Rashba-Edelstein Effect Research Articles

Spin-charge conversion in Bi([formula omitted][formula omitted]) [formula omitted]/Ag(111) structure

Working with spin pumping and spin-torque ferromagnetic resonance measurements, we investigate the spin-charge conversion in epitaxial Bi(3×3) R30°/Ag(111) structure grown by molecular beam epitaxy. The results show that the sign of the spin-charge conversion in our Bi/Ag structure is opposite to that in Sánchez et al. (2013), indicating the spin-charge conversion in our Bi/Ag structure is dominated by the (inverse) spin Hall effect rather than the (inverse) Rashba–Edelstein effect.

Controllable charge-spin conversion by Rashba-Edelstein effect at Cu/Ta interface

The Rashba-Edelstein effect typically originates from inversion symmetry breaking at an interface that allows charge to spin conversion efficiency comparable to or larger than the SHE. Its potential value is in converting charge current into spin current. Here, we demonstrate experimentally an efficient charge to spin conversion at a Cu/Ta Rashba interface. We exploit spin-torque ferromagnetic resonance to detect a spin current from Cu/Ta interface into adjacent FeNi magnetic layer. The Ta thickness dependence of charge to spin conversion efficiency unambiguously ascribed that interface effect caused FeNi magnetization to precess by generating nonzero spin current that exerts torques rather than bulk effect. The possibility of controllable charge-spin conversion efficiency at room temperature opens another route for modulating the charge to spin conversion by interface engineering.

Quantitative comparison of electrically induced spin and orbital polarizations in heavy-metal/ 3d -metal bilayers

Electrical control of magnetization is of crucial importance for integrated spintronics devices. Spin-orbit torques (SOT) in heavy-metal/ferromagnetic heterostructures have emerged as a promising tool to achieve efficiently current-induced magnetization reversal. However, the microscopic origin of the SOT is being debated, with the spin Hall effect (SHE) due to nonlocal spin currents and the spin Rashba-Edelstein effect (SREE) due to local spin polarization at the interface being the primary candidates. We investigate the electrically induced out-of-equilibrium spin and orbital polarizations in pure Pt films and in Pt/$3d$-metal (Co, Ni, Cu) bilayer films using ab initio electronic structure methods and linear-response theory. We compute atom-resolved response quantities that allow us to identify the induced spin-polarization contributions that lead to fieldlike (FL) SOTs, mostly associated with the SREE, and dampinglike (DL) SOTs, mostly associated with the SHE, and compare their relative magnitude, dependence on the magnetization direction, as well as their Pt-layer thickness dependence. We find that both the FL and DL components contribute to the resulting SOT at the Pt/Co and Pt/Ni interfaces, with the former contributions being larger at the Pt interface layer and the latter larger in the Co or Ni layers. Our calculations show that the electrically induced transverse orbital polarization is exceedingly larger than the induced spin polarization and present even without spin-orbit coupling, in contrast to the spin polarization.

Rashba-Edelstein magnetoresistance in two-dimensional materials at room temperature

We report the observation of the Rashba-Edelstein magnetoresistance (REMR) at room temperature in two two-dimensional (2D) materials, single layer graphene (SLG) and 2D semiconductor $\mathrm{Mo}{\mathrm{S}}_{2}$. The measurements were performed in heterostructures with yttrium iron garnet (YIG), namely, YIG/SLG and ${\text{YIG/MoS}}_{2}$, by means of the modulated magnetoresistance technique. We show that the action of the direct and inverse Rashba-Edelstein effects (REEs) in a YIG/2DM structure couples current-induced spin accumulation to the electric resistance, producing the REMR. The resistance change is similar to the one observed in spin Hall magnetoresistance experiments, but the origin of the change here lies in the 2D Rashba-Edelstein effects and not in the 3D spin Hall effects. The measured REE lengths for the two materials are in good agreement with the values obtained with the electric spin pumping technique.

Roadmap of Spin–Orbit Torques

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Large spin-to-charge conversion in ultrathin gold-silicon multilayers

Investigation of the spin Hall effect in gold has triggered increasing interest over the past decade, since gold combines the properties of a large bulk spin diffusion length and strong interfacial spin-orbit coupling. However, discrepancies between the values of the spin Hall angle of gold reported in the literature have brought into question the microscopic origin of the spin Hall effect in Au. Here, we investigate the thickness dependence of the spin-charge conversion efficiency in single Au films and ultrathin Au/Si multilayers by non-local transport and spin-torque ferromagnetic resonance measurements. We show that the spin-charge conversion efficiency is strongly enhanced in ultrathin Au/Si multilayers, reaching exceedingly large values of 0.99 +/- 0.34 when the thickness of the individual Au layers is scaled down to 2 nm. These findings reveal the coexistence of a strong interfacial spin-orbit coupling effect which becomes dominant in ultrathin Au, and bulk spin Hall effect with a relatively low bulk spin Hall angle of 0.012 +/- 0.005. Our experimental results suggest the key role of the Rashba-Edelstein effect in the spin-to-charge conversion in ultrathin Au.

Charge-spin interconversion in epitaxial Pt probed by spin-orbit torques in a magnetic insulator

We measure spin-orbit torques (SOTs) in a unique model system of all-epitaxial ferrite/Pt bilayers to gain insights into charge-spin interconversion in Pt. With negligible electronic conduction in the insulating ferrite, the crystalline Pt film acts as the sole source of charge-to-spin conversion. A small field-like SOT independent of Pt thickness suggests a weak Rashba-Edelstein effect at the ferrite/Pt interface. By contrast, we observe a sizable damping-like SOT that depends on the Pt thickness, from which we deduce the dominance of an extrinsic spin-Hall effect (skew scattering) and Dyakonov-Perel spin relaxation in the crystalline Pt film. Furthermore, our results point to a large internal spin-Hall ratio of $\approx$0.8 in epitaxial Pt. Our experimental work takes an essential step towards understanding the mechanisms of charge-spin interconversion and SOTs in Pt-based heterostructures, which are crucial for power-efficient spintronic devices.

Engineering the spin conversion in graphene monolayer epitaxial structures

Spin Hall and Rashba–Edelstein effects, which are spin-to-charge conversion phenomena due to spin–orbit coupling (SOC), are attracting increasing interest as pathways to manage rapidly and at low consumption cost the storage and processing of a large amount of data in spintronic devices as well as more efficient energy harvesting by spin-caloritronics devices. Materials with large SOC, such as heavy metals (HMs), are traditionally employed to get large spin-to-charge conversion. More recently, the use of graphene (gr) in proximity with large SOC layers has been proposed as an efficient and tunable spin transport channel. Here, we explore the role of a graphene monolayer between Co and a HM and its interfacial spin transport properties by means of thermo-spin measurements. The gr/HM (Pt and Ta) stacks have been prepared on epitaxial Ir(111)/Co(111) structures grown on sapphire crystals, in which the spin detector (i.e., top HM) and the spin injector (i.e., Co) are all grown in situ under controlled conditions and present clean and sharp interfaces. We find that a gr monolayer retains the spin current injected into the HM from the bottom Co layer. This has been observed by detecting a net reduction in the sum of the spin Seebeck and interfacial contributions due to the presence of gr and independent from the spin Hall angle sign of the HM used.

Unified Framework for Charge-Spin Interconversion in Spin-Orbit Materials

Materials with spin-orbit coupling are of great interest for various spintronics applications due to the efficient electrical generation and detection of spin-polarized electrons. Over the past decade, many materials have been studied, including topological insulators, transition metals, Kondo insulators, semimetals, semiconductors, and oxides; however, there is no unifying physical framework for understanding the physics and therefore designing a material system and devices with the desired properties. We present a model that binds together the experimental data observed on the wide variety of materials in a unified manner. We show that in a material with a given spin-momentum locking, the density of states plays a crucial role in determining the charge-spin interconversion efficiency, and a simple inverse relationship can be obtained. Remarkably, experimental data obtained over the last decade on many different materials closely follow such an inverse relationship. We further deduce two figure-of-merits of great current interest: the spin-orbit torque (SOT) efficiency (for the direct effect) and the inverse Rashba-Edelstein effect length (for the inverse effect), which statistically show good agreement with the existing experimental data on wide varieties of materials. Especially, we identify a scaling law for the SOT efficiency with respect to the carrier concentration in the sample, which agrees with existing data. Such an agreement is intriguing since our transport model includes only Fermi surface contributions and fundamentally different from the conventional views of the SOT efficiency that includes contributions from all the occupied states.

Negligible spin–charge conversion in Bi films and Bi/Ag(Cu) bilayers

Spin pumping experiments using ferromagnetic metals have reported highly efficient spin–charge conversion in Bi and at the Bi/Ag interface, possibly due to the inverse Rashba–Edelstein effect. However, longitudinal spin Seebeck effect experiments using the yttrium iron garnet ferrimagnetic insulator in Bi films and Bi/Ag bilayers do not show evidence of appreciable spin-to-charge conversion except the large Nernst signal inherent to Bi. These contrasting conclusions highlight the differences between magnetic metals and magnetic insulators as spin current injectors. Only the detected voltages that adhere to the inverse spin Hall effect of jC = (2e/ℏ)θSH jS × σ are due to spin currents.

Spin current related magnetoresistance in epitaxial Pt/Co bilayers in the presence of spin Hall effect and Rashba-Edelstein effect

We analyze the experimentally obtained spin current related magnetoresistance (MR) in epitaxial Pt/Co bilayers by using a drift-diffusion model that incorporates both bulk spin Hall effect and interfacial Rashba-Edelstein effect (REE). The MR analysis yields, for the Pt/Co interface, a temperature-independent Rashba parameter in the order of ${10}^{\ensuremath{-}11}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}\phantom{\rule{0.16em}{0ex}}\mathrm{m}$ that agrees with theoretical calculations, along with an effective interfacial REE thickness of several angstroms, which is in overall consistency with our previous spin-orbit torque analysis. Our results suggest that both bulk and interface charge-spin current interconversions need to be taken into account for the spin current related MR analysis in highly conductive magnetic heterostructures such as the epitaxial Pt/Co bilayers.

Absence of Significant Spin-Current Generation in Ti/Fe−Co−B Bilayers with Strong Interfacial Spin-Orbit Coupling

After one decade of the intensive theoretical and experimental explorations, whether interfacial spin-orbit coupling (ISOC) at metallic magnetic interfaces can effectively generate a spin current has remained in dispute. Here, utilizing the Ti/FeCoB bilayers that are unique for the negligible bulk spin Hall effect and the strong tunable ISOC, we establish that there is no significant charge-to-spin conversion at magnetic interfaces via spin-orbit filtering effect or Rashba-Edelstein(-like) effect even when the ISOC is stronger than that of a typical Pt/ferromagnet interface and can promote strong perpendicular magnetic anisotropy. We also find a minimal orbital Hall effect in 3d Ti.

Unveiling the spin-to-charge current conversion signal in the topological insulator Bi2Se3 by means of spin pumping experiments

We report an investigation of the spin-to-charge current conversion in sputter-deposited films of the topological insulator ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ onto single crystalline layers of yttrium iron garnet (YIG-${\mathrm{Y}}_{3}{\mathrm{Fe}}_{5}{\mathrm{O}}_{12}$) and polycrystalline films of permalloy ($\mathrm{Py}\text{\ensuremath{-}}{\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$). Pure spin current was injected into the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ layer by means of the spin pumping process produced by the spin precession in microwave driven ferromagnetic resonance of the ferromagnetic film. The spin-to-charge current conversion occurring at the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$/ferromagnet interface is attributed to the inverse Rashba-Edelstein effect (IREE). From the data, we verified that the voltage generated by the spin-to-charge current conversion process in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ has the same polarity as the inverse spin Hall effect in Ta, which is opposite to the one in Pt. Also, from the dependence of the voltage on the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ thickness we were able the to calculate the IREE length values and found that $1.2\phantom{\rule{0.16em}{0ex}}\mathrm{pm}\ensuremath{\le}|{\ensuremath{\lambda}}_{\mathrm{IREE}}|\ensuremath{\le}2.2\phantom{\rule{0.16em}{0ex}}\mathrm{pm}$. This result allows us to conclude that indeed the surface states of ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ have a dominant role in the spin-to-charge current conversion process, and the mechanism based on the spin diffusion process plays a secondary role.

Charge–spin interconversion and its applications in magnetic sensing

Charge–spin interconversion provides an effective way to generate spin current, spin–orbit torque, and unconventional magnetoresistance that is different from the magnetoresistance originated from spin-polarized current. A widely studied system that leads to all these phenomena is the ferromagnet/heavy metal bilayer, in which spin accumulation/current is generated through either the spin Hall effect in the heavy metal layer or Rashba–Edelstein effect at the ferromagnet/heavy metal interface. The subsequent interaction of the current-induced spins with the ferromagnet generates spin–orbit torque, and the inverse conversion of the backflow spin current to charge current in the heavy metal layer leads to different types of magnetoresistances. Many proof-of-concept devices and applications have been demonstrated based on the spin–orbit torque and magnetoresistance in the bilayer system, including non-volatile memory, logic, nano-oscillator, magnetic sensor, neuromorphic and scholastic computing, etc. In addition to the bilayer systems, recently there is also a growing interest in charge–spin interconversion in single-layer ferromagnets. In this Perspective, we first introduce the charge–spin interconversion in different systems based on phenomenological models, after which we show how the spin–orbit torque and spin Hall magnetoresistance in ferromagnet/heavy metal bilayers can be exploited for magnetic sensing applications. We also discuss charge–spin interconversion in single-layer ferromagnets via the anomalous Hall effect.

Origin of spin–orbit torque in single-layer CoFeB investigated via in-plane harmonic Hall measurements

The current-induced spin–orbit torque in single-layer ferromagnetic CoFeB thin films is quantitatively investigated by using in-plane harmonic Hall measurements. After the subtraction of thermal contributions such as the anomalous and ordinary Nernst effects, the obtained overall spin–orbit torque is successfully decomposed into damping-like (DL) and field-like (FL) terms. The DL and FL torques exhibit opposite trends of ferromagnetic layer thickness dependence before saturation, giving rise to distinctively different spin torque efficiencies: the DL torque efficiency shows a strong thickness dependence, while the FL torque efficiency is almost independent of the thickness. Such a result shows strong evidence that the DL torque originates from a spin-Hall-like charge-spin conversion in the ferromagnet, while the FL torque stems from interfacial effects such as the Rashba–Edelstein effect. With both DL and FL torques quantified in the single-layer CoFeB, our results exhibit an important step toward the understanding of nontrivial spin–orbit torques in single-layer ferromagnetic thin films.

Anisotropic Spin-Orbit Torque through Crystal-Orientation Engineering in Epitaxial Pt

One of the main objectives of spintronics is to provide power-efficient switching of magnetic layers through electrical means, and in order to achieve this goal, alternate material systems with enhanced spin-orbit torque (SOT) must be engineered. In this work we provide evidence of anisotropy in the SOT and spin Hall effect (SHE) in epitaxial $\mathrm{Pt}$(110) grown on $\mathrm{Mg}\mathrm{O}$(110) single-crystal substrates, and find that the spin Hall angle and the dampinglike torque are 20% larger when current is applied along the [001] crystallographic direction as compared to [$1\overline{1}0$], leading to an equivalent reduction in switching current density along [001]. The anisotropy in SOT is attributed to the bulk contributions of the SHE in the $\mathrm{Pt}$ layer through its anisotropic resistance in this specific orientation. Measurements additionally suggest that the Rashba-Edelstein effect at the $\mathrm{Pt}$/$\mathrm{Ti}$ interface due to the $\mathrm{Pt}$(110) surface has a non-negligible effect on the spin diffusion length and SOT. By providing experimental evidence of the crystal orientation dependence of SOT-induced magnetization switching, this work helps to establish a path for energy-efficient magnetization switching through the alignment of devices with crystallographic directions of enhanced SOT generation.

Opposite current-induced spin polarizations in bulk-metallic Bi2Se3 and bulk-insulating Bi2Te2Se topological insulator thin flakes

One of the most fundamental and exotic properties of three-dimensional (3D) topological insulators (TIs) is spin-momentum locking (SML) of their topological surface states (TSSs), promising for potential applications in future spintronics. However, other possible conduction channels, such as a trivial two-dimensional electron gas (2DEG) with strong Rashba-type spin-orbit interaction (SOI) and bulk-conducting states that may possess a spin Hall effect (SHE), can coexist in 3D TIs, making determining the origin of the current-induced spin polarization (CISP) difficult. In this work, we directly compared the CISP between bulk-insulating ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$ (BTS221) and bulk-metallic ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ thin flakes using spin potentiometry. In the bulk-insulating BTS221, the observed CISP has a sign consistent with the expected helicity of the SML of the TSS, but an opposite sign to its calculated bulk spin Hall conductivity. However, compared to BTS221, an opposite CISP is observed in the bulk-metallic ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, consistent with both the expectations of its Rashba-Edelstein effect of the band-bending induced 2DEG and bulk intrinsic spin Hall Effect (SHE). If one assumes a representative occupation of the Rashba band of $3\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}$ in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ with a relevant relaxation time of 100 fs, the contribution to the CISP could be more dominated by the bulk intrinsic SHE. Our results provide an electrical way to distinguish the TSS from other possible conducting channels in spin transport measurements on 3D TIs, and open ways for the potential applications in charge-spin conversion devices.

Roadmap of spin-orbit torques.

Spin-orbit torque (SOT) is an emerging technology that enables the efficient manipulation of spintronic devices. The initial processes of interest in SOTs involved electric fields, spin-orbit coupling, conduction electron spins and magnetization. More recently interest has grown to include a variety of other processes that include phonons, magnons, or heat. Over the past decade, many materials have been explored to achieve a larger SOT efficiency. Recently, holistic design to maximize the performance of SOT devices has extended material research from a nonmagnetic layer to a magnetic layer. The rapid development of SOT has spurred a variety of SOT-based applications. In this Roadmap paper, we first review the theories of SOTs by introducing the various mechanisms thought to generate or control SOTs, such as the spin Hall effect, the Rashba-Edelstein effect, the orbital Hall effect, thermal gradients, magnons, and strain effects. Then, we discuss the materials that enable these effects, including metals, metallic alloys, topological insulators, two-dimensional materials, and complex oxides. We also discuss the important roles in SOT devices of different types of magnetic layers, such as magnetic insulators, antiferromagnets, and ferrimagnets. Afterward, we discuss device applications utilizing SOTs. We discuss and compare three-terminal and two-terminal SOT-magnetoresistive random-access memories (MRAMs); we mention various schemes to eliminate the need for an external field. We provide technological application considerations for SOT-MRAM and give perspectives on SOT-based neuromorphic devices and circuits. In addition to SOT-MRAM, we present SOT-based spintronic terahertz generators, nano-oscillators, and domain wall and skyrmion racetrack memories. This paper aims to achieve a comprehensive review of SOT theory, materials, and applications, guiding future SOT development in both the academic and industrial sectors.

Thermal Hall effect from a two-dimensional Schwinger boson gas with Rashba spin-orbit interaction: Application to ferromagnets with in-plane Dzyaloshinskii-Moriya interaction

Recently, uncovering the sources of thermal Hall effect in insulators has become an important issue. In the case of ferromagnetic insulators, it is well known that Dzyaloshinskii-Moriya (DM) interaction can induce magnon thermal Hall effect. Specifically, the DM vector parallel to the magnetization direction induces complex magnon hopping amplitudes, so that magnons act as if they feel Lorentz force. However, the DM vector which is orthogonal to the magnetization direction has hitherto been neglected as a possible source of magnon thermal Hall effect. This is because they play no role in the linear spin wave theory, an often invoked approximation when computing the magnon thermal Hall effect. Here, we challenge this expectation by presenting the self-consistent Schwinger-boson mean field study of two-dimensional magnets with ferromagnetic Heisenberg interaction and in-plane DM interaction. We find that the relevant Schwinger-boson mean field Hamiltonian takes the form of two-dimensional electron gas with Rashba spin-orbit interaction, which is known to show anomalous Hall effect, spin Hall effect, and Rashba-Edelstein effect, whose thermal counterparts also appear in our system. Importantly, the thermal Hall effect can be induced when out-of-plane magnetic field is applied, and persists even when the magnetic field is large, so that the spins are significantly polarized, and the linear spin wave theory is expected to be a reasonable approximation. Since the linear spin wave theory predicts vanishing thermal Hall effect, our result implies that linear spin wave is not a sufficient approximation, and that magnon-magnon interaction must be taken into account to predict the correct thermal Hall conductivity.

Interface-induced field-like optical spin torque in a ferromagnet/heavy metal heterostructure

Abstract The manipulation of magnetization in a metallic ferromagnet by using optical helicity has been much attracted attention for future opto-spintronic devices. The optical helicity–induced torques on the magnetization, optical spin torque, have been observed in ferromagnetic thin films recently. However, the interfacial effect of the optical spin torque in ferromagnet/nonmagnetic heavy metal heterostructures have not been addressed so far, which are widely utilized to efficiently control magnetization via electrical means. Here, we studied optical spin torque vectors in the ferromagnet/nonmagnetic heavy metal heterostructures and observed that in-plane field-like optical spin torque was significantly increased with decreasing ferromagnetic layer thicknesses. The interfacial field-like optical spin torque was explained by the optical Rashba–Edelstein effect caused by the structural inversion symmetry breaking. This work will aid in the efficient optical manipulation of thin film nanomagnets using optical helicity.