Magnetism, spin dynamics, and quantum transport in two-dimensional systems

Two-dimensional (2D) quantum materials offer a unique platform to explore mesoscopic phenomena driven by interfacial and topological effects. Their tunable electric properties and bi-dimensional nature enable their integration into sophisticated heterostructures with engineered properties, resulting in the emergence of new exotic phenomena not accessible in other platforms. This has fostered many studies on 2D ferromagnetism, proximity-induced effects, and quantum transport, demonstrating their relevance for fundamental research and future device applications. Here, we review ongoing progress in this lively research field with special emphasis on spin-related phenomena. determination of the spin for spin precession in-plane and out-of-plane, spin by intervalley arises from short-range scattering as structural in graphene in the TMDC. These are well reproduced by numerical which indicate that the in-plane and out-of-plane spin This work shows magnetization switching at low current densities, indicating large spin  B by the


Introduction
Research on two-dimensional (2D) quantum materials (2DQMs) over the past decade has provided unique insights into condensed matter physics, yielding a multitude of novel effects. 1,2 Two-dimensional QMs, of which graphene is the prime example, include atomically thin materials with metallic, insulating, semiconducting, and magnetic behaviors, and may host intriguing topological properties. 3,4 Remarkable examples of novel phenomena have been continuously reported, such as the quantum spin Hall effect (QSHE) in monolayer WTe2, 5 2D ferromagnetism, 6 strongly correlated states in graphenebased heterostructures, 7  While having high electrical mobility, pristine graphene is a material with low spin-orbit coupling (SOC), which has precluded the observation of the QSHE 9 and the control and manipulation of spin currents. Enhancement of the SOC has been realized by combining it with high SOC layered crystals such as transition-metal dichalcogenides (TMDCs). 10 Such SOC enhancement has been recently proved for these heterostructures, [11][12][13][14][15] featuring a building block for electric-field control of graphene spin properties. 15,16 Another paradigmatic example of novel materials are topological insulators (TIs), which are characterized by electronic edge states that are protected from backscattering by time-reversal symmetry. The properties of TIs are derived from their bulk band structure following a band inversion driven by their large SOC. 4 The aim of this article is to examine recent developments for 2DQMs, with particular emphasis on their technological relevance to spin manipulation, spin-orbit-torque memories, 2D ferromagnets, and magnetic sensing.

Graphene-TMDC heterostructures
Enhanced SOC in graphene interfaced with different TMDCs has been experimentally demonstrated by weak (anti-)localization, [17][18][19][20] and recently, by spin precession experiments. 11,12,15 In the latter, proximity-induced SOC in graphene is inferred from the anisotropic spin relaxation and the spin-charge interconversion (SCI) driven by both the spin Hall effect (SHE) and the inverse spin galvanic effect (ISGE),where charge currents are converted into transverse spin currents and non-equilibrium spin densities respectively. In their reciprocals, the inverse spin Hall effect (ISHE) and spin galvanic effect (SGE), spin currents and non-equilibrium spin densities generate transverse charge currents. 13,14,15 Spin transport in graphene-TMDC heterostructures is well modelled by an effective hamiltonian, that describes the hybridization between graphene and dorbitals in the TMDC 21,22,23 . In this model, graphene preserves its characteristic linear band structure close to the Fermi level, while the proximity-induced SOC contributions arising from the TMDC and the Rashba type-SOC generated by the lack of space inversion symmetry in the system, open a band gap and remove the spin degeneracy. The strong spin-valley coupling also called valley Zeeman (VZ) interaction produces the out-of-plane spin polarization with opposite directions at the K and K' valleys while the Rashba-type SOC induces a winding in-plane spin component. 11,12,15,23 Such spin textures are imprinted in graphene, having a significant impact on the spin dynamics, resulting in spin lifetimes varying over orders of magnitude for spins pointing in-plane and outof-the graphene plane. 11,12,15,24 This model also enables quantification of the SCI mechanisms arising from the (intrinsic) SHE and SGE. 25,26 For the SHE, 27 numerical calculations of the spin Hall conductivity z xy, considering low disorder, display a non-zero spin Hall angle, which quantifies SCI efficiency. 25,28 Such numerical calculations predicts large spin Hall angle values for graphene-WS2 heterostructures with asymmetric responses for electron and holes, which is a signature of intrinsic SOC in graphene. 15 Although that SCI strongly depends on the degree of disorder in the structure, calculations performed by Garcia et al. 25 indicate that VZ interaction plays a crucial role for non-vanishing SHE as it breaks the valley degeneracy and prevents its cancelation as electrons experiences multiple scatter events at opposite valleys. For the SGE, 29 SCI is mainly driven by the winding in-plane spin texture imprinted in graphene due to the Rashba SOC. 26 In this case, the VZ interaction enhances the band splitting, causing an out-of-plane tilting in the spin textures, but it is found that the overall effect on the magnitude of the SGE is minimal.
Such features were recently demonstrated by spin precession experiments in lateral spin devices 15,30 (Figure 1a). In spin precession measurements, an electrical current, I, is applied through the ferromagnetic (F) injector (), creating nonequilibrium spin accumulation beneath the contact.
This spin accumulation diffuses along the graphene spin channel and is detected by using a ferromagnetic detector. An external magnetic field applied in an oblique configuration allowed for determination of the spin lifetime for spin precession in-plane and out-of-plane, being one order of magnitude larger for the latter. These experimental results suggest that the spin relaxation in such heterostructures is mostly driven by intervalley scattering, that arises from short-range scattering centers such as structural defects in graphene or vacancies in the TMDC. These results are well reproduced by numerical simulations, which indicate that the in-plane and out-of-plane spin lifetimes follow different relaxation mechanisms. 24,30 For SCI experiments, the devices in the design of Reference 15 are patterned into a Hall cross geometry, with the TMDC lying along one of the arms (Figure 1b). This Hall cross is contacted on the graphene pads underneath the TMDC with metal electrodes, so that the spin accumulation can be detected by SCI due to the SGE and the inverse spin Hall effect (ISHE), which are a consequence of the modified electron-hole states of graphene by proximity with the TMDC. [13][14][15] The ISHE was first reported in heterostructures comprising multilayer graphene-MoS2 and encapsulated graphene-WS2 heterostructures (Figure 2a-b). 13,14 In contrast to theoretical predictions, 25 the larger SCI efficiency of the former is explained by including additional contributions associated with intrinsic SOC and staggered potentials. 13 More recently, in the case of WS2 heterostructures, 14 the SHE and SGE contributions were differentiated from the symmetric and antisymmetric features of the experimental signals, which were also contrasted with numerical simulations. 14 Here, additional second harmonic signals suggest the onset of thermal effects. These experiments, however, do not independently monitor the electrical conductivity of the TMDC, thus preventing the full discrimination of SCI from proximity and TMDC-related effects.
In a recent report, proximity-induced SCI has been unambiguously demonstrated at room temperature in graphene-WS2 heterostructures. 15 Here, the measurement protocol, using the device in Figure 1b, is based on spin precession to separate and quantify the SHE and SGE contributions ( Figure   2c-d). Additionally, the SGE and SHE are shown to be tunable by electrostatic gating, being large near the charge neutrality point, and in agreement with theoretical calculations (Figure 2e-f). 25,26 Notably, the magnitude of the equivalent SCI efficiency at room temperature, which takes into consideration the long spin relaxation length, is among the largest observed to date, holding promise for spin-logic applications. 16 These findings show the potential of graphene/TMDCs heterostructures for generation and manipulation of spin currents in 2D systems, which can be used to act on the magnetization through the spin torque phenomena, providing a promising approach toward ultracompact memory devices.
Despite reasonable agreement between theory and recent experiments, some open questions need to be addressed. For instance, intervalley scattering is predicted to produce a suppression of the SHE while being necessary for spin-lifetime anisotropy. [24][25][26] It turns out that both effects were measured in a recent experiment on the same device, thus contradicting the proposed theory. 15 Furthermore, the SGE is predicted to be proportional to the conductivity at the Rashba pseudogap, 26 which does not seem the case in the experiments. Besides, the spin-dependent disorder, such as magnetic impurities or vacancies, is believed to enhance the SHE, but it is not clear how this will manifest in the experiments. Finally, numerical calculations discard the complexity of measured device geometries, and while an upper limit is predicted, the interplay between the SCI, the geometry, and relaxation processes remains largely unexplored, and thus limits the optimization of practical devices.

Two-dimensional ferromagnets
The recent discovery of intrinsic 2D ferromagnetism (2D-FM) in pristine vdW materials has opened new venues for spintronics, valleytronics, and quantum transport in layered heterostructures. 31,32 Long-range magnetism was first observed below room temperature in single and few layers exfoliated crystals of CrI3, 6 Cr2Ge2Te6, 33 and Fe3GeTe2, 34 and later at room temperature in epitaxially grown TMDCs such as VSe2 35 and MnSex. 36 Additional 2D-FMs include magnetically doped TMDCs, 37,38 the FePS3 materials family, 39 and intercalated layered materials such as V5S8. 40 These materials present wide electronic and magnetic properties-CrI3 is a 2D Ising FM with strong anisotropy and interlayer antiferromagnetic ordering, 6 Cr2Ge2Te6 is an insulating Heisenberg FM with weak anisotropy, 33 Fe3GeTe2 is a semimetallic itinerant 2D Ising FM, 34 whereas doped TMDCs are diluted FM semiconductors. 37 This wealth of attributes allows us to experimentally test models of magnetism in low dimensions by tuning the anisotropy and long-range interactions, both essential aspects for the emergence of 2D magnetism. For instance, the Curie temperature of Fe3GeTe2 was found to be strongly sensitive to the shape anisotropy. 41 In addition, the low-dimensional nature of 2D-FMs introduces new degrees of freedom acting on the magnetic order. Interestingly, the Curie temperature of Fe3GeTe2 can be increased above room temperature by electrostatic gating with an ionic liquid. 34 Also noteworthy is electric-field control of the interlayer magnetic coupling, which was also achieved in CrI3 where the ferromagnetic/antiferromagnetic transition can be triggered electrically. 6,42 Two-dimensional-FMs can further be employed as building blocks of spintronics devices. Tunneling through insulating CrI3 has been used as a probe of the magnetic order, yielding large magnetoresistance as a result of the controlled tunneling of spin polarised currents, which depends on the specific magnetic arrangement of the layers (spin filtering effect). Such behavior, shown in (Figure 3a-c) has been recently reported using electrical and optical means. [43][44][45] Spin-orbit torques and current-induced magnetization switching were also reported in Pt/Fe3GeTe2. 46,47 A large anomalous Hall effect arises in Fe3GeTe2 due to its band topology and large Berry curvature, 48 effective magnetic field generated by the symmetries and high SOC of the system, and in Cr2Ge2Te6 proximitized to a TI. 49 Two-dimensional-FMs are additionally expected to enable substantial progress in valleytronics, which aims at exploiting the electronic valley degree of freedom in information processing.
The magnetic proximity effect in TMDC/2D-FM bilayers could lift the valley degeneracy in TMDCs. Alternatively, a "ferrovalley" ground state could be achieved in ferromagnetic TMDCs such as 2H-VSe2 50 or diluted magnetic TMDCs.
The practical use of 2D-FMs will however require higher Curie temperatures and the development of scalable fabrication methods. Various proximity effects still demand experimental validation, requiring smart design of 2D-FMs and vdW heterostructures.

Spin-orbit torques in FM/2D heterostructures
The large SOC and resulting spin-momentum textures of 3D-TIs and TMDCs make them ideal materials for SCI through the SGE. 29 At the interface with a magnetic layer, the nonequilibrium spin density generated by SGE transfers angular momentum to the magnetization, m, and exerts torque on it. 51  The SCI efficiency, ξ, inferred from the measured antidamping SOT is often found to be larger than in conventional heavy metals. However, the reported values span several orders of magnitudes (ξ ~ 0.08 − 52 as compared to spin Hall efficiencies of |ξ|~0.06 − 0.33 with Pt, Ta, and W). 51 The large scatter of experimental results and the difficulty in unambiguously determining the microscopic origin of the SOTs can be ascribed to several experimental limitations. The determination of ξ requires knowing the spatial distribution of the charge current, which is made difficult by the use of low resistivity FMs that strongly shunt the current. TI/metal interfaces also suffer from substantial charge transfer and orbital hybridization. 59,60 This strongly alters the energy and spin texture of topological surface states and leads to the formation of a Rashba-split 2DEG coexisting with them. 61 Moreover, TI thin films are usually defective, with a sizable bulk conductivity that allows a contribution of the SHE to the SOTs. Chalcogenides tend to intermix with metals, forming poorly defined interfaces 62 The torques in TMDC/FM bilayers are generally weaker than in TI/FM ones, but interestingly, SOTs with unconventional symmetries may be produced due to the reduced crystal symmetry of the TMDC layers. Of relevance for actuating perpendicularly magnetized FMs, an out-of-plane damping-like torque has been observed in WTe2/Fe-Ni 66 and NbSe2/Fe-Ni. 67 The underlying mechanisms governing the symmetry and magnitude of SOTs remain to be elucidated. TMDCs further enable the study of SOTs in ultimately thin devices, down to monolayer TMDCs, 68 and potentially, their tuning with light or electrostatic gating.

Graphene-based devices
Quantum transport driven by the quantum Hall effect (QHE) appears in highmobility 2DQMs. In the QHE, the band structure of the 2DQM turns into discretized energy levels usually called Landau's levels (LLs) by the action of a strong magnetic field, leading to dissipationless quantum conduction. The QSHE emerges in the absence of magnetic fields in 2DQMs that are bulk insulators and possess conducting helical spin-edge states protected by time reversal symmetry. 4 The QSHE was initially observed in quantum well semiconductors systems. 69 Owing to the small band gap in these systems, the conductance quantization manifests at ultralow temperatures. This has promoted recent research toward new 2DQMs, where graphene and TMDCs have rised as promising candidates due to their unique and tunable electronic properties. 3,7 In graphene, early QHE experiments showed a characteristic quantization, arising from its linear band structure, topology, and the fourfold degeneracy of the LLs. 70,71 Interestingly, the energy spectrum driven by the competition between spin and sublattice (valley) interactions displays a zero LL at the Dirac point 72 73,74,77 Such an edge mode configuration is analogous to the intrinsic QSHE 9 and can also be modulated from chiral to helical edge modes transport by adding an in-plane magnetic field. 74 Recently, the fractional quantum Hall effect, consisting on the noninteger quantization of the Hall conductivity (σxy) as a result of the interaction between electrons at partially filled LLs, has been observed in dual-gated encapsulated devices. The ultralow disorder of these encapsulated devices enabled observation of striking QH features at low magnetic fields. 7,78 The quantification of the LL broadening by thermal activation gap measurements is found to be comparable to high-quality GaAs quantum wells. 78 Spintransport studies through the CAF state in graphene have been recently reported. 75,79 Notably, Stepanov et al. 75   Additionally, the electric-field and temperature dependence of the conductance display exponential behavior, in agreement with the expected band gap opening due to Zeeman interaction (Figure 4c). The prevalence of the QSHE up to 100K sheds light toward realization of low-dissipation vdW devices working above cryogenic temperatures. 3

Conclusions and perspective
In