Quantum Materials for Spin and Charge Conversion

Spintronics aims to utilize the spin degree of freedom for information storage and computing applications. One major issue is the generation and detection of spins via spin and charge conversion. Quantum materials have recently exhibited many unique spin-dependent properties, which can be used as promising material candidates for efficient spin and charge conversion. Here, we review recent findings concerning spin and charge conversion in quantum materials, including Rashba interfaces, topological insulators, two-dimensional materials, superconductors, and non-collinear antiferromagnets. Important progress in using quantum materials for spin and charge conversion could pave the way for developing future spintronics devices.


Introduction to pure spin current
Spintronics aims to utilize the spin degree freedom of electrons for potential applications such as novel information storage and computing 1-3 . Compared to conventional devices using electron's charge properties, spintronic devices potentially have several major advantages, including non-volatility, faster data processing speed, higher integration densities, and less electric power consumption. The key challenges are the efficient generation and detection of pure spin current, which does not accompany any charge current, as illustrate in Fig. 1a 1 . The pure spin current could be used as information transistors and logic devices [4][5][6] . For example, spin-based field effect transistors can provide on and off operations via the manipulation of the spin current in the spin channel 4,7 . As shown in Fig. 1b, the pure spin current that carries the information flows from the injector to the detector via the spin channel. Due to the spin relaxation, the spin-dependent chemical potential exponentially decays during the spin diffusion ( Fig. 1c). Thus, for the purpose of spin transistor and logic device applications, the spin channel with long spin lifetimes and long spin diffusion length is needed. Graphene might hold the promise for this purpose since the demonstration of its fantastic spin dependent properties at room temperature arising from its low spin orbit coupling and high mobility 8,9 .
Besides serving as a transmitter of information, the spin current also carries angular momentum. As illustrated in Fig. 1a, the spin current can also be viewed as the transfer of angular momentum, which could be used for magnetization switching applications via spin transfer torque 10,11 . In the last several years, the spin orbit torque, arising from pure spin current in nonmagnetic materials (NM) (Fig. 1d), can be used to switch the magnetization of adjacent ferromagnets (FM) [12][13][14][15][16] . As illustrated in Fig. 1e, the spin current provides a spin transfer torque to the magnetization that can be expressed by: where  is the reduced Plank constant, m is the magnetization vector, and σ represents the spin polarization direction of the spin current. For this purpose, significant spin orbit coupling is usually required for the nonmagnetic materials, which is essential for the conversion of charge current to spin current. There are two major mechanisms for the conversion of charge to spin current, namely spin Hall effect [17][18][19][20][21][22][23][24][25] and Edelstein effect 26 . The major difference between these two effects is that spin Hall effect is usually considered as a bulk effect, which means that the spins diffuse in the direction perpendicular to the charge current, whereas the Edelstein effect is often referred as an interface effect that the spins and electrons are confined in the twodimensional (2D) state. The spin Hall effect in conventional metals and semiconductors has already been described in several review articles 27,28 .
In this review article, we focus on the spin and charge conversion in recent quantum materials, including spin-momentum locked Rashba interfaces and topological insulator surface states, 2D materials, quasiparticles in superconductors, as well as non-collinear antiferromagnets

Spin and charge conversion in Rashba interfaces
The spin and charge conversion in Rashba interfaces is often referred as Edelstein effect or Rashba-Edelstein effect; a nonzero spin accumulation is accompanied with a charge current flowing in 2D asymmetric systems 26 . At the interface, the coupling between the momentum and spin polarization directions can be expressed by the following Hamiltonian 26,29 : where is the Rashba coefficient that is proportional to the spin orbit coupling ( ) and the electrical field (E) perpendicular to the interface ( = , e is the electron charge), is the unit vector perpendicular to the interface, k is the wave vector,  is the spin Pauli matrices vector. As a result of interaction between spins and the momentum directions of the carriers, the energy dispersion exhibits two contours at the Fermi surface, as illustrated in Fig. 3a. These energy dispersion curves can be experimentally revealed by angle-resolved photoemission spectroscopy (ARPES). The splitting in energy dispersion curves for spin-up and spin-down carriers could be used to extract the Rashba coefficient at the interface/surface, i.e., large Rashba coefficient has been identified at the interface of Bi with other metallic materials 30,31 .
The spin and charge conversion can be explained based on the shift of the Fermi contours in the presence of electric fields. For the two Fermi contours (Fig. 3a), the inner one has spinmomentum locking feature with a clockwise spin texture, while the outer one has a counterclockwise spin texture. These two Fermi contours are symmetric without an electric field.
However, in the presence of an electric field, as illustrated in Fig. 3b, both of these Fermi circles shift towards positive kx direction. Shift of the outer Fermi circle gives rise to an increase in spinup density. While shift in inner Fermi circle causes an increase in spin-down density. Usually, the net effect is a spin-up density accompanying the charge current, since the outer Fermi circle plays the major role. Quantitatively, the generated spin density (Ŝ ) is proportional to charge current density (ˆC J ), described by the following relationship: Thus, for the efficient charge to spin conversion, a large Rashba coefficient is favored. Similar to the inverse spin Hall effect, the inverse Edelstein effect refers to that spin accumulation in inversion 2D asymmetric systems could generate an in-plane electric field perpendicular to the spin polarization direction for both systems with weak and strong spin orbit couplings 32,33 . As illustrated in Fig. 3c, the injection of spin-up polarized carriers results in the shift of the outer/inner Fermi circles to the positive/negative kx direction, generating a net charge current along the positive kx direction. In the last several years, intensive investigations of the Edelstein effect and inverse Edelstein effect have been performed on the Rashba-split states at the non-magnetic metal interfaces [33][34][35][36] , insulating oxide interfaces [37][38][39][40][41] , and metal-insulating oxide interfaces 42,43 .
We first discuss the Edelstein effect and inverse Edelstein effect of the Rashba-split interfaces between two metallic layers. To probe the Edelstein effect at the Ag/Bi interface, Zhang et al 34 have used the spin-polarized positron beam to detect the spin polarization of the outermost surface electrons in the presence of a charge current. This method is ultra-sensitive to the surface spin polarization since the bound state of a positron and an electron is a Positronium.
Since Positronium can only be formed for low electron density, only the outermost surface in a metal could satisfy this condition, which makes this technique ultra-sensitive to the surface.
During the measurement, as illustrated in Fig. 3d, a transversely spin-polarized positron beam is generated by a 22 Na source and an electrostatic beam apparatus, and then guided to inject into the Ag/Bi samples. A high-purity Ge detector is used to detect the Positronium annihilation γ rays, from which the component of the surface spin polarization can be obtained in the presence of a charge current flowing in the Rashba interfaces of Ag/Bi. Due to the large difference of the resistivity between Bi and Ag, the charge current mainly flows in the Ag layers. By systematically varying the thickness of Bi in the bilayer structures of α-Al2O3 (0001)/Ag (25 nm)/Bi, the charge-to-spin conversion effect of the Rahsba interface is investigated. For pure Ag thin films, the surface spin polarization is estimated to be 0.5% with JC = 15 A/m, which is mall and most likely arising from the small spin Hall effect of Ag. A giant enhancement of the surface spin polarization is probed when the Bi thickness is ~ 0.3 nm with a value of 4.1% with JC = 15 A/m, which is more than ten times higher than that of pure Ag films, indicating the dominant role of the Ag/Bi interface. Fig. 3e shows the Bi thickness dependence of surface spin polarization for the α-Al2O3 (0001)/Ag (25 nm)/Bi bilayer samples. Clearly, there is a strong enhancement when the Bi reaches 0.3 nm, which is approximately monolayer considering the Bi atomic radius of 0.15 nm. As the Bi thickness further increases, the detected surface spin polarization decreases, which is expected since the interface is the source for the spin generation.
When the surface is far away from the interface, there is a spin depolarization due to spin scattering, following an exponential relationship ( exp( / ) The inverse Edelstein effect, spin to charge conversion, of Ag/Bi Rashba interface states has been investigated by the Rojas-Sanchez et al 33 . To generate the spin current in the Rashba interfaces, a thin NiFe (Py) layer is grown on the Bi/Ag, which acts as a spin pumping source.
The spins are generated from the Py layer under its magnetization resonance conditions, which results in the generation of spin currents at the interface. This dynamic spin injection method is called spin pumping, which is a well-established technique to inject spin polarized carriers into various materials, including metals, semiconductors, Rashba interface states, etc 23,25,33,44,45 . It can be considered as a process of transferring angular momentum from the FM layer into the adjacent NM layer, and the angular momentum in the NM layer is mediated by pure spin current. Since the pioneering work that reported the high mobility conducting two-dimensional electron gas (2DEG) between two insulating oxides (SrTiO3 and LaAlO3) 46 , many interesting physical properties have been discovered 47,48 . A particular interesting point is that all these physical properties are gate-tunable via a perpendicular electric field. This oxide interface becomes conducting when the LaAlO3 layer exceeds a critical thickness of 3-4 unit cells. As illustrated in Fig. 4a-b, the polar oxide LaAlO3 consists of two layers, (LaO) + , and (AlO2) -, and the top surface of SrTiO3, a thin TiO2 layer, becomes conducting. To account for the high mobility 2DEG at the interface, several mechanisms have been proposed, including the "polar catastrophe", an electric field with thickness of the polar LaAlO3 layer resulting in charge transfer from the LaAlO3 surface to the interface 49 , cation intermixing giving La doping in the SrTiO3 surface 50 , and oxygen off-stoichiometry to form SrTiO3-x conducting layer 51 . Particularly intriguing for spintronics, a large Rashba coefficient has been reported via weak anti-localization measurements at T = 1.5 K 52 and it can be markedly modulated from 1 × 10 -12 to 5 × 10 -12 eVm by applying an electric field. Recently, the inverse Edelstein effect of the oxide interface has been achieved experimentally and its spin and charge conversion efficiency is highly gate tunable 37,38 .
Song et al 38 performed the room temperature inverse Edelstein effect experiments on the SrTiO3 and LaAlO3 interface using a thin Py metallic layer (~ 20 nm) as the spin pumping source.
The spins are injected via spin pumping into the oxide interface, and are converted to a charge current that could be measured using a voltage meter. The angular momentum is transferred from Py to the 2DEG across the LaAlO3 layer via spin tunneling across the LaAlO3 layer and/or localized states in the LaAlO3 layer (i.e. oxygen vacancies). To achieve the gate tunable inverse Edelstein effect, a sample of the critical thick LaAlO3 layer of 3-unit cell is used, of which the interfacial conductivity can be modulated dramatically by an electric field at room temperature.
During the spin pumping measurement, an electrode of silver paste is used on the other side of SrTiO3 substrate to serve as a back gate, as schematically shown in the inset of Fig. 4c. The gate tunable spin signal of the Rashba 2DEG between SrTiO3 and 3-unit cell LaAlO3 has been observed ( Fig. 4c). It is clearly seen that the inverse Edelstein effect voltage (VIEE), resulting from spin to charge conversion at the Rashba-split 2DEG, can be tuned markedly by the gate voltage. Under negative gate voltages, the VIEE is significantly lower, which means a lower effective spin-to-charge conversion. Whereas, the large spin signal and low resistance of the 2DEG under positive gate voltage indicate a larger spin-to-charge conversion. This observation is attributed to the gate tunability of the carrier density, Rashba coefficient at the interface, and the spin pumping efficiency that is related to the spin mixing conductance between Py and the Rashba 2DEG. Furthermore, the gate dependence of the spin to charge conversion has been theoretically investigated 39 , which shows a good agreement with the experiential results at room temperature.
Since the dielectric constant of SrTiO3 increases significantly at low temperature, the gate voltage modulation of the VIEE at low temperatures is expected to be significantly enhanced.

reported a large gate tunable inverse
Edelstein effect for the Rahsba-split 2DEG between SrTiO3 and 2-unit cell LaAlO3, where the spin to charge conversion sign could be even reversed. The 2-unit cell LaAlO3 is able to produce a conducting Rashba 2DEG because the critical thickness of LaAlO3 for the formation of the conducting 2DEG is reduced due to the deposition of ferromagnetic metallic layers, including both Co and Py 37,53 . A large spin to charge conversion efficiency (λIEE = / ) of 6.4 nm is reported, which is more than one order larger than that of Rashba interface states between metallic layers 33 . The gate dependence of the spin to charge conversion efficiency is shown in The carrier density across Lifshitz points corresponds to ~ 1.8 × 10 13 cm -2 , as indicated by the schematic of the band structure for the oxide interface (inset of Fig. 4d). To further confirm the scenario above, the detailed band structures are essential, which can be revealed by spin-ARPES measurements.
For potential applications such as magnetic switching via spin orbit torque, the Edelstein effect, charge to spin conversion, has to be demonstrated. Recently, a significantly large spin orbit torque arising from the Edelstein effect at the SrTiO3 and LaAlO3 interface on an adjacent CoFeB layer is reported at room temperature 41 . Beyond the spin and charge conversion, the oxide-based interface and materials can also serve as a channel for the conducting spins, and the spin injection has been successfully performed [54][55][56] .
Besides the Rashba states for metal-metal and oxides interfaces, the interfaces between metal and oxide have also been investigated for spin and charge conversion 42 . Fig. 4e shows the measurement geometry and the sample structure, where Py layer is the ferromagnetic layer for spin pumping source, and the Cu/Bi2O3 is the Rashba interface that converts spin current into inplane charge current via inverse Edelstein effect. As shown in Fig. 4f This experimental work also reports that about only two thirds of the total spin relaxation occurs at the interface 43 , which points an interesting direction for future work towards the 100% contribution from pure interface states.  SmB6, a Kondo insulator, has been theoretically proposed to be a topological insulator at low temperature due to the band inversion between 4f and 5d orbitals 88,89 [90][91][92][93][94][95] . A unique property of SmB6 is that below ~ 3 K, the bulk states are insulating, and only surface carriers contribute to the conduction, as illustrated in Fig. 6c, which can be evident by the surface Hall measurement and saturation of the resistance of bulk SmB6 single crystals (Fig. 6d).

Spin and charge conversion in 2D materials
The isolation of graphene and related 2D materials has created new opportunities for spintronics. For example, graphene is potentially useful for spin channels in spin transistor and logic devices due to long spin lifetime and spin diffusion length 8,9,73,101 . TMDCs are potentially useful for spintronics and valleytronics devices arising from the spin-valley coupling 102,103 .
Regarding the spin current generation/detection, it has been recently demonstrated that 2D materials can be potentially used for efficient spin and charge conversion, including graphene with large spin orbit coupling due to proximity effect with other materials, TMDCs with low crystalline symmetry (MoS2 and WTe2).
Although the intrinsic spin orbit coupling is rather weak in pristine graphene, it can be largely enhanced via proximity effect with other materials that have large spin orbit coupling, such as ferromagnetic insulator, Yttrium Iron Garnet (YIG) [104][105][106] , and TMDCs 107,108 , etc.
Recently, it has been shown that YIG/graphene could be a promising material candidate for efficient spin and charge conversion 105,106 . The spin current is generated via spin pumping from YIG thin film grown on GGG substrates (Fig. 7a), and then converted to a charge current in graphene due to the enhanced spin orbit coupling and inverse Edelstein effect. The spin signal arising from the charge current flowing in graphene is measured via two Ag contacts at the ends of graphene channel. The typical magnetic field dependence curves of the spin pumping voltage measured on YIG/Graphene are shown in Fig. 7b. When the external magnetic field is applied along the graphene channel (ϕ = 90°), the pumped spin polarized carriers will be converted to a charge current perpendicular to the graphene channel. Thus, no spin pumping voltage could be detected (black line in Fig. 7b). When the external magnetic field is applied perpendicular to the graphene channel (ϕ = 0° and 180°), the pumped spin polarized carriers will be converted to a charge current with a direction along the graphene channel, giving rise to spin pumping voltages (red and blue lines in Fig. 7b). Furthermore, ionic liquid gating provides a large electric field on the graphene surface, which has been demonstrated to strongly modulate the spin to charge conversion efficiency of YIG/graphene 106

Very interestingly, recent experimental results show a large out-of-plane spin orbit torque in
WTe2 arising from the low crystalline symmetry 111 . The surface crystalline structure of WTe2 belongs to the space group mn2 1 P , and the crystal structure near the surface is shown in Fig. 7c.

Quasiparticle-mediated spin Hall effect in superconductors
Superconductor spintronics is an emerging field focusing on the interplay between superconductivity and spintronics 112 . In the FM/superconductor heterostructures, the magnetization of FM layer can strongly modulate the superconducting critical temperature of the superconducting layer [113][114][115][116] . Spin dynamics of superconducting films could be measured via spin pumping from an adjacent ferromagnetic insulating layer, which has been recently theoretically proposed and experimentally investigated 117,118 . The underlying mechanism is that the A critical parameter for the quasiparticle-mediated spin Hall effect is the length scale (λQ) as illustrated in Fig. 8c. After the formation of the quasiparticle-mediated charge current via inverse spin Hall effect, the quasiparticles will condensate into Coopers pairs, which gives rise to a charge imbalance effect and a spacing-dependent inverse spin Hall voltage signal. When the voltage probes are far away from the Cu/NbN interface (d2 in Fig. 8c), the charge imbalance or inverse spin Hall signal is not observable. Fig. 8d compares the inverse spin Hall signal for two devices with different distances (d1 = 400 nm and d2 = 10 µm) from the Cu/NbN interfaces measured at T = 3 K with a spin injection current of 1 µA. A tiny inverse spin Hall signal for the device with d2 = 10 µm is observed, which is markedly suppressed compared to the device with d1 = 400 nm.
Both the spin injection current and the voltage probe distance dependences of the inverse spin Hall signal confirm that the inverse spin Hall effect is mediated by the quasiparticles of the superconducting NbN layer. This novel mechanism mediated by quasiparticles gives rise to a huge enhancement of the inverse spin Hall effect, which is more than 2,000 times larger than that in the normal state mediated by electrons in the presence of spin orbit coupling. These results pave the way to realize a sensitive spin detector with superconductors. To use superconductors as spin generators, quasiparticle-mediated spin Hall effect which generates spin current from quasiparticle charge imbalance needs future studies.

Anomalous Hall and spin Hall effects in non-collinear antiferromagnets
Since the early work done by Edwin Hall on ferromagnetic metals 125 , anomalous Hall effect has been intensively studied, from the mechanisms (intrinsic, skew scattering, side jump scattering) to various materials including ferromagnetic metals, diluted ferromagnetic semiconductors, and heavy fermions, etc [126][127][128] . Different from the anomalous Hall effect in FM, which is usually assumed to be proportional to its magnetization, the non-collinear antiferromagnets are predicted to hold a large anomalous Hall effect arising from a real-space

Summary and outlook
In conclusion, the conversion between spin and charge using quantum materials has attracted a great deal of attention recently and quantum materials have exhibited unique spin dependent properties. Looking forward, novel mechanisms that can generate spin current would be particularly interesting, arising from crystalline symmetry, or coupling with other degrees of freedom, such as phonon, magnon, spinon, and valley/layer degree of freedom, etc 103,[145][146][147][148] . The spin and charge conversion in these quantum materials could be also very important for the detection of the spin current generated via various mechanisms 146 , the probe of the non-trivial magnetic fluctuations [149][150][151][152] , and search for new quantum states 153,154 . Besides, the efficient spin current generation may pave the way for future spintronics device applications, including magnetic random accessory memory, domain wall Racetrack memory, and skyrmion Racetrack memory, etc [155][156][157][158] .