# Control of spin-charge conversion in van der Waals heterostructures

Regina Galceran, Bo Tian, Junzhu Li, Frédéric Bonell, Matthieu Jamet, Céline Vergnaud, Alain Marty, Juan Sierra, Marius Costache, Jose García, et al.

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Regina Galceran, Bo Tian, Junzhu Li, Frédéric Bonell, Matthieu Jamet, et al. Control of spin-charge conversion in van der Waals heterostructures. APL Materials, 2021, 9 (10), pp.100901. 10.1063/5.0054865. hal-03409472

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# Control of spin-charge conversion in van der Waals heterostructures

Cite as: APL Mater. 9, 100901 (2021); doi: 10.1063/5.0054865

Submitted: 22 April 2021 • Accepted: 6 July 2021 •

Published Online: 12 October 2021

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Regina Galceran,<fnref n="1" /> ID Bo Tian,<fnref n="2" /> ID Junzhu Li,<fnref n="2" /> Frédéric Bonell,<fnref n="3" /> ID Matthieu Jamet,<fnref n="3" /> ID

Céline Vergnaud,<fnref n="3" /> ID Alain Marty,<fnref n="3" /> ID Jose H. García,<fnref n="1" /> ID Juan F. Sierra,<fnref n="1" /> ID Marius V. Costache,<fnref n="1" /> ID

Stephan Roche,<fnref n="1" />,<fnref n="4" /> Sergio O. Valenzuela,<fnref n="1" />,<fnref n="4" /> ID Aurélien Manchon,<fnref n="5" /> Xixiang Zhang,<fnref n="2" /> ID

and Udo Schwingenschlögl<fnref n="2" />,<fnref n="4" />⁾ ID

## AFFILIATIONS

**Note:** This paper is part of the Special Topic on Emerging Materials for Spin-Charge Interconversion.

a) Author to whom correspondence should be addressed: udo.schwingenschlogl@kaust.edu.sa

## ABSTRACT

The interconversion between spin and charge degrees of freedom offers incredible potential for spintronic devices, opening routes for spin injection, detection, and manipulation alternative to the use of ferromagnets. The understanding and control of such interconversion mechanisms, which rely on spin-orbit coupling, is therefore an exciting prospect. The emergence of van der Waals materials possessing large spin-orbit coupling (such as transition metal dichalcogenides or topological insulators) and/or recently discovered van der Waals layered ferromagnets further extends the possibility of spin-to-charge interconversion to ultrathin spintronic devices. Additionally, they offer abundant room for progress in discovering and analyzing novel spin-charge interconversion phenomena. Modifying the properties of van der Waals materials through proximity effects is an added degree of tunability also under exploration. This Perspective discusses the recent advances toward spin-to-charge interconversion in van der Waals materials. It highlights scientific developments which include techniques for large-scale growth, device physics, and theoretical aspects.

© 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0054865

## I. INTRODUCTION

In the search for continued miniaturization of microelectronic devices, two-dimensional (2D) materials, such as graphene and its siblings, offer opportunities to radically change the technology landscape by enabling the discovery of revolutionary device paradigms.<sup>1,2</sup> Although the path to technological implementation is long and hard, the extraordinary burst of 2D material synthesis during the last decade allowed for the fabrication of a wide variety of 2D materials,<sup>1,3</sup> opening thrilling avenues for the design of innovative atomically flat devices. 2D materials possess strong covalent bonds between atoms in the plane, but their out-of-plane

interaction is mediated by 1000 times weaker van der Waals (vdW) forces, which enables an easy delamination of these layered materials. The interfaces obtained are defect-free and extremely sensitive to their environment.<sup>4</sup> This offers a unique playground of study, as the properties of one material can be transferred to its neighbor by proximity effects when stacking different materials in complex vdW heterostructures. While the device performance is yet to challenge the existing traditional technology,<sup>5</sup> their ability for unconventional operation nurtures the search for innovative concepts, such as the inclusion of the spin, pseudospin, and valley degrees of freedom.<sup>6,7</sup>

To address the issues related to the energy loss in devices (e.g., gate leakages, interconnects, and refreshing non-volatile

<footnote n="1">¹Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, 08193 Barcelona, Spain</footnote>

<footnote n="2">²King Abdullah University of Science and Technology (KAUST), Physical Science and Engineering (PSE), Thuwal 23955-6900, Saudi Arabia</footnote>

<footnote n="3">³University of Grenoble Alpes, CNRS, CEA, Spintec, 38000 Grenoble, France</footnote>

<footnote n="4">⁴ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain</footnote>

<footnote n="5">⁵Aix-Marseille Université, CNRS, CINaM, Marseille, France</footnote>
memories), spin angular momentum can be used to store, trans-
mit, and manipulate information with high efficiency in terms of
energy consumption. 2,8–11 In fact, highly efficient spin transport 12–14
and long spin diffusion 15–21 can be achieved in graphene and transi-
tion metal dichalcogenides (TMDs), 22,23 enabling the fabrication of
spin-field effect transistors 24–26 and novel spin filtering devices. 27,28
However, traditional spin-devices require spin injection from mag-
netic elements, usually made of transition metal materials such as
NiFe or CoFe, and the application of magnetic fields to define their
magnetization orientation. This is a challenge because good interface
quality between the ferromagnet (FM) and the 2D vdW substrate
is of critical importance and difficult to achieve. 12,13,29 Furthermore,
the use of magnetic fields to switch the magnetization limits the den-
sity of magnetic elements. These limitations severely hindered the
performance of flat spintronic devices despite the apparent appeal of
2D systems. However, they may be circumvented and new opportu-
nities may arise by adopting different strategies. These range from
the use of recently discovered 2D magnetic materials (CrSe₂, VSe₂,
etc.) to the exploitation of the spin-charge interconversion (SCI)
that takes place in materials with large spin-orbit coupling (SOC),
among which we find TMD semimetals and topological insulators
(TIs). The SCI enables electrical generation of spin currents or spin
densities, which in turn can be used to generate a torque on an
adjacent FM, thus allowing for all-electrical manipulation of the
magnetization direction in the FM.

SOC is the responsible interaction for the locking between the
spin and the orbital angular momenta and results in a large number
of physical phenomena, such as magnetic anisotropy and damp-
ing, 30,31 spin relaxation, 32 and the spin Hall effect (SHE). 33,34 The
latter is of particular importance for spintronic technologies because
it offers a route for the electrical generation of spin currents, one of
the most crucial limiting factors in current devices. This is why in
recent years much attention is drawn toward materials presenting
large SOC and inversion symmetry breaking, both needed for most
of the spin-orbit phenomena of interest. In addition, a particular
type of SOC that enables the direct coupling between the spin of
the electron and its linear momentum can be used for the electrical
generation of non-equilibrium spin density, offering a different path
for the electrical manipulation of magnets through the spin. Such an
effect is referred to as the inverse spin galvanic effect (iSGE) or the
Rashba–Edelstein effect.

Recently, researchers proposed to use the iSGE³⁵,³⁶ and SHE³⁷,³⁸ to generate current-driven spin-orbit torque (SOT), enabling the electrical manipulation of ultrathin magnets. ³⁹⁻⁴¹ The recent observation of current-driven magnetization switching in inversion symmetry broken transition metal systems (Pt/Co,⁴² Ta/NiFe,⁴³ etc.) initiated a massive amount of effort in this direction. Ultrafast switching was demonstrated,⁴⁴,⁴⁵ and SOT is currently considered a promising method for the next generation of magnetic random-access memories, as explicitly stated in the international roadmap for devices and systems and currently being pursued by major industries.⁴⁵

Among the vast catalog of novel 2D materials, TMDs stand
out as a versatile platform for the advancement of disruptive
flat microelectronics and spintronics.⁵,⁶,¹¹,⁴⁶⁻⁴⁸ Indeed, in contrast
to graphene, TMDs have a large SOC⁴⁹⁻⁵¹ that was successfully
exploited for gate-controlled spin manipulation in graphene/TMD
inter interfaces.²⁵,²⁶,⁵² In addition, some TMDs, such as WS₂ and MoS₂,

possess a large bandgap that promotes optoelectronic operation⁵³,⁵⁴
and the realization of light-driven spin-valley coupling.⁵⁵⁻⁶⁰ Beyond
the most commonly found semiconducting phase, the TMD fam-
ily also exhibits a wide variety of electronic behaviors ranging from
a Weyl semi-metallic state⁶¹⁻⁶³ to superconductivity⁶⁴,⁶⁵ as well
as magnetism.⁶⁶ These features are particularly appealing for the
realization of vdW heterostructures⁵⁰,⁵¹ that could combine all of
them.²⁵,²⁶

Another important class of vdW materials concern bismuth-
antimony chalcogenides that display topological properties. TIs
have an insulating bulk and spin-orbit coupled surface states.⁶⁷,⁶⁸
The large spin-momentum locking of their surface states makes
them ideal candidates for SCI. Recent progress includes the real-
ization of current-driven SOT in systems using Bi-chalcogenide TIs
(Bi₂Se₃/NiFe)⁶⁹,⁷⁰ and the realization of current-driven switching at
room temperature⁷¹⁻⁷³ with record low currents required. Note that
SOT also was realized using TMD monolayers⁷⁴,⁷⁵ but with a much
weaker efficiency as compared to TIs.

In this Perspective, we present the current state of the art
and perspectives on the control of SCI in vdW materials toward
the realization of ultra-compact spintronic devices. The complexity
of the studied phenomena and the continued surge of new mate-
rials make synergy between experiment and theory particularly
useful in developing improved large-scale growth methods of such
vdW materials to facilitate their implementation in upcoming
technologies.

## II. GROWTH AND MANIPULATION OF 2D MATERIALS AND VDW HETEROSTRUCTURES

### A. Chemical vapor deposition (CVD)

Currently, most 2D materials for fundamental research are pro-
duced by mechanical exfoliation, which ensures high crystal quality
but with limited yield and size.⁷⁶ Since the report on the synthe-
sis of graphene using chemical vapor deposition (CVD),⁷⁷ in which
volatile precursors react or decompose, this method developed into
a popular and reliable technique for the synthesis of different 2D
materials, such as h-BN, MoS₂, WSe₂, CrI₃, CrTe, MoS₂, and 2D
vdW heterostructures⁵⁰,⁷⁸ (Fig. 1).

For wafer-scale synthesis of 2D materials, a number of
approaches were developed, including precise control of the growth
process,⁷⁹⁻⁸¹ substrate engineering,⁸²⁻⁸⁴ chemical doping,⁸⁵⁻⁸⁷
transfer,⁸⁸⁻⁹⁰ surface morphology,⁹¹⁻⁹³ and twisted bilayers,⁹⁴⁻⁹⁶
Interestingly, adlayer-free large-area single-crystal graphene was
realized on single-crystal Cu foil,⁹⁷ which was obtained from
commercial Cu foil by the contact-free annealing method.⁹⁸ The
CVD growth of h-BN, a popular 2D insulator resembling the
hexagonal crystal structure of graphene, and 2D heterostructures
of h-BN with graphene and TMDs attracted great interest.⁹⁹⁻¹⁰¹
For example, large-area high-quality h-BN was synthesized on
single-crystal Cu.¹⁰²

Many 2D materials with excellent semiconductor character-
istics and high current on/off ratios, such as MoS₂, MoSe₂, WS₂,
and WSe₂, were fabricated using CVD.⁷⁸,¹⁰³,¹⁰⁴ In particular, stable
and controllable growth of large-scale MoS₂ films was achieved by
a number of research groups.¹⁰⁵,¹⁰⁶ A growth and transfer method
of large-area high-quality single-crystal MoS₂ was also reported.¹⁰⁷
Using S and MoO₃ as the growth source and Ar and Ar/O₂ as
<figure><img src="image_5.png" /><figcaption>FIG. 1. 2D materials synthesized by the CVD method: graphene, BN, TMDs, magnetic 2D materials, 2D Janus materials, and 2D van der Waals heterostructures.</figcaption></figure>

the carrier gas, the growth was successfully achieved at 930 °C on the sapphire substrate. In addition to $MoS_2$, there were attempts to grow $MoSe_2$ by CVD.$^{108,109}$ A promoter-assisted liquid-phase CVD method was reported to synthesize high-quality large-area monolayer $MoSe_2$.¹¹⁰ A method to grow wafer-scale monolayer $WS_2$ used $H_2S$ gas instead of sulfur powder, as the sulfur source reacts

after decomposition with $WO_3$ powder, eventually leading to a 4-in. wafer-scale single-layer $WS_2$ film.¹¹¹ Going beyond individual TMDs, synthesis and precise control of 2D vdW heterostructure arrays was also achieved.¹¹²

For applications in the field of spintronics, potential magnetic 2D materials include $FeX_2$, $CoX_2$, $NiX_2$, $VX_2$, $CrX_2$, and $MnX_2$ ($X = I, Br$, and Cl).¹¹³ For the synthesis of large-scale 2D transition metal tellurides by CVD, the use of a mixture of Cr, $CrCl_3$, and Te was reported to lead to a CrTe film.¹¹⁴

## B. Molecular beam epitaxy (MBE)

An alternative method to grow large-scale 2D materials is molecular beam epitaxy (MBE), a physical deposition technique based on co-evaporation of individual elements under ultra-high vacuum on a crystal surface held at a controlled temperature (Fig. 2). Directional molecular beams are produced by thermal evaporation in effusion cells or by electron-beam evaporation. MBE yields materials with high crystalline quality and centimeter-scale areas. The ultra-high vacuum environment ensures minimal contamination and offers the possibility to use surface analysis techniques to characterize in situ the properties of the films. The film composition, doping, and thickness can be accurately controlled, thanks to the low fluxes (typically 1–10 Å/min). Heterostructures consisting of a stack of vdW materials can be formed with abrupt interfaces and an arbitrary number of layers. The growth of layered materials by MBE is based on the method of vdW epitaxy, consisting in film growth either on a passivated surface with a very low density of dangling bonds [e.g., F-terminated $BaF_2(111)$] or on a layered vdW substrate (e.g., SiC/graphene or mica).¹¹⁶ The weak interaction between the epilayer and the substrate largely releases the constraint of lattice matching and leads to the formation of fully relaxed layers. The advantage of vdW epitaxy is the potential to arbitrarily combine vdW materials with atomically sharp interfaces, free from contaminants.

<figure><img src="image_6.png" /><figcaption>FIG. 2. (a) Schematics of the MBE deposition technique. (b) Reflection high-energy electron diffraction (RHEED) intensity oscillations recorded during the epitaxy of various vdW materials, showing layer-by-layer growth. (c)–(f) Characterization of a $WSe_2$ monolayer grown by MBE on mica. (c) RHEED patterns in two azimuths showing the single crystallinity of the film. (d)–(f) Plane-view transmission electron microscopy near the boundary between in-plane rotated twin domains (marked A and B). (g) and (h) Cross-sectional high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of a multilayer $WSe_2$ film grown on SiC/graphene. (i) Cross-sectional HAADF-STEM image of a $Cr_2Ge_2Te_6/(Bi,Sb)_2Te_3/Cr_2Ge_2Te_6$ epitaxial heterostructure [reproduced with permission from Mogi et al., Phys. Rev. Lett. 123, 016804 (2019). Copyright 2019, American Physical Society].¹¹⁵</figcaption></figure>
The epitaxial growth of layered TIs by MBE was reported on various substrates [e.g., graphene, Si(111), Al₂O₃(0001), GaAs(111), Ge(111), BaF₂(111), InP(111), and SrTiO₃(111)].¹¹⁷⁻¹²³ Crystals of high quality are commonly produced, but suppressing defects such as chalcogen vacancies or twin boundaries requires fine optimization of the growth parameters.¹¹⁸,¹²⁰,¹²³ It is possible by MBE to adjust in (Bi₂-xSbₓ)(Te₃-ySe_y) alloys the Dirac point energy through the Te/Se ratio¹²⁴ and the chemical potential through the Bi/Sb relative content,¹¹⁹,¹²⁰ yielding bulk-insulating materials with designed topological Fermion dynamics. Magnetic doping of (Bi₂-xSbₓ)Te₃ with Cr and V¹²⁵⁻¹²⁸ as well as epitaxy of the antiferromagnets MnBi₂Se₄¹²⁹,¹³⁰ and MnBi₂Te₄¹³¹,¹³² were reported, enabling the experimental realization of the quantum anomalous Hall effect.¹³³ For the large-area growth of TIs, other physical deposition techniques were employed recently, such as sputtering and pulsed laser deposition.⁷³,¹³⁴

Efforts in the MBE of TMDs are more recent. Epitaxy was reported for a variety of TMDs and TMD heterostructures, including MoSe₂, WSe₂, HfSe₂, PtSe₂, VSe₂, ZrTe₂, MoTe₂, and WTe₂.⁶⁶,¹³⁵⁻¹⁴⁹ Inert vdW surfaces, such as graphene, mica, or hBN, make it possible to stabilize very flat monolayers of high structural quality, as shown for mica/WSe₂.¹⁴⁹ However, the weak interfacial interaction often results in an in-plane misorientation of crystal grains, which probably remains the main difficulty in the MBE of TMD monolayers. The misorientation is due to atomic position coincidences between the TMD monolayer and the substrate, favoring the formation of grains with an orientation away from the exact epitaxial relationship. These

configurations being metastable, high-temperature growth and/or post-deposition annealing might improve the in-plane crystal quality. Another strategy consists in orienting the grains by nucleation at step edges using vicinal surfaces. In addition, quasi-vdW epitaxy on non-vdW surfaces may promote a better crystal alignment at the expense of a stronger substrate interaction¹⁴⁶ and a possible loss of the intrinsic TMD properties. Recently, substrate-induced strain was used to stabilize the metastable semimetallic 1T' phase in WSe₂¹⁵⁰ and WTe₂.¹⁵¹

Reports on the MBE of 2D-FMs include diluted magnetic TMDs, such as V-doped WSe₂¹⁵²,¹⁵³ and Mn-doped MoSe₂¹⁵⁴,¹⁵⁵ intercalated vdW compounds, such as V₅Se₈¹⁵⁶ and Cr₂Te₃,¹⁵⁷ and intrinsic FMs, such as Cr₂Ge₂Te₆,¹⁵⁸ Fe₃GeTe₂,¹⁵⁹⁻¹⁶¹ CrBr₃,¹⁶² CrCl₃,¹⁶³ and CrI₃.¹⁶⁴ Intrinsic ferromagnetism was also claimed for MBE-grown monolayer MnSeₓ¹⁶⁵ and VSe₂,⁶⁶ although in the latter case, a charge density wave tends to suppress ferromagnetism.¹⁶⁶,¹⁶⁷ TI/2D-FM multilayers with abrupt epitaxial interfaces were achieved by MBE only recently.¹⁵⁸,¹⁶¹

### III. FABRICATION OF DEVICES

SCI can be probed and exploited in different types of spintronic devices. The two most prominent examples are the non-local Hall cross spin devices and the SOT devices. The non-local Hall cross devices [sketched in Fig. 3(a)] combine different materials with specific purposes. In the case of vdW heterostructures, they consist of a spin channel made of a low-SOC material (typically

<figure><img src="image_7.png" /><figcaption>**FIG. 3.** Schematic illustration of the (a) non-local lateral device, (b) second-harmonic Hall device, and (c) SOT-FMR device. (d) Representative room-temperature non-local resistance ($R_{xy} = V_{xy}/I$) vs magnetic field ($B_x$) measurements in the iSHE configuration in a graphene-WS₂ device. Open and closed symbols correspond to the magnetization of the FM aligned in the -y and +y directions, respectively. (e) Representative second-harmonic Hall voltage for a TMD/NiFe bilayer as a function of the angle between the in-plane magnetic field and the direction of the current for different magnitudes of the magnetic field. (f) Typical SOT-FMR resonances in a TMD/NiFe bilayer for different frequencies with the in-plane magnetic field applied at 35° relative to the direction of the current. The characteristic resonance frequencies $f_{min}$ and $f_{max}$ are in the 1–20 GHz range. (d) Adapted with permission from Benítez et al., Nat. Mater. **19**, 170–175 (2020). Copyright 2020, Springer Nature Limited. (e) Adapted with permission from Gupta et al., Nano Lett. **20**, 7482–7488 (2020). Copyright 2020, American Chemical Society.</figcaption></figure>
graphene) where the spins can propagate over long distances (tens of µm). Spins are injected and detected either through a FM or by taking advantage of SCI in materials with large SOC. Due to the atomically thin nature of graphene, its very weak SOC can be enhanced by proximity effects when stacking the material with other vdW materials, including TMDs, semimetals, and TIs, which are characterized by large SOC.

As the *in situ* growth of vdW heterostructures is still at an early stage, most of the studied systems to date are obtained by stacking mechanically exfoliated crystals. Owing to the nature of the studied effects and stability issues of some of the utilized materials at ambient conditions, the heterostructures are fabricated under controlled atmosphere with a low concentration of H₂O and O₂ (around 0.1 ppm), thus providing at the same time ultra clean interfaces. The stacks are obtained by transferring the 2D materials using a dry transfer method, in which viscoelastic stamps are used to pick-up and release flakes in a controlled manner. Precise alignment between the flakes is achieved by using a micro-positioner stage and an optical microscope. To avoid gas bubbles and blisters and to ensure better attachment between the layers, the finished stacks are usually annealed in an Ar/H₂ atmosphere or high vacuum.

The stacking process is followed by electron-beam lithography and reactive etching steps to define electrical contacts and to pattern the heterostructure with specific shapes and dimensions. Devices for SCI experiments consist of graphene etched in a Hall bar geometry. The graphene channel, typically 1 µm wide and tens of µm long, includes a graphene Hall arm capped with a large-SOC material (see Sec. IV for further details). The device includes a combination of metal and FM contacts. Metal contacts, typically Ti/Au or Ti/Pd, are attached to the graphene Hall cross and can be used either for applying an electric current or for measuring the voltage along the Hall bar. FMs (typically Co) are used to both inject and detect the spin current. Efficient spin injection and detection require the insertion of thin insulating barriers between the FM contacts and graphene to alleviate the conductance mismatch.<sup>168,169</sup>

SOT devices are made of bilayer heterostructures of FMs and large-SOC materials, the device geometry depending on the measurement technique [Figs. 3(b) and 3(c)]. In the case of SOT ferromagnetic resonance (FMR) experiments [Fig. 3(c)], large-SOC/FM bilayers are embedded into high-frequency coplanar waveguides, whereas for harmonic Hall voltage measurements, the bilayer is patterned in a Hall bar geometry [Fig. 3(b)]. Most of the vdW-based SOT devices studied to date feature heterostructures combining vdW materials with well-known bulk systems. Various studies considered mechanically exfoliated TMD flakes (under vacuum or flowing N₂, or in a glovebox with inert Ar atmosphere) with a thin film of a FM (typically NiFe due to its low magnetic damping) deposited on top. Further studies spanned from exfoliated crystals to materials grown by CVD (TMDs such as MoS₂ or WSe₂<sup>74,170</sup>) or MBE [TIs such as Bi₂Se<sup>69,70</sup> and (Bi₁-xSbₓ)₂Te₃<sup>171,172</sup>]. The FM is deposited using grazing angle sputtering in various reports, to avoid damaging the underlying TMD, and capped to prevent oxidation. Similarly, vdW FMs, such as Fe₃GeTe₂ and Cr₂Ge₂Te₆, obtained from exfoliation methods can be combined with heavy-metal layers of Pt and Ta. Due to the high sensitivity of these 2D FMs to ambient conditions, they are typically rapidly transferred to a deposition chamber and the heavy metal layer is sputtered on top<sup>173,174</sup> (in

some cases, preceded by a short etching with Ar plasma to clean the interface<sup>175,176</sup>).

SOT devices (with sizes of up to 20 × 100 µm²) are commonly patterned either by electron beam or by optical lithography techniques, followed by ion milling and the deposition of metal contacts. However, when investigating magnetization switching mechanisms, it is important to take into account the dimensions of the device; for large devices, switching occurs by domain nucleation and motion, which results in low switching currents. To date, fewer studies were realized for all-vdW SOT devices. These include *in situ* MBE-grown (Bi₀.₅Sb₀.₅)₂Te₃/(Cr₀.₀₈Bi₀.₅₄Sb₀.₃₈)₂Te₃ bilayers with a capping, which were patterned by photolithography and dry etching.<sup>177</sup> More recently, switching of Fe₃GeTe₂ on WTe₂ was reported.<sup>178</sup> The samples were prepared similarly to the above-mentioned lateral structures by dry transfer of mechanically exfoliated flakes inside an inert Ar atmosphere glove box, further protected by electron-beam evaporated Al capping. Progress in the *in situ* growth of vdW heterostructures may greatly simplify the fabrication steps required to preserve the interfaces from degradation due to air exposure.<sup>161</sup>

# IV. SCI: EXPERIMENTS

## A. Non-local Hall cross devices

Pioneering SCI experiments were conducted in metallic systems using non-local detection techniques. These devices use a FM contact for injecting spins into a non-magnet, typically Cu and Al, acting as the spin transport channel. Spins diffuse and are absorbed by a heavy-metal, e.g., Pt and Ta, in which a transversal voltage, generated by the iSHE, is measured in a Hall cross geometry.<sup>33</sup> Later, the same geometry is used by replacing the spin transport channel by graphene (see hybrid systems in Table I), providing a highly efficient spin injection that results in enhanced measured SCI efficiencies.

Over the last few years, SCI in lateral spin devices regained attention. The rich variety of vdW materials and possible combinations opened up the possibility to realize SCI in all-vdW systems. When combining graphene, which possesses excellent spin transport properties, with a non-conducting vdW material with large SOC, typically a semiconducting TMD, SCI occurs in graphene due to proximity effects. In the graphene/TMD region, the SOC of graphene is enhanced and the electronic band structure is modified significantly, with the most prominent features being the opening of an energy gap in the meV range at the K and K' points, lifting of spin degeneracy, and imprinting of an out-of-plane spin texture (with the spin orientation depending on the valley and a winding in-plane component far from the charge neutrality point).<sup>179</sup>

The device geometry [as sketched in Fig. 3(a)] is slightly different and consists of a graphene Hall cross with one of its arms shrouded with a TMD. The pristine graphene region (not covered by the TMD) is used to transport spin information from the spin injector to the Hall arm and vice versa. A spin current is injected into graphene by means of a planar FM contact with magnetization along its long axis.<sup>10</sup> When diffusing toward the Hall arm region, the spins experience precession under an external magnetic field. The relative direction between the magnetic field and the injected spins is key to distinguish between the different spin-to-charge conversion mechanisms (SGE or iSHE). In the case of the SGE, an out-of-plane
<table><caption>**TABLE I.** SCI efficiencies in non-local devices based on metallic, hybrid, and all-vdW systems. The parameters are defined as follows: $y^{SH} = j_c/j_s$, $\alpha^{SGE} = j_c/j_s$ (see x, y, and z directions in Fig. 3); $j_c$ is the charge current flowing along the y direction, i.e., along the Hall cross; $j_s$ is the spin current along the z direction (arising from the iSHE); $j_s^x$ is the spin relaxation lengths of spins precessing in-plane and out-of-plane, respectively, and $\alpha^{*SGE} = 2REV_Fp\tau^x$, with RE being the strength of the SGE, $\rho$ being the resistivity of the graphene beneath the TMD, $v_F$ being the Fermi velocity, and $\tau^x$ being the spin lifetime of the in-plane spins.</caption><thead><tr><th>Comments</th><th>SCI mechanism</th><th>SCI (%)</th><th>SCI efficiency (nm)</th><th>References</th></tr></thead><tbody><tr><td colspan="5" style="text-align:center; font-weight:bold;">Metallic</td></tr><tr><td>Cu/Ta</td><td>ρ(Ta) = 333 μΩ cm (10 K)<br>λ<sub>s</sub> (Ta) = 2.7 nm (10 K)</td><td>iSHE</td><td>γ<sup>SH</sup> (Ta) = -0.37 ± 0.20 (10 K)</td><td>γ<sup>SH</sup>·λ<sub>s</sub>(Ta) = 0.01 (10 K)</td><td>180</td></tr><tr><td>Cu/Pt</td><td>ρ(Pt) = 17.9 μΩ cm (RT)<br>λ<sub>s</sub> (Pt) = 7 nm (RT)</td><td>iSHE</td><td>γ<sup>SH</sup> (Pt) = 0.9 (RT)</td><td>γ<sup>SH</sup>·λ<sub>s</sub>(Pt) = 0.06 (RT)</td><td>181</td></tr><tr><td>Cu/Pt</td><td>ρ(Pt) = 44.1 μΩ cm (10 K)<br>λ<sub>s</sub> (Pt) = 0.75 nm (10 K)</td><td>iSHE</td><td>γ<sup>SH</sup> (Pt) = 8.5 ± 1.3 (10 K)</td><td>γ<sup>SH</sup>·λ<sub>s</sub>(Pt) = 0.06 (10 K)</td><td>182</td></tr><tr><td colspan="5" style="text-align:center; font-weight:bold;">Hybrid</td></tr><tr><td>Bi<sub>2</sub>O<sub>3</sub>/graphene</td><td>Bilayer graphene</td><td>iSHE (in proximitized graphene)</td><td>γ<sup>SH</sup> = 0.10 ± 0.05 (RT)<br>γ<sup>SH</sup> = 0.6 ± 0.1 (10K)</td><td>λ<sub>s</sub> not measured in the SCI region</td><td>183</td></tr><tr><td>Pt/graphene</td><td>Single-layer graphene<br>ρ(Pt) = 46 μΩ cm (RT)<br>λ<sub>s</sub> (Pt) = 5 nm (RT; taken from the literature)</td><td>iSHE (in Pt)</td><td>γ<sup>SH</sup> (Pt) = 15 ± 1 (RT)</td><td>γ<sup>SH</sup>·λ<sub>s</sub>(Pt) = 0.75 (RT)</td><td>184</td></tr><tr><td>Pt/graphene</td><td>Few-layer graphene<br>ρ(Pt) = 134 μΩ cm (RT)<br>λ<sub>s</sub> (Pt) = (2.1 ± 0.4) nm (RT) (taken from the literature)</td><td>iSHE (in Pt)</td><td>γ<sup>SH</sup> (Pt) = 23.4 ± 2.5 (RT)</td><td>γ<sup>SH</sup>·λ<sub>s</sub>(Pt) = 0.50 ± 0.02 (RT)</td><td>185</td></tr><tr><td colspan="5" style="text-align:center; font-weight:bold;">All-vdW</td></tr><tr><td>MoS<sub>2</sub>/graphene</td><td>Few-layer graphene<br>Spin absorption by MoS<sub>2</sub></td><td>iSHE (in proximitized graphene and MoS<sub>2</sub>)</td><td>γ<sup>SH</sup> = -0.33 ± 0.04 (RT)<br>γ<sup>SH</sup> = -4.5 ± 0.9 (10 K)</td><td>λ<sub>s</sub> not measured in the SCI region</td><td>186</td></tr><tr><td>WS<sub>2</sub>/graphene</td><td>Single-layer graphene<br>(Non-conducting) multilayer WS<sub>2</sub></td><td>SHE-iSHE (in proximitized graphene)<br>SGE-iSGE (in proximitized graphene)</td><td>γ<sup>SH</sup> = 0.3 (RT)<br>α<sup>iSGE</sup> = 0.1 (RT)</td><td>γ<sup>SH</sup>·λ<sub>s</sub><sup>x</sup> (gr/WS<sub>2</sub>) = 3.75 (RT)<br>α<sup>iSGE</sup>·λ<sub>s</sub><sup>x</sup> (gr/WS<sub>2</sub>) = 0.42 (RT)</td><td>187</td></tr><tr><td></td><td>λ<sub>s</sub><sup>x</sup> (gr/WS<sub>2</sub>) = 1.25 μm<br>λ<sub>s</sub><sup>x</sup> (gr/WS<sub>2</sub>) = 420 nm</td><td></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>TABLE I. (Continued.)</caption><thead><tr><th></th><th>Comments</th><th>SCI mechanism</th><th>SCI (%)</th><th>SCI efficiency (nm)</th><th>References</th></tr></thead><tbody><tr><td>WS<sub>2</sub>/graphene</td><td>Single-layer graphene (Non-conducting) single-layer WS<sub>2</sub> λ<sub>s</sub><sup>⊥</sup> (gr/WS<sub>2</sub>) = 1.58 µm λ<sub>s</sub><sup>‖</sup> (gr/WS<sub>2</sub>) = 31.3 nm</td><td>SHE-iSHE (in proximitized graphene) SGE-iSGE (in proximitized graphene)</td><td>γ<sup>SH</sup> = 0.13 (4 K), vanishes at T > 20K α<sup>*SGE</sup> = 2.8 (4 K) α<sup>*SGE</sup> = 0.56 (RT)</td><td>Different definition of α<sup>*SGE</sup> (see the table caption)</td><td>188</td></tr><tr><td>WS<sub>2</sub>/graphene</td><td>Few-layer graphene Spin absorption by WS<sub>2</sub></td><td>iSHE (in proximitized graphene)</td><td>γ<sup>SH</sup> = 1.7 ± 0.2 (RT) γ<sup>SH</sup> = 2.8 ± 0.3 (10 K)</td><td>λ<sub>s</sub> not measured in the SCI region</td><td>189</td></tr><tr><td>2H-TaS<sub>2</sub>/graphene</td><td>Few-layer graphene Multilayer TaS<sub>2</sub> (metallic)</td><td>SGE-iSGE (in proximitized graphene and TaS<sub>2</sub>)</td><td>α<sup>SGE</sup> = -1.4-4.3 (RT) (Gate-tunable)</td><td>λ<sub>s</sub> not measured in the SCI region</td><td>190</td></tr><tr><td>(BiSb)<sub>2</sub>Te<sub>3</sub>/graphene</td><td>Single-layer graphene Multilayer BST</td><td>SGE (in proximitized graphene)</td><td>α<sup>SGE</sup> = 0.17; 2.5; 1; 4.8 (RT)</td><td>λ<sub>s</sub> not measured in the SCI region</td><td>191</td></tr><tr><td>MoTe<sub>2</sub>/graphene</td><td>Few-layer graphene Multilayer MoTe<sub>2</sub></td><td>Unconventional SCI (in MoTe<sub>2</sub>)</td><td>α<sup>SCI</sup> ≥ 0.21 (RT) (conventional) α<sup>SCI</sup> ≥ 0.10 (RT) (unconventional)</td><td>λ<sub>s</sub> not measured in the SCI region</td><td>192</td></tr><tr><td>WTe<sub>2</sub>/graphene</td><td>Single-layer graphene Multilayer WTe<sub>2</sub>λ<sub>s</sub> (WTe<sub>2</sub>) = 8 nm</td><td>Unconventional SCI (in WTe<sub>2</sub>)</td><td>α<sup>SCI</sup> = 9 (RT)</td><td>α<sup>SCI</sup> · λ<sub>s</sub> (WTe<sub>2</sub>) = 0.72 (RT)</td><td>193</td></tr></tbody></table>
magnetic field causes an in-plane spin precession leading to a volt-
age along the Hall arm driven exclusively by the SGE. In the case
of the iSHE, a magnetic field is applied to graphene along the spin
diffusion channel. The spins diffusing toward the Hall cross precess
out-of-plane, generating a voltage driven exclusively by the iSHE
[Fig. 3(d)].

For the reciprocal effect, i.e., charge-to-spin conversion, a
charge current flowing along the Hall arm generates a transversal
spin current and a non-equilibrium in-plane spin density due to
the SHE and the iSGE, respectively. In the case of the SHE, the
spins point out-of-plane, whereas in the case of the iSGE, a non-
equilibrium spin density with the spins pointing in-plane and per-
pendicular to the charge current is generated at the graphene/TMD
interface. These two spin components (perpendicular to each other)
can be probed by a FM acting as a spin detector, with the magneti-
zation perpendicular to both spin components, and are disentangled
by varying the direction of the external magnetic field.

SCI experiments in lateral spin devices were initially reported for multilayer graphene combined with MoS₂.¹⁸⁶ Shortly after, spin-charge interconversions driven by both the SHE and SGE were probed in the graphene-WS₂ heterostructure at room temperature.¹⁸⁷,¹⁸⁸ Remarkably, both SCI mechanisms exhibit a gate-tunable magnitude that can be controlled by electrostatic gating. This knob is, in fact, essential to determine whether the SCI occurs exclusively in graphene. The electrostatic gating not only varies the carrier density in the graphene layer but also shifts the Fermi energy in the TMD. The latter may alter the insulating character, resulting in spin absorption and related SCI within the TMD if the Fermi level shifts toward the conduction (or valence) band. More recently, SCI driven only by the SHE was reported for the graphene-WS₂ heterostructure.¹⁸⁹

Beyond semiconducting TMDs, SCI experiments combin-
ing graphene with other large-SOC materials were also reported
for Bi₂O₃,¹⁸³ metallic layered 2H-TaSe₂,¹⁹⁰ the layered p-type
TI (Bi₀.₁₅Sb₀.₈₅)₂Te₃,¹⁹¹ and the semimetals 1T'-MoTe₂¹⁹² and
WTe₂.¹⁹³ Overall, the SCI efficiency in all-vdW heterostructures,
defined as γSH.λs with λs being the spin relaxation length in
the region where the SCI takes place, compares favorably with
fully metallic or hybrid systems based on heavy metals, such
as Pt and Ta. Table 1 summarizes experimental measurements
of the SCI efficiency for metallic systems, hybrid systems, and
all-vdW heterostructures, specifying which SCI mechanism takes
place and where. We note that some studies consider an effec-
tive λeff of the whole channel (not only the SCI region, i.e.,
include a large contribution of regular graphene). These values
are not included in Table 1, as they could overestimate the SCI
efficiency.

B. SOT devices

Aside from the non-local Hall cross, two other methods are
commonly employed to study the SCI in TMD/FM and TI/FM bilay-
ers [Figs. 3(b) and 3(c)]. The second-harmonic Hall (2ω-Hall)¹⁹⁴ and
SOT ferromagnetic resonance (SOT-FMR)³⁷ techniques both mea-
sure the current-driven SOT in the FM, from which the charge-to-
spin conversion efficiency is inferred. Additionally, the spin pump-
ing effect, based on the reciprocal effect of spin transfer, can be
used to measure the SCI efficiency.¹⁹⁵ In 2ω-Hall and SOT-FMR

experiments, the current-driven SOT induces precession of the mag-
netization, which results in time-dependent changes in the longi-
tudinal and transverse resistances. Frequency mixing between the
resistance and current oscillations leads to measurable direct cur-
rent and second-harmonic voltages [Figs. 3(e) and 3(f)]. The magni-
tude, direction, and nature (conservative/dissipative) of the SOT are
deduced from the field and angle dependences of these voltages. In
spin pumping experiments, magnetization precession is driven by
an external microwave magnetic field. Spins aligned with the aver-
age magnetization are pumped into the adjacent large-SOC material,
where spin-to-charge conversion gives rise to a measurable direct
charge current.

Because of the spin-polarized surface states of TIs, the TI/3D-FM bilayers are among the most widely used SOT systems that include vdW materials. Seminal works showed very large SCI efficiencies for Bi₂Se₃/NiFe⁶⁹ and Bi₂Se₃/CoFeB.⁷⁰ A strong Fermi level dependence of the SOT was found in BiₓSb₂₋ₓTe₃/NiFe,¹⁷¹ and electrostatic gating of the SOT was demonstrated in magnetic Cr-doped BiₓSb₂₋ₓTe₃.¹⁹⁶ A large in-plane damping-like SOT is generally observed, enabling efficient current-driven magnetization switching.¹⁹⁶,¹⁹⁷ Noteworthy, there is less evidence of large field-like SOT, expected to be a clear signature of the iSGE. The reported damping-like SOT efficiency is typically 0.1–1, which is significantly larger than in heavy metals.⁴¹ The corresponding Edelstein inverse length *q* is in the range 0.1–1 nm⁻¹.¹⁷¹,¹⁷² On the other hand, the Edelstein length λ measured with spin pumping is typically 0.01–0.1 nm,¹⁹⁸ which is rather low in comparison to other 2D systems (0.2–0.4 nm for the Bi/Ag Rashba interface¹⁹⁵ and 2.1 nm for the surface of the α-Sn Ti²⁰⁰).

SOT measurements were reported for various TMD/3D-FM bilayers.²⁰¹ Semiconducting (MoS₂, WS₂, and WSe₂), semimetallic (WTe₂, β-MoTe₂, TaTe₂, and PtTe₂), and metallic (NbSe₂ and TaS₂) TMDs were interfaced with NiFe, Co, or CoFeB. Salient results are the gate-modulation of the SOT with WS₂²⁰² and the generation of unconventional SOT with low-symmetry TMDs.²⁰³,²⁰⁴ ST-FMR measurements of 1T'-WTe₂/NiFe devices revealed an unusual out-of-plane damping-like SOT whose magnitude depends on the direction of the current with respect to the crystallographic axes, reflecting the reduced symmetry of the bilayer.²⁰³,²⁰⁴ 2ω-Hall measurements in similar bilayers showed an anisotropic field-like SOT, which was attributed to the contribution of topological Fermi arcs.²⁰⁵ The reported SOTs are generally weaker with TMDs than with TIs. Nonetheless, efficient and field-free current-driven magnetization switching was recently achieved in WTe₂/NiFe.²⁰⁶ Further work is required to clarify the SCI mechanisms at play with TMDs, as contrasting results were reported about the damping-like/field-like SOT ratios and the bulk or interfacial origin of the SOT. Spin pumping studies of TMD/FM systems are still scarce. Spin pumping measurements of MoS₂/YIG yielded an Edelstein length λ of 0.4 nm.²⁰⁷

More recently, the SOT was studied in large-SOC/2D-FM het-
erostructures, with significant efficiencies and magnetization switch-
ing reported in Fe₃GeTe₂/Pt.¹⁷³,¹⁷⁵ Single 2D-FM layers are also
interesting candidates for the generation of unconventional SOT.
For example, the low symmetry of monolayer Fe₃GeTe₂ allows for
a SOT akin to a current-driven magnetic anisotropy.²⁰⁸,²⁰⁹ Exper-
imental hints of such a SOT were also reported for multilayer
Fe₃GeTe₂.²¹⁰
In contrast to lateral spin devices in which the spin injection, transport, and detection are spatially well separated, these processes occur in vertical bilayers within a couple of nanometers near the interface. As recently shown for TI/FM bilayers,¹⁷² the SOT is thus extremely sensitive to the structural, chemical, and electronic properties of the interface, where band bending, orbital hybridization, spin memory loss, material intermixing, and magnetic dead layers were reported.²¹⁻²¹⁵ These phenomena are generally detrimental to the SOT, complicate the analysis of the SCI, and are probably responsible for the large experimental spread in the SCI efficiencies. It is expected that all-vdW heterostructures combining 2D-FMs with TIs or TMDs will display enhanced SOT and will constitute model systems, thanks to their sharp and weakly interacting interfaces. Indeed, a recent study found a SOT efficiency of 4.6 in WTe₂/Fe₃GeTe₂.¹⁷⁸

Apart from the novel spin phenomena due to proximity effects between different vdW materials, there is promise to solve a challenge that exists in today's magneto-resistive random access memory technology. Here, perpendicular magnetization switching is more attractive because it is faster and more scalable. Efficiently switching a perpendicular magnetization using SOT requires the spins to have a large out-of-plane component (out-of-plane anti-damping SOT), which is very difficult to realize by common materials. Recent evidence shows that vdW materials with low-crystalline symmetry, in principle, can be used to control the direction of the current-induced SOT.²⁰⁴,²¹⁶ A summary of experimental parameters describing the SCI in vdW-based SOT devices is given in Table II.

## V. SCI: THEORETICAL CONTRIBUTIONS

Successful integration of vdW heterostructures in the technological workflow relies on achieving efficient electrical control. For low-power applications, where a small current flow is essential, linear response theory provides a general framework to determine any observable electrical response. The central figure of merit of the SCI is the spin Hall angle $γ_{SH}$, which determines the amount of pure spin current generated for an incoming charge current.³³ For quantifying the SOT efficiency, it is usual to evaluate the torque efficiency $χ_T$, which measures the amount of torque felt by a magnet per unit of current density and can be rewritten as an effective spin Hall angle.⁴¹ The crystal symmetries prescribe the spin orientation via the SOC. In combination with group theory, the theory of invariants enables a relatively straightforward method to determine the allowed directions.²¹⁷,²¹⁸ First, one identifies the minimum set of point symmetries capable of expanding the whole point group (generating elements) and then imposes invariance of the linear response tensor with respect to those symmetries. By doing so, one finds a set of constraints limiting the number of finite elements and fixes the allowed directions for a given current.

The combination of disorder, exchange interaction, and SOC defines the efficiencies. Therefore, it is essential to properly describe the band structure, spin texture, and exchange splitting of the considered vdW system and evaluate the role of disorder in the diffusive regime, which is the most common experimental situation.²¹⁹⁻²²¹ Recent reports suggest that the use of symmetry-based models derived from ab initio methods provides the most cost-effective way to describe simple systems, such as graphene²²⁰ and WTe₂.²²²

However, although computationally inefficient, Wannier Hamiltonians are the preferred choice for more complex vdW heterostructures.²²³,²²⁴ On the other hand, linear scaling quantum transport methodologies are the only computational approaches capable of addressing the diffusive regime, since the systems involved demand for models containing many millions of atoms.²²⁵ Most of these methods are numerical implementations of the Kubo formula, either in the time or energy domain, allowing us to determine a system's properties for different transport regimes.

For honeycomb-based vdW heterostructures, spin-valley coupling and broken inversion symmetry make the two valleys inequivalent in terms of the spin and Berry curvature, providing a unique platform for efficient SCI.¹⁸⁶,¹⁸⁷,²²²,²²⁶,²²⁷ In Fig. 4, we present a sketch of how lowering the symmetries enables modifications in the band structure that enable different spin-related effects. In a highly symmetric system, such as graphene, combination of the inversion and time-reversal symmetries does not allow for spin-momentum locking and, therefore, prevents the Rashba-Edelstein effect and its associated SOTs. In TMDs, the presence of chalcogen and metal atoms lifts the inversion symmetry and enables band-splitting due to the SOC. However, since there is a horizontal mirror plane, the system cannot host a vertical electrical field, which prevents the typical in-plane spin-momentum locking. Yet, the broken inversion symmetry enables a novel torque not related to the Rashba effect that acts as an electrically controlled magnetic anisotropy, which is a promising gateway to magnet-free switching of perpendicular magnetizations.²²⁸ In honeycomb-based heterostructures, the presence of dissimilar layers finally removes the horizontal mirror plane and reduces the symmetry to a $C_{3v}$ point group, which supports the conventional field-like and damping-like torques, as well as an electrically controlled magnetic anisotropy,²²⁸ as demonstrated experimentally in $L_{11}$ CoPt/CuPt bilayers.²²⁹ However, this switching depends on the threefold rotation, and systems such as graphene and TMDs, where the Fermi level lies on an isotropic surface, are not expected to display the effect. Recently, tremendous efforts focused on synthesizing a new class of materials, the magnetic Janus TMDs, built by replacing the chalcogen atoms on one side of a TMD with different ones. Janus materials show simultaneously spin-valley coupling and a large Rashba effect due to their intrinsic electrical dipole¹⁷⁸ and magnetism due to the presence of magnetic metal atoms.²²⁴ Although Janus materials are still in their infancy, they combine multiple desirable properties for technological applications and deserve scrutiny. For instance, they are ideal for achieving all-in-one SOT, where the magnetization is electrically switchable in a single material via a current.²²⁴

The valley-driven spin Hall effect is a phenomenon where the electron motion is monitored by a spin-dependent Lorentz force opposite in each valley.¹⁸⁶,¹⁸⁷,²²⁷ The broken inversion symmetry of heterostructures can also generate a Rashba interaction, which, when combined with spin-valley coupling, leads to valley-dependent SOT²²⁸ and yields optimal SCI via the Rashba-Edelstein effect.²²⁷ The interplay between spin-valley coupling, Rashba interaction, and magnetism is not extensively studied to date. In magnetic systems with a Zeeman splitting, the valley-Zeeman effect²²¹ leads to valley polarization, as predicted for TMD/2D-magnet heterostructures²³⁰,²³¹ and recently realized in WSe₂/CrI₃.²³² Nevertheless, understanding the combined impact of the valley-Zeeman
<table><caption>TABLE II. SCI in vdW-based SOT devices. The parameters are defined in Ref. 41, where additional non-vdW structures are reviewed. For TMDs, a complementary comparative study can be found in Ref. 201.</caption><thead><tr><th rowspan="2">Fabrication</th><th rowspan="2">Method</th><th colspan="2">B<sub>DL</sub>/j</th><th colspan="2">Dimensionless</th><th colspan="2">ξ<sup>E</sup><sub>DL</sub></th><th colspan="2">ξ<sup>E</sup><sub>FL</sub></th><th colspan="2">λ<sub>REE</sub></th><th rowspan="2">Other torques</th><th rowspan="2">References</th></tr><tr><th>mT/(10<sup>11</sup> A/m<sup>2</sup>)</th><th>ξ<sup>E</sup><sub>DL</sub></th><th>ξ<sup>E</sup><sub>FL</sub></th><th></th><th></th><th>10<sup>5</sup> h/2e (Ωm)<sup>-1</sup></th><th>q<sub>REE</sub></th><th>nm<sup>-1</sup></th></tr></thead><tbody><tr><td colspan="14" style="text-align: center;">Non-vdW</td></tr><tr><td>Pt(3)/Co(0.6)/AlO<sub>x</sub>(1.6)<br>Ta(1.5-5)/CoFeB<br>(0.8-1.1)/MgO(2)</td><td>Sputtering</td><td>2ω-Hall</td><td>-6.9</td><td>4</td><td>0.13</td><td>-0.073</td><td>3.5</td><td>-2</td><td></td><td></td><td></td><td></td><td>41</td></tr><tr><td></td><td>Sputtering</td><td>2ω-Hall</td><td>1.3-4.4</td><td>-2(19)</td><td>(-0.03-0.11)</td><td>0.04-0.47</td><td>(-0.14-0.68)</td><td>0.22-0.67</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Bi(8)/Ag(5-20)/Py(15)</td><td>Evaporation</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.2-0.4</td><td></td><td></td><td>199</td></tr><tr><td>α-Sn(30 Ml)/Ag(2)/Fe(5)</td><td>MBE</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td></td><td></td><td></td><td>2.1</td><td></td><td></td><td>200</td></tr><tr><td colspan="14" style="text-align: center;">TI</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(8)/Py(8,16)/<br>AlO<sub>x</sub>(2)</td><td>MBE</td><td>ST-FMR</td><td></td><td></td><td>2.0-3.5<sup>c</sup></td><td>2.5-2.8<sup>b</sup></td><td>1.1-2.0</td><td>1.4-1.6</td><td></td><td></td><td></td><td>69</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(20)/CoFeB(5)/<br>MgO(1)/SiO<sub>2</sub>(3)</td><td>MBE</td><td>ST-FMR<br>RT<br>~20 K</td><td></td><td></td><td>0.05-0.11<br>~0.4</td><td>0-0.1<br>~0.2</td><td></td><td></td><td></td><td></td><td></td><td>70</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(10)/Ag(5)/CoFeB(7)/<br>MgO(2)/SiO<sub>2</sub>(4)</td><td>MBE</td><td>ST-FMR</td><td>5.3</td><td>3.2</td><td>0.5<sup>c</sup></td><td>0.3<sup>b</sup></td><td></td><td></td><td></td><td></td><td></td><td>233</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(7.4)/<br>CoTb(4.6)/SiN<sub>x</sub>(3)</td><td>MBE</td><td>Coercivity</td><td>6.1</td><td></td><td></td><td>0.16</td><td></td><td></td><td></td><td></td><td></td><td>71</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(8)/Py(6)/<br>MgO(1)/SiO<sub>2</sub>(4)</td><td>MBE</td><td>Coercivity</td><td></td><td></td><td></td><td>1.71</td><td></td><td></td><td></td><td></td><td></td><td>72</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(5)/CoFeB(7)/<br>MgO(2)/Al<sub>2</sub>O<sub>3</sub>(3)</td><td>MBE</td><td>ST-FMR</td><td></td><td></td><td></td><td>1.75</td><td></td><td></td><td>0.82</td><td></td><td></td><td>72</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(20)/CoFeB(7)/<br>MgO(2)/Al<sub>2</sub>O<sub>3</sub>(3)</td><td>MBE</td><td></td><td></td><td></td><td></td><td>0.3<sup>c</sup></td><td></td><td></td><td>~0.1<sup>c</sup></td><td></td><td></td><td></td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(5-35)/<br>Py(20)/SiO<sub>2</sub>(30)</td><td>MBE<br>+ Ar milling</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td>0.0093</td><td></td><td></td><td></td><td></td><td></td><td>234</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(5,10)/<br>CoFeB(5)/MgO(2)</td><td>MBE</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td>0.021-0.43</td><td></td><td></td><td></td><td></td><td></td><td>235</td></tr><tr><td>Bi<sub>2</sub>Se<sub>3</sub>(10)/CoFeB(5)/MgO(2)</td><td>MBE</td><td>ST-FMR</td><td></td><td></td><td></td><td>0.3-1.7</td><td></td><td></td><td></td><td></td><td></td><td>235</td></tr><tr><td>Ge/Bi<sub>2</sub>Se<sub>3</sub>(10)</td><td>MBE</td><td>Non-local</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.026<sup>c</sup></td><td></td><td>236</td></tr><tr><td>Bi<sub>x</sub>Se<sub>1-x</sub>(4)/CoFeB(5)/<br>MgO(2)/Ta(5)</td><td>Sputtering</td><td>2ω-Hall<br>ST-FMR</td><td>99</td><td></td><td></td><td>18.6<br>8.7</td><td>1.45</td><td></td><td></td><td></td><td></td><td>73</td></tr><tr><td>YIG/Bi<sub>2</sub>Se<sub>3</sub>(6-60)</td><td>MBE</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.035</td><td></td><td>237</td></tr></tbody></table>
<table><caption>TABLE II. (Continued.)</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Fabrication</th><th rowspan="2">Method</th><th rowspan="2">B<sub>DL</sub>/j<br>mT/(10<sup>11</sup> A/m<sup>2</sup>)</th><th colspan="2">B<sub>FL</sub>/j</th><th rowspan="2">ξ<sup>E</sup><sub>DL</sub><br>10<sup>5</sup> h/2e (Ωm)<sup>-1</sup></th><th rowspan="2">q<sub>REE</sub><br>nm<sup>-1</sup></th><th rowspan="2">λ<sub>REE</sub><br>nm</th><th rowspan="2">Other<br>torques</th><th rowspan="2">References</th></tr><tr><th>ξ<sup>E</sup><sub>DL</sub></th><th>ξ<sup>E</sup><sub>FL</sub></th></tr></thead><tbody><tr><td>YIG/(Bi,Sb)<sub>2</sub>Te<sub>3</sub>(6)</td><td>MBE</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>MgO(2)/Bi<sub>2</sub>Te<sub>3</sub>(8)/<br>CoTb(6)/TaO<sub>x</sub>(1.5)</td><td>Sputtering</td><td>2ω-Hall</td><td>87</td><td>~0</td><td>3.3</td><td></td><td></td><td></td><td></td><td>238</td></tr><tr><td>(Bi<sub>1-x</sub>Sb<sub>x</sub>)<sub>2</sub>Te<sub>3</sub>(8)/<br>Cu(8)/Py(10)</td><td>MBE</td><td>ST-FMR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>171</td></tr><tr><td>x = 0.5, 0.7, 0.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>0.8 &lt; x &lt; 0.9</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>(E<sub>F</sub> near Dirac point)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>(Bi<sub>0.4</sub>Sb<sub>0.6</sub>)<sub>2</sub>Te<sub>3</sub>(9)/<br>Py(5)/AlO<sub>x</sub>(2)</td><td>MBE</td><td>ST-FMR</td><td>0.02-0.1<br>mT/(A/m)<sup>d</sup></td><td>0 &lt; -B<sub>FL</sub> &lt; B<sub>Oe</sub><sup>c</sup></td><td>(0.88)<sup>a</sup></td><td></td><td></td><td>0.45-0.57</td><td></td><td></td></tr><tr><td>(Bi<sub>0.4</sub>Sb<sub>0.6</sub>)<sub>2</sub>Te<sub>3</sub>(9)/Ag(7)/<br>Py(5)/AlO<sub>x</sub>(2)</td><td>MBE</td><td>ST-FMR</td><td>0.01-0.07<br>mT/(A/m)<sup>d</sup></td><td>B<sub>FL</sub> ≈ -B<sub>Oe</sub><sup>c</sup></td><td></td><td></td><td></td><td>0.1-0.2</td><td></td><td></td></tr><tr><td>(Bi<sub>0.4</sub>Sb<sub>0.6</sub>)<sub>2</sub>Te<sub>3</sub>(9)/Al(6)/<br>Py(5)/AlO<sub>x</sub>(2)</td><td>MBE</td><td>ST-FMR</td><td>0.01-0.06<br>mT/(A/m)<sup>d</sup></td><td>0 &lt; B<sub>Oe</sub> &lt; -B<sub>FL</sub><sup>c</sup></td><td></td><td></td><td></td><td>0.11-0.48</td><td></td><td></td></tr><tr><td>Cr<sub>0.16</sub>(Bi<sub>0.54</sub>Sb<sub>0.38</sub>)<sub>2</sub>Te<sub>3</sub>(6)/<br>(Bi<sub>0.5</sub>Sb<sub>0.5</sub>)<sub>2</sub>Te<sub>3</sub>(3)</td><td>MBE</td><td>2ω-Hall<br>1.9 K</td><td>48 000<br>-146 000</td><td>140-425<sup>e</sup></td><td></td><td></td><td></td><td></td><td></td><td>177</td></tr><tr><td>Cr<sub>0.16</sub>(Bi<sub>0.5</sub>Sb<sub>0.42</sub>)<sub>2</sub>Te<sub>3</sub>(7)/<br>Al<sub>2</sub>O<sub>3</sub>(20)</td><td>MBE</td><td>2ω-Hall<br>1.9 K</td><td>46 900<sup>b</sup></td><td>116<sup>e</sup></td><td></td><td></td><td></td><td></td><td></td><td>196</td></tr><tr><td>(Bi<sub>0.22</sub>Sb<sub>0.78</sub>)<sub>2</sub>Te<sub>3</sub>(6)/<br>Py(12)</td><td>MBE</td><td>Spin<br>pumping</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.075</td></tr><tr><td>(Bi<sub>0.22</sub>Sb<sub>0.78</sub>)<sub>2</sub>Te<sub>3</sub>(6)/<br>NiO(5)/Py(12)</td><td>MBE</td><td>Spin-<br>Seebeck<br>effect</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.076</td></tr><tr><td colspan="12" style="text-align: center; font-weight: bold;">TMD</td></tr><tr><td>MoS<sub>2</sub>(0.8)/CoFeB(3)/<br>TaO<sub>x</sub>(3)</td><td>CVD</td><td>2ω-Hall</td><td>~0</td><td>0.078<sup>b</sup></td><td>~0</td><td>-0.14</td><td>~0</td><td>0.0288</td><td></td><td>74</td></tr><tr><td>WS<sub>2</sub>(0.8)/CoFeB(3)/<br>TaO<sub>x</sub>(3)</td><td>CVD</td><td>2ω-Hall</td><td>~0</td><td>0.114<sup>b</sup></td><td>~0</td><td>~0</td><td>~0</td><td>0.0552</td><td></td><td></td></tr><tr><td>MoS<sub>2</sub>(0.8)/Py(5)</td><td>CVD</td><td>ST-FMR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>170</td></tr><tr><td>WTe<sub>2</sub>(1.8-15)/Py(6)/<br>AlO<sub>x</sub>(2)</td><td>Exfoliation</td><td>ST-FMR/<br>2ω-Hall</td><td></td><td></td><td>0.03*</td><td>~0</td><td>0.08</td><td>0.09</td><td>Out-of-<br>plane DL</td><td>204</td></tr><tr><td>WTe<sub>2</sub>(5.6-7)/Py(6)/Ru(4)</td><td>Exfoliation</td><td>2ω-Hall<br>RT</td><td></td><td>B<sub>FL</sub> &gt;&gt; B<sub>Oe</sub></td><td></td><td></td><td>~1<sup>f</sup></td><td></td><td></td><td>205</td></tr><tr><td>WTe<sub>2</sub>(20-31)/Py(6)/Ru(4)</td><td>Exfoliation</td><td>2ω-Hall<br>RT</td><td></td><td></td><td></td><td></td><td>~2.5<sup>f</sup></td><td></td><td></td><td>205</td></tr><tr><td></td><td></td><td>&lt;50 K</td><td></td><td></td><td></td><td></td><td>~0</td><td></td><td></td><td></td></tr><tr><td></td><td></td><td>&lt;50 K</td><td></td><td></td><td></td><td></td><td>~4<sup>f</sup></td><td></td><td></td><td></td></tr></tbody></table>
<table><caption>TABLE II. (Continued)</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Fabrication</th><th rowspan="2">Method</th><th rowspan="2">B<sub>DL</sub>/j<br>mT/(10<sup>11</sup> A/m<sup>2</sup>)</th><th colspan="2">B<sub>FL</sub>/j</th><th rowspan="2">ξ<sub>DL</sub><sup>f</sup></th><th rowspan="2">ξ<sub>FL</sub><sup>f</sup></th><th rowspan="2">ξ<sub>DL</sub><sup>E</sup><br>10<sup>5</sup> h/2e (Ωm)<sup>-1</sup></th><th rowspan="2">q<sub>REE</sub><br>nm<sup>-1</sup></th><th rowspan="2">λ<sub>REE</sub><br>nm</th><th rowspan="2">Other<br>torques</th><th rowspan="2">References</th></tr><tr><th>Dimensionless</th><th>Dimensionless</th></tr></thead><tbody><tr><td>WTe<sub>2</sub>(5.8–122)/Py(6)</td><td>Exfoliation</td><td>ST-FMR<br>coercivity</td><td>0.09–0.79</td><td>~0</td><td></td><td>0.02–0.6<sup>f</sup></td><td></td><td></td><td></td><td></td><td>Out-of-plane DL</td><td>206</td></tr><tr><td>YIG/MoS<sub>2</sub>(2.4)</td><td>Exfoliation</td><td>Spin<br>pumping</td><td>0.15–0.65</td><td>0.32</td><td></td><td></td><td></td><td></td><td>0.4</td><td></td><td></td><td>207</td></tr><tr><td>TaTe<sub>2</sub>(4.5–19.7)/Py(6)/<br>AlO<sub>x</sub>(2)</td><td>Exfoliation</td><td>ST-<br>FMR/2ω-<br>Hall</td><td>~0</td><td>~0</td><td>~0</td><td>~0</td><td>~0</td><td>~0</td><td></td><td></td><td></td><td>239</td></tr><tr><td>MoTe<sub>2</sub>(0.7–14.2)/<br>Py(6)/AlO<sub>x</sub>(2)</td><td>Exfoliation</td><td>ST-FMR</td><td></td><td></td><td></td><td>0.058</td><td>0.15</td><td></td><td></td><td></td><td></td><td>240</td></tr><tr><td>PtTe<sub>2</sub>(3–20)/Py(2.5–10)</td><td>CVD</td><td>ST-FMR</td><td></td><td></td><td>0.05–0.15</td><td>~0.004</td><td>0.2–1.6</td><td></td><td></td><td></td><td></td><td>241</td></tr><tr><td>NbSe<sub>2</sub>(0.6–6)/<br>Py(6)/AlO<sub>x</sub>(2)</td><td>Exfoliation</td><td>ST-FMR</td><td></td><td></td><td></td><td></td><td>0.03</td><td>0.40</td><td></td><td></td><td></td><td>242</td></tr><tr><td>TaS<sub>2</sub>(0.88)/Py(7)/AlO<sub>x</sub>(3)</td><td>Plasma-<br>assisted<br>sulfuriza-<br>tion</td><td>ST-FMR</td><td></td><td>0.25</td><td>~0</td><td>14.9</td><td>~0</td><td></td><td></td><td></td><td></td><td>243</td></tr><tr><td>WTe<sub>2</sub>(10)/CoTb(6)/Ta(2)</td><td>Sputtering</td><td>Magnetic<br>loop shift</td><td></td><td>0.20</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>244</td></tr><tr><td colspan="13" style="text-align: center;">2D FM</td></tr><tr><td>Fe<sub>3</sub>GeTe<sub>2</sub>(4)/Pt(6)</td><td>Exfoliation</td><td>2ω-Hall<br>low T</td><td>53.4</td><td>24.3</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>173</td></tr><tr><td>Cr<sub>2</sub>Ge<sub>2</sub>Te<sub>6</sub>(19.6)/Pt(10)</td><td>Exfoliation</td><td>2ω-Hall<br>5 K</td><td>2.0</td><td>~0</td><td>~0</td><td>0.25</td><td>~0</td><td></td><td></td><td></td><td></td><td>174</td></tr><tr><td>Fe<sub>3</sub>GeTe<sub>2</sub>(23)/Pt(5)</td><td>Exfoliation</td><td>2ω-Hall<br>180 K</td><td></td><td></td><td>0.14</td><td></td><td></td><td></td><td></td><td></td><td></td><td>175</td></tr><tr><td>Cr<sub>2</sub>Ge<sub>2</sub>Te<sub>6</sub>(8)/Ta(5)</td><td>Exfoliation</td><td>Coercivity<br>~80</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>176</td></tr><tr><td>WTe<sub>2</sub>(12.6)/Fe<sub>3</sub>GeTe<sub>2</sub>(7.3)/<br>AlO<sub>x</sub>(2.6)</td><td>Exfoliation</td><td>Coercivity<br>160 K</td><td></td><td></td><td>4.6</td><td>2.25</td><td></td><td></td><td></td><td></td><td></td><td>178</td></tr><tr><td>Fe<sub>3</sub>GeTe<sub>2</sub>(6–21)</td><td>Exfoliation</td><td>Coercivity<br>2 K</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Anisotropy torque</td><td>210</td></tr></tbody></table>

<footnote>a Assuming 3D carriers.</footnote>

<footnote>b Inferred from other quantities.</footnote>

<footnote>c Contribution of non-topological Rashba states included in the interpretation.</footnote>

<footnote>d Assuming 2D carriers.</footnote>

<footnote>e Reference 197 later showed that ξ<sub>DL</sub> is largely overestimated in magnetic TIs when the asymmetric magnon scattering is disregarded in 2ω-Hall measurements.</footnote>

<footnote>f Anisotropic.</footnote>
<figure><img src="image_8.png" /><figcaption>FIG. 4. Transition of the band structure and spin orientation of Dirac materials while lowering the symmetries. The quantization axis is assumed to be out-of-plane. Red and blue colors represent the bands with up and down spin. The $D_{6h}$ point group contains 24 symmetries, including the inversion and time-reversal symmetries, which prevents spin splitting and only allows for the iSHE as the SCI mechanism due to the SOC. The $D_{3d}$ point group contains 12 symmetries, with the inversion symmetry absent, allowing for the SHE and spin-splitting and anisotropy-like SOT. Finally, the $C_{3v}$ point group contains six symmetries and allows for the SHE, anisotropy-like SOT, and Rashba–Edelstein effect.</figcaption></figure>

and Rashba interactions on the magnetization dynamics remains to be achieved and, beyond resolving some inconsistent reports of its symmetries,²⁰¹ can lead to unprecedented features for efficient SOT applications such as zero magnetic field switching, a long sought-after mechanism for improving non-volatile memory technologies.

## VI. CONCLUSIONS AND OUTLOOK

In this Perspective, we discussed the main challenges and recent results concerning materials synthesis, device fabrication, and optimization for eventually achieving the highest figures of merit for SCI in vdW heterostructures. On the material growth side, MBE is becoming an essential technique to obtain magnetic layered materials, although CVD-growth approaches and integration of two-dimensional materials in nano-electronics were already demonstrated. The next challenge is to demonstrate efficient integration of vdW materials in spintronic building blocks, such as in magnetic tunneling junctions, stimulating further research toward industry-oriented activities, for instance, in the fields of spin-transfer torque and SOT magneto-resistive random access memories. Current results concerning the SCI in vdW heterostructures combining 2D systems and topological materials are already encouraging, since they evidence high figures of merit even at room temperature in scalable materials. Besides these encouraging experimental results, advanced modeling techniques make it possible to reach a deep level of data interpretation and to predict SOT properties of arbitrary combinations of materials, even prior to their measurement, therefore acting as a pathfinder for more targeted experimental efforts. However, there are still complex theoretical issues to be tackled, such as developing very accurate effective Hamiltonian models

based on first-principles. For instance, Wannier interpolation techniques, which boil down to fitting the band structure using maximally localized Wannier functions, have proven to be very accurate in realistic charge transport simulations. Nonetheless, their extension to the investigation of non-equilibrium spin properties can be problematic, as the Wannier functions do not necessarily map the crystal structure accurately. This limitation is particularly serious for SOT simulations. Indeed, the interplay between magnetism and SOC in vdW heterostructures of interest demands special care in the study of resulting ground state spin textures in the reciprocal space as well as their modification under external electric or magnetic fields. On the experimental side, current fabrication techniques demand specific material treatment to prevent rapid degradation of produced devices, which embed some materials sensitive to oxidation effects. Efforts to synthesize materials and fabricate devices in situ are under way, but experimental methods to produce more air-stable heterostructures are an important task to be dealt with in the near future. As a conclusion, the field of SCI in vdW heterostructures is attracting more and more attention from various scientific communities, which gives hope that progress will be achieved in the years to come in the design of ultra-compact spin devices of relevance for non-volatile technology and spin logics.

## ACKNOWLEDGMENTS

The authors thank H. Okuno for the images in Figs. 2(d)–2(h). All authors acknowledge financial support from the King Abdullah University of Science and Technology under Grant No. ORS-2018-CRG7-3717. The ICN2 authors were also supported by the European Union Horizon 2020 research and innovation program under Grant Agreement Nos. 881603 (Graphene Flagship), 824140 (TOCHA, H2020-FETPROACT-01-2018), and 840588 (GRISOTO, Marie Sklodowska-Curie fellowship). ICN2 is also funded by the CERCA Programme/Generalitat de Catalunya and is supported by the Severo Ochoa program from Spanish MINECO (Grant Nos. SEV-2017-0706, PID2019-111773RB-100/AEI/10.13039/501100011033, and RYC2019-028368-I/AEI/10.13039/501100011033). The CNRS-CEA authors acknowledge financial support from the European Union Horizon 2020 research and innovation program under Grant Agreement No. 881603 (Graphene Flagship), the French ANR projects MAGICVALLEY (Grant No. ANR-18-CE24-0007), and ELMAX (Grant No. ANR-20-CE24-0015) and from the UGA IDEX IRS/EVASPIN.

## DATA AVAILABILITY

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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