attributed to the spin-dependent asymmetric scattering Fig. 1(b).^27,31,32,33 Therefore, when an in-plane charge current passes through the source material with SOC, it produces a spin current in the transverse direction. Spin currents generated by SHE can be described by $J_{s} = (ℏ$ $J_{s} = (ℏ$ /2 $e) \times θ_{SH}$ $e) \times θ_{SH}$ ( $J_{c} \times σ$ $J_{c} \times σ$ ) where $σ$ $σ$ is the polarization of the spin current, $ℏ$ $ℏ$ , e and $θ_{SH}$ $θ_{SH}$ denote the reduced Planck constant, elementary charge and spin Hall angle (SHA), respectively. The SHA is an intrinsic property of the source materials, whose sign and value describe the polarization and SOT efficiency direction.

2.2. Rashba–Edelstein effect (REE)

Another effective method to generate spin currents is the interfacial current that induces spin accumulation, known as Rashba–Edelstein effect.^25,26 It originated from an interfacial spin phenomenon and was first proposed in semiconductors and 2D electron gases with broken inversion symmetry.²⁶ Under such circumstances, an internal electric field $(E_{R})$ $(E_{R})$ perpendicular to the film plane is generated at the HM/FM interface because of spatial inversion symmetry breaking, and the magnitude gets prominent for metal with high Z value (Fig. 1(c)). When the conduction electrons have momentum, $p$ $p$ moves through this field and experiences an effective magnetic field parallel to $E_{R} \times p$ $E_{R} \times p$ . This interfacial SOC-induced effective magnetic field is known as Rashba field $H_{R}$ $H_{R}$ , which polarizes the electrons, resulting in spin accumulation at the interface. Here, the Rashba effect is described as $J_{s} \propto (α_{R}$ $J_{s} \propto (α_{R}$ / $ℏ e) z \times J_{e}$ $ℏ e) z \times J_{e}$ , where $J_{e}$ $J_{e}$ is the applied charge current and $J_{s}$ $J_{s}$ is the spin current density, $z$ $z$ is the out-of-plane unit vector, and $α_{R}$ $α_{R}$ is the Rashba parameter governed by the potential drop at the interface.

2.3. Measurement techniques

Experimental techniques for measuring the SOT depend on investigating the effect of the electric current applied in the direction of the magnetization. An effective way is to determine the magnetization angle as a function of the amplitude and phase of the applied current and to derive the effective magnetic field by observing the changes in transverse or longitudinal conductivity. The three primary techniques involved in the quantitative characterization of current-induced spin torque are the second harmonic Hall voltage technique (SHH).^{30,34,35,36,37,38} spin-torque ferromagnetic resonance (ST-FMR)^39,40,41 and magneto-optical Kerr effect (MOKE).^42,43 The harmonic Hall voltage method for measuring SOT is performed by analyzing the second harmonic Hall voltage that arises due to the homodyne mixing of the low-frequency ac current (typically up to a few kHz) with the Hall resistance modulated by the oscillations of the magnetization induced by the SOTs.⁴⁴ Therefore, it provides an accurate calibration of damping and field-like torques in both perpendicular (out of plane)⁴⁵ and in-plane materials.^27,46 The ST-FMR method involves the ferromagnetic magnetization excitation by employing a radio-frequency charge current. The excitation of the magnetization in the sample is done through spin torque and exhibits FMR when an applied current or magnetic field is altered. In MOKE, the detection of both in-plane and out-of-plane magnetization components by rotating the light polarization upon reflection from a magnetic surface is recorded.⁴³

3. 2D Materials for SOT Devices

Commonly used spin source materials are HM, such as Pt, Ta and W, with strong spin Hall effects. But they have poor energy-efficient switching mechanisms and the switching energy is significant. 2D materials for SOT devices address both challenges since they exhibit a large damping-like SOT efficiency and have a much lower switching current density. Besides these, they possess strong tunability by interface effects, very strong SOC and low crystal symmetry. For example, TMDs and TIs could produce transverse polarized spin current via the spin Hall effect.^47,48 2D magnetic materials possess highly tunable magnetism and low magnetization at small thicknesses. Therefore, SOTs generated by 2D materials have the utmost importance in spintronics.

3.1. Synthesis of 2D materials for SOT devices

The synthesis approach of 2D materials can broadly be classified as top-down and bottom-up methods. In top-down processes, a larger or bulk material can be converted into 2D nanosheets in a controlled way. In contrast, in the bottom-up approach, 2D nanosheets are grown from the atomic or molecular precursors. Bottom-up approaches are known for producing 2D materials in larger amounts and are economical, while top-down approaches are inherently more straightforward for 2D nanosheets. As of now, the most common adaptable methods to study current-induced SOT in 2D vdW materials are mechanical exfoliation, chemical vapor deposition, molecular beam epitaxy, magnetron sputtering, etc.

3.2. Chemical vapor deposition (CVD)

It is a method to produce high-quality thin films widely used in the industry. In recent years, TMDs have been synthesized extensively using the CVD technique for SOT applications.⁴⁹ The main reason is to gain control of the chemical reactions and their large-scale production. First, the CVD technique showed great promise in terms of high-quality growth of 2D magnetic materials like CrSe₂⁵⁰ and CrTe₂.⁵¹ However, the CVD technique is still facing some challenges, like the synthesis of ternary 2D magnets like Cr₂Ge₂Te₆ (CGT),¹⁷ Fe₃GeTe₂ (FGT).¹⁸ Second, the CVD growth of TMDs is limited to monolayer only, and multilayers of single crystal growth remain a challenge. Third, the sharp and ordered interface of the CVD-grown magnetic heterostructure is difficult to achieve.

3.3. Mechanical exfoliation (ME)

It is the easiest and the fastest way to prepare pristine, highly crystalline, atomically thin layers of 2D vdW materials for SOT devices. Currently, mechanical exfoliation is employed to prepare atomically thin layers of 2D vdW materials from their bulk single crystals. Thus, multiple combinations of the vdW heterostructures can be stacked easily through this process to develop novel SOT devices. However, during the integration of the vdW materials, the air exposure in the gap between two layers may cause interfacial oxidation or contamination, which directly impacts the SOT efficiency by degrading the interface quality found in FGT/Pt heterostructures.⁵¹

3.4. Molecular beam epitaxy (MBE)

CVD requires a very high growth temperature, which leads to the growth of many vacancies in 2D materials. On the other hand, in mechanical exfoliation, the surface quality of the atomically thin sheet may be damaged during the process, and some residue may interfere with the interface quality. MBE could be advantageous in terms of layer-by-layer growth of ultrapure large atomic sheets under low growth temperatures and ultra-high vacuum.⁴⁹

Recently, FGT/(Bi $_{0.4}$ $_{0.4}$ Sb $_{0.6})_{2}$ $_{0.6})_{2}$ Te₃ (BST)⁵² bilayers were grown epitaxially by MBE on BaF₂ substrate and another TI-based heterostructure like (Bi $_{1 - x}$ $_{1 - x}$ Sb)₂Te₃/CoTb,⁵¹ CGT/(BiSb)₂Te₃⁵³ are also grown by MBE technique. Though MBE has the advantage in terms of controlling material thickness, its complex process and low growth efficiency remain a challenge.

3.5. Magnetron sputtering

Another synthetic strategy to grow 2D magnets is magnetron sputtering, frequently used in the semiconductor industry. Its large area of homogeneous growth and repeatability is the main advantage that makes it compatible with industry. The quality of the thin film depends on the growth pressure, base pressure, RF or DC power and substrate temperature. Recent work on the preparation of 2D materials for SOT devices includes PtTe₂⁵⁴ and TdS₂,⁵³ WTe₂/CoFeB⁵⁵ devices. It is observed that the Spin Hall conductivity prepared by sputtering has a significant value with respect to many 2D VDW materials.

Most of the 2D single crystalline TIs are grown epitaxially by the MBE technique. Still, it lacks in terms of mass production in the semiconductor industry, which has left the dependency on nonepitaxial TI thin film deposition techniques such as sputtering, CVD, etc. For example, high-quality BiSb films grown by MBE can be fabricated using sputtering techniques on Sapphire substrate.

4. SOT based on TIs

TIs are quantum materials with insulating bulk and metallic topological surface states (TSS). The TIs family remains an extensively pursued candidate to study the current-induced magnetic switching via SOT. The Bi₂Se₃ family are among the most promising one because of its extremely strong SOC arising from the electron’s spin and its orbital angular momentum interaction due to asymmetry in the crystal structure of the materials. Owing to this, TSS has a larger spin polarization efficiency. Thus, when conduction electrons flow through the topological surface states (TSS), they exhibit strong spin momentum locking, which, under the applied electric field, induces a nonequilibrium spin accumulation.⁵⁶ That’s why TI materials are considered to be efficient SOT materials. The main advantage of TI over conventional HM in NM/FM heterostructure is the efficient charge-to-spin conversion (SOT efficiency).²⁷

4.1. Experimental progress of TI-based SOT

The carrier density of TSS plays a vital role in influencing the efficiency of SOT in heterostructures based on TI. The SOT efficiency can be improved by adjusting the carrier density of TSSs through doping, as reported by Fan et al.⁵⁷ In 2014, Mellnik et al.⁵⁸ first reported the current induced SOT in Bi₂Se₃/Py heterostructure with a giant DL-SOT efficiency of 3.5 at room temperature using the ST-FMR technique. Although TIs have high resistivity, the damping-like spin conductivity ( $T_{DL})$ $T_{DL})$ is found to be similar to that of NM/FM heterostructure, but the magnitude of $T_{DL}$ $T_{DL}$ per unit current is much larger than that of heavy metals.⁵⁶ In the same year, Fan et al.⁵⁷ reported a heterostructure made of a magnetically doped TI and intrinsic topological insulator, Cr-(Bi_xSb $_{1 - x})$ $_{1 - x})$ 2Te3/(Bi_xSb $_{1 - x})_{2}$ $_{1 - x})_{2}$ Te at 1.9K where SOT strength increases by a factor of four upon doping with Cr on applying a top gate voltage. Khang et al.⁵⁹ have demonstrated ultralow power SOT-induced magnetization switching in BiSb/MnGa heterostructure. They reported the highest spin hall angle of 52 and the critical current for magnetization switching was $1.5 \times 1 0^{6}$ $1.5 \times 1 0^{6}$ A/cm² (Table 1). Wu et al.⁶⁰ have shown that the current density of TSS can be improved by varying the BiSb ratio in (Bi $_{1 - x}$ $_{1 - x}$ Sb $_{x})_{2}$ $_{x})_{2}$ Te₃ based heterostructure. Wang et al.⁶¹ have reported that the SOT efficiency depends on the thickness of the Bi₂Se₃/Py heterostructure. The efficiency increases with the decrease of TI thickness due to decreasing bulk states and 2D electron gas and increasing TSSs usually coexist in TIs.

The SOT efficiency of TI-based heterostructure is sensitive to temperature. They show much higher SOT efficiency at lower temperatures, primarily associated with the higher spin generation in the TSS at lower temperatures.⁶¹ Mahendra et al.²⁹ demonstrated the industry-friendly sputtering method to deposit Bi_xSe $_{1 - x}$ $_{1 - x}$ /CoFeB and achieve PMA by inserting a metal layer (Ta) at the junction of the structure. Here, the critical current ( $4.3 \times 1 0^{5}$ $4.3 \times 1 0^{5}$ A/cm $^{2})$ $^{2})$ to switch the magnetization was reduced from the previous order of 10⁶–10⁸A/cm² at room temperature. Shao et al.⁶² found that inserting a light metal (Mo) between TI and an FM layer like in Bi₂Se₃/, Bi₂Te₃/ and (BiSb)₂Te₃/Mo/CoFeB structures instead of a heavier one (Ta) could enhance the SOT efficiency due to less hindering of the spin diffusion, thermal stability and strong PMA at room temperature. The low switching current and high SOT efficiency obtained for the device Bi_xSe $_{1 - x}$ $_{1 - x}$ /Mo/CoFeB was $3 \times 1 0^{5}$ $3 \times 1 0^{5}$ A/cm² and 2.66. TIs have many different advantages, which makes them attractive for SOT applications. First, they possess extremely strong SOC and the conduction electron in the topological surface state exhibits strong spin momentum locking that causes spin current to flow perpendicular to the thin film. Second, the surface has Dirac-like band dispersion, resulting in a large intrinsic spin Hall effect. There are many TIs-based heterostructures having high SOT efficiencies, including (Bi $_{0.5}$ $_{0.5}$ Sb $_{0.5})_{2}$ $_{0.5})_{2}$ Te₃,⁵⁷ BixSe $_{1 - x}$ $_{1 - x}$ ,²⁹ Bi₂Se₃,⁶³ and others. So far, the largest SOT efficiency observed in (Bi $_{0.5}$ $_{0.5}$ Sb $_{0.5})_{2}$ $_{0.5})_{2}$ Te₃ is near about 450 at reduced temperature.⁵⁷ Room-temperature magnetization switching by spin torques was realized in topological material-based devices, and the switching current density $J_{C}$ $J_{C}$ is on the order of ∼10⁵A/cm², which is ∼1–2 orders of magnitude smaller than that in traditional NMs.⁵⁶

**Table 1. Comparison of different factors like SOT efficiency, spin Hall conductivity and switching current density for various TI/FM-based heterostructures.**
SOT material/FM	Fabrication/deposition technique	Spin Hall angle (SHA)	Conductivity ( $Ω$ $Ω$ m) $^{- 1}$ $^{- 1}$	$J_{C}$ $J_{C}$ (Acm $^{- 2}$ $^{- 2}$ )	Spin torque conductivity ( $ℏ$ $ℏ$ /2e) ( $\times 1 0^{3} Ω$ $\times 1 0^{3} Ω$ m) $^{- 1}$ $^{- 1}$	Measurement techniques	T (K)	Remarks	References
Bi₂Se₃ (8nm)/Py (8nm)	MBE	$ξ_{DL}$ $ξ_{DL}$ = 2–3.5	$5.7 \times 1 0^{4}$ $5.7 \times 1 0^{4}$		$σ_{DL} = 110$ $σ_{DL} = 110$ –200	ST-FMR	300	Thickness-dependent SOT efficiency	Mellnik⁵⁸
		$ξ_{FL} = 2$ $ξ_{FL} = 2$ –5			$σ_{FL} = 150$ $σ_{FL} = 150$
Bi $_{0.5}$ $_{0.5}$ Sb $_{0.5}$ $_{0.5}$ )2Te₃/(Cr $_{0.08}$ $_{0.08}$ Bi $_{0.54}$ $_{0.54}$ Sb $_{0.38}$ $_{0.38}$ ) Te₃ 3quintuple layer/6 quintuple layer	MBE	$ξ_{DL} = 150$ $ξ_{DL} = 150$ –450	$2.2 \times 1 0^{4}$ $2.2 \times 1 0^{4}$	$8.9 \times 1 0^{4}$ $8.9 \times 1 0^{4}$	$σ_{DL} = 1540$ $σ_{DL} = 1540$ –4675	SHH	1.9	Performed at 1.9K	Fan et al.⁵⁷
		$ξ_{FL} = 26$ $ξ_{FL} = 26$			$σ_{FL} = 286$ $σ_{FL} = 286$
Bi₂Se₃ (7.4nm/Co $_{0.77}$ $_{0.77}$ Tb $_{0.23}$ $_{0.23}$ (4.6nm)	MBE	0.16	—	$2.8 \times 1 0^{6}$ $2.8 \times 1 0^{6}$	—	—	300		Han et al.⁶⁴
Bi $_{0.9}$ $_{0.9}$ Sb $_{0.1}$ $_{0.1}$ /MnGa (10nm/3nm)	MBE	$ξ_{S} = 52$ $ξ_{S} = 52$	$2.5 \times 1 0^{5}$ $2.5 \times 1 0^{5}$	$1.5 \times 1 0^{6}$ $1.5 \times 1 0^{6}$	$σ_{DL} = 13000$ $σ_{DL} = 13000$	ST-FMR	300	The highest value of Hall angle at room temperature	Khang et al.⁵⁹
Bi_xSe $_{1 - x}$ $_{1 - x}$ /CoFeB	Sputtering	0.45–18.67	$7.8 \times 1 0^{3}$ $7.8 \times 1 0^{3}$	$4.3 \times 1 0^{5}$ $4.3 \times 1 0^{5}$	$σ_{DL} = 145$ $σ_{DL} = 145$	SHH	300	Thickness dependence and Bi_xSe $_{1 - x}$ $_{1 - x}$ is a polycrystalline structure	Mahendra et al.²⁹
			1.56–8.67			ST-FMR
Bi $_{0.85}$ $_{0.85}$ Sb $_{0.15}$ $_{0.15}$ (10nm)	Sputtering	$ξ_{DL} = 10.7$ $ξ_{DL} = 10.7$	$1.5 \times 1 0^{5}$ $1.5 \times 1 0^{5}$		$σ_{D} = 1600$ $σ_{D} = 1600$	SHH	300	Temperature-dependent SHA	Fan et al.⁷⁰
(Bi $_{0.2}$ $_{0.2}$ Sb $_{0.8}$ $_{0.8}$ )₂Te₃	MBE	$ξ_{DL} = 3.36$ $ξ_{DL} = 3.36$	—	$3.6 \times 1 0^{5}$ $3.6 \times 1 0^{5}$	$σ_{DL} = 84$ $σ_{DL} = 84$	SHH MOKE	300	Mo insertion layer leads to the high temperature stability	Pan et al.⁷¹
Bi₂Se₃/Gd_x (FeCo) $_{1 - x}$ $_{1 - x}$ (BiSb)₂ (6nm) Te₃ (15nm)	MBE	$ξ_{DL} = 3$ $ξ_{DL} = 3$	$1.8 \times 1 0^{4}$ $1.8 \times 1 0^{4}$	$1.2 \times 1 0^{5}$ $1.2 \times 1 0^{5}$	$σ_{s} = 120$ $σ_{s} = 120$	Optical MOKE	300	Compensated ferrimagnet is used	Wu et al.⁷¹

4.2. SOT based on Weyl semimetal

The Weyl semimetals are another class of topological materials possessing low energy linear dispersion and doubly degenerated points called Weyl points in the band structure. Electrons near the Weyl points behave as massless relativistic particles and have a strong spin-orbit coupling due to the nontrivial topology of the materials. They exhibit sufficiently large SOT due to time reversal-protected bulk and surface state and offer great potential for generating and controlling spin currents. Their natural high conductivities combined with strong SOC and high SOT efficiency make them a promising candidate for low-power magnetization switching. When an electrical current pass through the Weyl semimetal, the electron with distinct chirality near the Weyl points starts to move in response to the applied electric field. This movement of the electrons generates the spin current due to spin-momentum coupling. The generated spin current carries the spin angular momentum. It is transferred to the adjacent magnetic layers, which exert the torque on the magnetic layers, resulting in changes in the magnetization orientation. MacNeil et al.^68,69 did the pioneering work on 2D semimetal for SOT application in 2017 on WTe₂, and its SOT efficiency was 3.5. The SOT efficiency analyzed in WTe₂/NiFe (Permalloy) heterostructure using ST-FMR measurements with current along the b-axis varies from 0.09 to 0.51, showing a thickness dependence behavior.⁷⁰ These values are larger as compared to the typical heavy metals. The relation between the critical current density and thickness reveals the bulk-like characteristics of WTe₂. This bulk-like nature is related to the SHE, which generates the spin current. Due to broken inversion symmetry in WTe₂, there is no 180^∘ rotational symmetry about the c-axis. Therefore, it can exhibit a series of anisotropic phenomena. Further, the NiFe layer on the WTe₂ layer exhibits uniaxial magnetic anisotropy with an easy and hard axis along the a- and b-axis of WTe₂. In another heterostructure of WTe₂/Py, SOT efficiency was found to be 0.51,⁷⁰ and the power consumption required to switch the magnetization is much lower than the TI/FM and NM/FM-based heterostructure. The inherent out-of-plane damping like SOT in Weyl semimetals, like WTe₂, will facilitate the magnetic field-free magnetization switching for perpendicular anisotropy magnets, which is required for device applications.⁷¹

5. SOT based on TMDs

In TIs, spin momentum locking was responsible for nonequilibrium spin accumulation at the interface. In TMDs, spin momentum locking is also predicted due to TSS and large SOC. Materials with high SOC are a prerequisite to gain excellent SOT. So accordingly, Transition Metal Dichalcogenides (TMDs) become an obvious choice for SOT devices due to the presence of intrinsically strong SOC. They possess naturally strong SOC due to heavy metals like Mo, W and broken inversion symmetry.^16,71,72 TMDs have a general chemical formula MX₂ (M: Mo, W, Ta) and (X: S, Se, Te). As mentioned, the physical origin of SOT is the transfer of the orbital angular momentum through an exchange process between an NM layer and an FM layer. Now, replacing NM with TMDs, the monolayer limit can produce pure spin current in the interface, and because of the layered structure, they have tunable conductivity.

5.1. Experimental progress of SOT in TMDs/FM heterostructure

To date, numerous research achievements have been made in the TMD/FM heterostructures. A number of synthesis techniques are used for TMDs, namely ME, CVD, MBE, sputtering and measurement techniques used like MOKE, SHH and ST-FMR. The pioneering work from MacNeill et al.⁶⁸ on TMD semimetals using the ST-FMR technique in the field of spintronics was based on the characterization of DL and FL-SOTs of transverse, longitudinal and perpendicular spins generated in exfoliated semimetals and 3d ferromagnets. The conventional SOT torque conductivity ( $σ_{FL})$ $σ_{FL})$ found to be $3.6 \times 1 0^{3}$ $3.6 \times 1 0^{3}$ ( $ℏ$ $ℏ$ /2e) ( $Ω$ $Ω$ m) $^{- 1}$ $^{- 1}$ when current flows along a-axis and corresponding $σ_{FL}$ $σ_{FL}$ and $σ_{DL}$ (unconventional SOT) are, respectively, $9 \times 1 0^{3}$ ( $ℏ$ /2e) ( $Ω$ m) $^{- 1}$ and $8 \times 1 0^{3}$ ( $ℏ$ /2e) ( $Ω$ m) $^{- 1}$ . Shi et al.⁷⁰ have observed the SOTs of WTe₂/Py heterostructure switch the Py layer with weak in-plane magnetic anisotropy at a current density of $3 \times 1 0^{5}$ A/cm². Shao et al.⁴⁶ examined the REE-induced SOTs generated by CVD growth single layer (SL) MoS₂ and WSe₂ with CoFeB at room temperature. They performed the current-induced SOT using the second harmonic Hall (SHH) approach and concluded that the strong SOC and inversion symmetry-breaking REE are responsible for the field-like torque ( $τ_{FL})$ in the SL MX₂/CoFeB system. The spin conductivity of MoS₂ and WSe₂ was $2.9 \times 1 0^{3}$ and $5.5 \times 1 0^{3}$ ( $ℏ$ /2e) ( $Ω$ m) $^{- 1}$ , respectively, indicating both SL of MoS₂ and WSe₂ indicate an appreciable SOT efficiency. Zhang et al.⁷³ reported the SOTs in a monolayer MoS₂/Py heterostructure. There, the observed symmetric peak is about four times bigger than the antisymmetric peak, as confirmed by the ST-FMR ( $τ_{FL} < < τ_{DL})$ . Stiehl et al.⁷⁴ observed the DL-SOT of transverse and perpendicular spins in the $β$ -MoTe₂/Py heterostructure. The DL-SOT of perpendicular spins is one-third stronger than the WTe₂/Py and was attributed to the perpendicular spin current contribution from the surface of the $β$ -MoTe₂. Therefore, perpendicular spins can be produced without breaking the inversion symmetry. However, in the 1T’-MoTe₂/Py heterostructure, the nonmagnetic layer produces no DL-SOT of perpendicular spins. Instead, it generates a nonzero DL-SOT of transverse spins that switches the magnetization of Py at a current density of $6.7 \times 1 0^{5}$ A/cm $^{- 2}$ .⁷⁵ Recently, Bangar et al. demonstrate spin-to-charge conversion in large-area ML TMDs, namely, MoS₂, MoSe₂, WS₂ and WSe₂ with the efficiency that exceeds that of the traditional HMs such as Pt by about at least one order⁷⁶ while Bansal et al. demonstrate the magnetization dynamics on MoS2/Py heterostructure and observed the enhanced damping in 3.5L MoS2/Py structure. The enhanced damping is attributed to the presence of defects present in the interface.⁷⁷ In addition to the above systems, several other TMDs like 1T-TaS₂,^78,79 1T-PtTe₂,⁸⁰ NbSe₂⁸¹ and ZrTe₂⁸² were explored as spin torque generating materials.

However, from a practical application viewpoint, the in-plane magnetic TMD/FM is not preferred due to their poor thermal stability down to small-scale limits. To improve the system stability, Xue et al.⁸³ have introduced the TMD/NM/FM-based heterostructure, in which the NM interlayer is used to establish the perpendicular magnetic anisotropy of the FM layer and generates a sufficient spin current. In contrast, the TMD layer serves as spin absorption to enhance the SOT effect. They performed a comprehensive investigation on the electrical transport properties of WSe₂/Pt/Co/AlO_x heterostructures and found that spin efficiency increases with the WSe₂ thicknesses, suggesting that WSe₂ acts as a good spin sink layer (Table 2).

**Table 2. Comparison of different factors like spin Hall angle, spin Hall conductivity and switching current density for different TMD/FM-based heterostructures.**
SOT material/FM	Space/point group	Nature	Fabrication/deposition technique	Spin hall angle (SHA)	Conductivity ( $Ω$ m) $^{- 1}$	Spin torque conductivity ( $ℏ / 2 e$ ) ( $\times 1 0^{3} Ω$ m) $^{- 1}$	Measurement techniques	Remarks	References
MoS₂ (1L)/CoFeB (3nm)	P6/mmc	Semiconductor	CVD	0.592	$2.1 \times 1 0^{4}$	$σ_{FL} = 2.88$	SHH	Thickness-dependent SOT efficiency	Shao et al.⁴⁶
WSe₂ (1L)/CoFeB (3 nm)	P6/mmc	Semiconductor	CVD	—	—	$σ_{FL} = 5.2$	SHH	Thickness-dependent SOT efficiency	Shao et al.,⁴⁶
WTe₂ (5.5nm)/Py (6nm)	Pmn2₁	Semimetal	Exfoliation	—	—	$σ_{A} = 9 \pm 3$	ST-FMR	Thickness independent $< 10$ nm	MacNeill et al.⁶⁸
						$σ_{S} = 8 \pm 2$
						$σ_{B} = 3.6 \pm 0.8$
WTe₂ (5.8–122nm)/Py (6nm)	Pmn2₁	Semimetal	Exfoliation	0.09–0.51 (current along the b-axis)0.029 (current along a-axis)	—	$σ_{FL}$ : Oersted field contribution $σ_{DL} =$ 4–60 $σ_{DL} (u) = 6$	ST-FMR	Layer-dependent SOT efficiency	Shi et al.⁷⁰
MoTe (0.7–14.2nm)/Py (6nm)	P2₁m	Semimetal	Exfoliation	0.032	$1.8 \times 1 0^{5}$	$σ_{FL}$ : Oersted field contribution	ST-FMR	Layer-dependent SOT efficiency	Stiehl et al.⁷⁴
						$σ_{DL} =$ 4.7–8.2
						$σ_{D L}^{(U)} =$ 0–1.8
						$σ_{FL} (u) =$ 0–1
PtTe₂ (5nm)/Py (2.5–10nm)	P3m1	Semimetal	Two-step sputtering	0.05–0.15	0.3– $3 \times 1 0^{- 6}$	$σ_{s} =$ 20–160	ST-FMR	Layer-dependent SOT efficiency	Xu et al.⁸⁰
				$ξ_{DL} = 0.09$
				$ξ_{FL} = -$ 0.004
NbSe₂ (0.9–7)/Py (6nm)	P63/mmc	Metal	Exfoliation	0.005–0.013	$6 \times 1 0^{5}$	$σ_{A}$ : Oersted field contribution	ST-FMR	Layer-dependent SOT efficiency	Guimaraer et al.⁸¹
						$σ_{s} =$ 0–14
						$σ_{B} =$ 2–3.5
						$σ_{s} = - 1.5$ –3.5

6. SOT Based on 2D vdW Magnets

Apart from the nonmagnetic layer, the ferromagnet (FM), ferrimagnet and antiferromagnetic (AFM) layers play a crucial role in realizing efficient SOT-based devices. Compared to AFM, ferromagnets and ferrimagnets are easily integrated into electric circuits and show efficient switching by SOTs. The electrical measurements of the magnetization states and switching are much more challenging in the case of AFM.^84,85 However, AFMs have great potential in data storage and high-frequency terahertz device applications. A typical application is to stabilize the magnetization of the “fixed layer” in magnetic tunnel junctions or spin valves. In vdW AFM/FM heterostructures, exchange bias is induced via exchange coupling,^86,87,88 and such type of exchange coupling can be tuned by the gate voltage.⁸⁹ This brings the realization of the efficient SOT devices in such devices, for instance, providing in-plane exchange bias for SOT switching PMA magnets.

6.1. Experimental progress of SOT in vdW magnets

The discovery of vdW FMs Fe₃GeTe₂ (FGT), Cr₂ Ge₂Te₂ (CGT) and CrI₃^17,18 brought a significant impact on the field of magnetism and spintronics. In fact, before 2017, it was believed that long-range magnetic order could not exist at finite temperatures in the 2D system according to the Mermin–Wagner theorem.⁸² However, after the groundbreaking work from Gong et al. and Huang et al.,^17,18 it was found that the magnetic properties can be retained down to atomic layer thickness.^90,91 Most strikingly, the other properties like curie temperature,^92,93 magnetic domain structure and coercivity^92,93 can be tuned significantly by simply controlling the layer thickness, strain,⁹² exchange bias^86,98 and proximity effect.⁹⁵ SOT among the vdW magnets was first demonstrated on FGT/Pt heterostructure by Wang et al.⁹⁶ and Alghamdi⁹⁷ (Table 3). In this system, the spin current generated by SHE due to the presence of heavy metal Pt exerts a damping-like SOT of 0.1 on the magnetic layer and has relatively high stable PMA and coercivity (Fig. 2). Critical current density for magnetization switching was in the order of 10⁷Acm $^{- 2}$ .^51,83 Zhang et al.⁹⁴ investigated this system and were able to improve the damping like SOT to 0.18 by improving the interface quality, which is an important parameter to improve the SOT efficiency.

Fig. 2. Current driven perpendicular magnetization switching for (a) FGT/Pt heterostructure under an in-plane magnetic field of 500 Oe and 100K $^{96}$ and (b) CGT/W heterostructure under an in-plane magnetic field of 1000 Oe and 150K.⁹⁹

**Table 3. Comparison of different factors like spin Hall angle, switching current density for different magnetic vdW/FM-based heterostructures.**
SOT material/FM	Fabrication/deposition technique	Spin Hall angle (SHA)	Temperature (K)	Current density (A-cm²)	Measurement techniques	Remarks	References
FGT (4nm)/Pt (6nm)	Exfoliation	0.12	120	$7.4 \times 1 0^{7}$	SHH	High depinning field and strong PMA	Wang et al.⁹⁶
FGT (15–23nm)/Pt(5nm)	Exfoliation	0.11–0.14	224.5	$1.2 \times 1 0^{7}$	SHH	Sufficiently high Tc,	Alghamdi et al.⁹⁷
FGT (FL)/Pt (2 layer)	Exfoliation	0.18	208	10⁶	SHH	Large switching in magnetization	Zhang et al.⁹⁴
CGT (8nm)/Ta (10nm)	Exfoliation	0.25	<65	$5 \times 1 0^{5}$	SHH	Low temperature value	Ostwal et al.⁹⁵
CGT (10nm)/W (7nm)	Sputtering	—	150	$2.4 \times 1 0^{6}$	MOKE	Elevation in Tc and enhanced PMA	Zhu et al.⁹⁹
CrI₃ (30–150nm)/Pt(5nm)	Exfoliation	—	—	$2.5 \times 1 0^{6}$	MOKE	Thickness dependence	Tang Su, et al.⁵⁶
WTe₂ (10–15nm)/Fe $_{2.78}$ GeTe₂ (7.3nm)	Exfoliation	4.6	150	$3.9 \times 1 0^{6}$	—	Thickness-dependent, unconventional SOT	Shin et al.¹⁰¹
WTe₂ (25.8nm)/Fe $_{2.78}$ GeTe₂ (10.2nm)	Exfoliation	—	190	$4.2 \times 1 0^{6}$	—	Thermally assisted field-free magnetization switching with PMA	Kao et al.¹⁰⁰
Bi₂Te₃ (8nm)/Fe₃GeTe₂ (4nm)	MBE	0.7	300	$2.2 \times 1 0^{6}$	SHH	Temperature and thickness-dependent SOT efficiency	Wang¹⁰²
FGT (6nm)/Bi $_{1 - x}$ Sb_x)₂Te₃ (8nm)	Exfoliation	—	100	$5.8 \times 1 0^{6}$	—	Current density increases as × increases	Fujimura et al.¹⁰³
			180	$1.7 \times 1 0^{6}$

CGT is another well-studied vdW ferromagnet.¹⁸ SOT-based study has been demonstrated on CGT/Ta heterostructure (curie temperature <65K), which has a low current density of $5 \times 1 0^{5}$ Acm $^{- 2}$ for switching the magnetization.⁹⁵ Zhu et al.⁹⁹ reported that SOT switching on the CGT/W bilayers with enhanced interface quality leads to improving the Curie temperature to 150K.

Recently, current-induced SOT for TI-based vdW magnets brought an exciting flavor to this field as nearly 88% magnetization switching becomes possible in MBE-grown CGT/(Bi $_{1 - x}$ Sb $_{x})_{2}$ Te₃ heterostructure.⁷³ The current density for Sb doped (Bi $_{0.7}$ Sb $_{0.3})_{2}$ Te₃/FGT was $5.8 \times 1 0^{6}$ Acm $^{- 2}$ at 100K.⁹⁵ In TMD-based vdW magnetic heterostructure WTe₂/Fe $_{2.78}$ GeTe₂, field-free switching magnetization with current density along a low symmetry axis of $9.8 \times 1 0^{6}$ Acm $^{- 2}$ at 170K has been observed.¹⁰⁰ In the same bilayer structure, Shin et al.¹⁰¹ also reported the magnetization switching at a current density of $3.9 \times 1 0^{6}$ Acm $^{- 2}$ (Table 3), showing that the heterostructures achieved SOT properties and performed excellently but at low temperatures. In general, heavy metals like Pt are used as a preferred material for achieving SOT switching of FGT.^96,97 But Wang et al.¹⁰² have reported that the TI of Bi₂Te₃ is superior for charge-spin conversion with 2D vdW ferromagnet, hinting toward the possible reason for the interfacial spin transparency arising due to the vdW gapped interface between Bi₂Te₃ and FGT.¹⁰²

6.2. SOT based on vdW Monochalcogenides

2D vdW ferroelectric materials have introduced a fresh prospect in the next generation toward nanoelectronics and spintronics. They possess a broken inversion symmetry and are known as ferroelectric Rashba semiconductors (FERSCs) because they are ferroelectric in nature and display giant Rashba spin splitting of the bulk bands, with an additional advantage that their direction of the spin in each Rashba sub-band can be reversed by switching the ferroelectric polarization (Fig. 3(b)).^104,105 Their spontaneous polarization is nonvolatile and switchable, ideal for electric field control of spintronic devices resulting in low power consumption,^102,106 and the same has been reported for 2D vdW ferroelectrics such as BiTeI and GeTe.^104,106 Therefore, 2D FERSC/metals with strong SOC may trigger a revolution for the next generation of spintronics devices such as spin transistors and memories.

Fig. 3. (a) Set up for studying the ferroelectric switching of spin current conversion in GeTe. (b) Showing the changes in the converted current demonstrating the nonvolatile ferroelectric control of the spin current conversion by the polarization switching of GeTe. SMU: source meter unit, H: magnetic field, Ic: charge current density, $μ_{0} H$ : applied magnetic field, $P_{in}$ : inward ferroelectric polarization, $P_{out}$ : outward ferroelectric polarization. Figures are reproduced from Ref. 105.

6.3. Potential applications of SOT

SOT has attracted a huge amount of attention as it has overcome the difficulties in STT technology like high speed, low power consumption for manipulating the magnetization, writing information and good endurance value. Though STT still remains a dominant writing mechanism due to its local action and scalability, rigorous progress in SOT-MRAM is urgently required.

6.4. SOT-MRAM

In contrast to STT-MRAM, SOT-MRAM (MTJ) has three terminals where reading and writing paths are decoupled, providing a high-speed operation, high endurance for high-speed cache memories and compatibility with the existing CMOS technology. The SOT-MRAM units developed so far can be categorized based on the orientation of the magnetic anisotropy (magnetic easy axis) of the MTJ: (i) collinear with charge current in the film plane (x-type), (ii) perpendicular to the current in the film plane (y-type) (iii) out of the film plane (z-type) as shown in Figs. 4(a)–4(c), respectively.¹⁰⁷ The z-type has the advantage of its larger thermal stability over other types at downscale. The x- and z-type exhibit very fast switching due to perpendicular alignment of the spin polarization and magnetic easy axis as it immediately fixed the torque.

Fig. 4. (Color online) Schematics of the three main device geometries of three-terminal SOT-MRAM (a) x-type, with a switching layer (grey) has the easy axis in the film plane and an external field along z-axis (b) y-type, with a switching layer has an in-plane easy-axis (c) z-type, with a switching layer has an out-of-plane magnetic easy axis and an external field along x-axis. Arrows in red, brown and blue indicate the current, magnetization of the switching layer and flow of the spin-polarized electrons, respectively.

The operation of SOT-MRAM devices has been reported by many groups.⁹⁶ For practical use of such devices, the critical current required for effective magnetization switching is about 100 $μ$ A or less.¹⁰⁸ Larger write current invites bigger cell size and high-power operation. An important milestone was reached by Natsui et al.¹⁰⁸ by demonstrating the first SOT-MRAM chip with 4kB capacity. In order to achieve excellent SOT devices, SOT materials of high efficiency must be incorporated. As discussed above, a group of materials with high effective SOT efficiency, including TIs, semimetals, TMDs and other magnetic vdW materials, will play a critical role in its potential applications: first, reducing switching current density; second, free switching. 2D vdW materials have the potential to normalize the above two.

6.5. SOT spin logic

SOT-based spin logic is based on the SHE to switch the magnetization for Boolean logic operation and is an alternative to the conventional CMOS technology in terms of high computing capability and low power dissipation. Besides being a three-terminal device, it has decoupled reading and writing paths, making the processing faster. Actually, there are five essential characteristics for building practical logic applications: (a) nonlinearity: output with nonlinear response to the input; feedback elimination: outputs should not affect the states of inputs; gain: with an independent power source for signal output, concatenability: input and output in the same form, and a complete set of Boolean operations (AND, OR and NOT, NAND and NOR, say).^109,110 Exploring the prospective candidates of spin logic gate devices, which make the computer process faster (sub-nanosecond range), is highly desirable to confront the huge volumes of data nowadays. For that, one must integrate different logic functions into a single cell, which remains a con for current silicone-based logic devices. Therefore, the SOT has the role of eliminating the current deficiency of the silicon-based technology by inducing SHE in the NM(HM)/FM-based structure discussed above to achieve PMA. The spin logic cell integrated with the maximum number of Boolean functions like AND, OR, NOT, NAND and NOR can be programmed between multiple logic functions by changing the direction of the magnetic field and the initial state of the magnetic field. A magnetoelectric spin-orbit (MESO)¹¹¹ logic devices have been introduced to develop computer architectures with enhanced logic density, minimum energy consumption and nonvolatility.

6.6. SOT in neuromorphic computing

The name suggests that the circuitry idea of neuromorphic computing is inspired by the brain itself. However, execution on the processor is fundamentally different from the brain. In the Artificial Intelligence (AI) era, the existing computing technology suffers from high power consumption and slow processing speed, putting a stray in computational works. SOT devices can be engineered to have required properties like nonvolatility, outstanding read/write endurance, and high-speed voltage operation that can carry information across distances via spin currents.¹⁰⁸ Magnetic bilayer-based Hall devices can show SOT switching without any magnetic field and behave as artificial synapses. Zhang⁶⁶ have reported the NM/FM-based memristive devices. Kurenkov et al.⁶⁵ demonstrated the key functionalities of a synapse in the AFM/FM bilayer. Using SOT nanooscillators, the realization of high-density and low-power computation becomes easy to achieve. 2D materials, due to their peculiar properties down to monolayer dimension, can expected to achieve much faster and more robust SOT devices for neuromorphic computation. The atomically thin channels of 2D materials coupled with the atomically abrupt interfaces in vdW heterojunctions result in exceptionally strong electrostatic coupling, especially in a dual-gated geometry. This exquisite gate control enables tunable synaptic learning without relying on complicated circuitry to control the pulse shapes, as is often required in conventional memristor-CMOS circuits. The planar architecture of 2D materials is also a natural platform for multiterminal synaptic devices to mimic biological functionality (e.g., hetero-synaptic plasticity) and implement reservoir computing algorithms.⁶⁷

7. Conclusions and Future Outlook

Current induced SOT becomes a powerful technique for controlling the magnetization without dependence on external magnetic stimuli, which could provide high-performance spintronic devices, namely SOT-MRAM, SOT spin logic and neuromorphic computing. The popularity gained by SHE since its introduction by Hirsch et al.²³ in 1999 is just unimaginable. Since then, the research has shifted noticeably from fundamentals to applied, particularly on the SOT materials and improvement in the switching mechanism. Continuous efforts are still going on to enhance the SOT efficiency and lower the critical current density required for switching the magnetization. SOT-based materials are better than STT in terms of charge-to-spin conversion and are easily tunable by applying an electric field. Thus, SOT is becoming a novel way to switch the magnetization more efficiently. Focusing on 2D vdW materials is one of the stories of that continuous effort. Among many numbers from the 2D vdW family members, TMDs, TIs and vdW magnets have proved to be more mature for realizing large SOT efficiency. For the same reason, 2D materials-based SOTs are becoming hotspots in the field of spin torque and spin current.

For practical SOT devices, our effort must be to connect this new technology with the existing one, i.e., CMOS technology, and to bring the small-scale production of SOT devices to wafer scale. Magnetic materials possess excellent intrinsic qualities like gate tunability layer-dependent magnetic properties, whereas nonmagnetic materials act as superior spin source materials. Integration of both could benefit the SOT industry and must be our fundamental research interest.

The magnetization switching efficiency of a SOT device is much more dependent on the interface quality between the heterolayers. For example, the efficiency of the FGT/Pt device studied by Alghamdi et al.⁹⁷ was nearly 0.1, whereas Zhang et al.⁹⁴ found about 0.18 by improving the interface quality. Researchers in this field are trying to employ the in-situ synthesis method to enhance the quality of the materials and the interface. Zhang et al.⁹⁴ introduce the vacuum exfoliation approach to fabricate the device.

Most atomically thin magnetic materials have relatively low Curie temperature ( $T_{c})$ and strong PMA. But for practical purposes, we need to develop high $T_{c}$ magnetic materials. Efforts are going on to enhance the $T_{c}$ by assembling the layers with other materials and introducing the light metals at the interface,⁴⁶ doping and strain.⁵⁶

In the era of information processing and storage of extensive data systems and faster communications, SOT-based MRAM proved to be an excellent candidate for next-generation memory in terms of low power consumption and high speed. Though introducing the 2D vdW materials as an active layer on the SOT device stimulates higher efficiency, still further optimization is required.

SOT-based spin logic shows great promise with the prospect of using spin instead of charge leads to process the information. In this quantum era, ultrafast, programmable and multifunctional spin logic devices based on SOTs have become necessary.

Artificial synapses and neural networks based on the SOTs for artificial intelligence applications need further optimization with prospects of high speed and high endurance to meet the current requirements.

ORCID

Towhidur Rahaman https://orcid.org/0009-0001-3318-4446

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