Universal intrinsic spin Hall effect

Direct visualization of current-induced spin accumulation in topological insulators

Charge-to-spin conversion in various materials is the key for the fundamental understanding of spin-orbitronics and efficient magnetization manipulation. Here we report the direct spatial imaging of current-induced spin accumulation at the channel edges of Bi2Se3 and BiSbTeSe2 topological insulators as well as Pt by a scanning photovoltage microscope at room temperature. The spin polarization is along the out-of-plane direction with opposite signs for the two channel edges. The accumulated spin direction reverses sign upon changing the current direction and the detected spin signal shows a linear dependence on the magnitude of currents, indicating that our observed phenomena are current-induced effects. The spin Hall angle of Bi2Se3, BiSbTeSe2, and Pt is determined to be 0.0085, 0.0616, and 0.0085, respectively. Our results open up the possibility of optically detecting the current-induced spin accumulations, and thus point towards a better understanding of the interaction between spins and circularly polarized light.

Theory of in-plane current induced spin torque in metal/ferromagnet bilayers

Using a semiclassical approach that simultaneously incorporates the spin Hall effect (SHE), spin diffusion, quantum well states, and interface spin-orbit coupling (SOC), we address the interplay of these mechanisms as the origin of the spin-orbit torque (SOT) induced by in-plane currents, as observed in the normal metal/ferromagnetic metal bilayer thin films. Focusing on the bilayers with a ferromagnet much thinner than its spin diffusion length, such as Pt/Co with  ∼10 nm thickness, our approach addresses simultaneously the two contributions to the SOT, namely the spin-transfer torque (SHE-STT) due to SHE-induced spin injection, and the inverse spin Galvanic effect spin-orbit torque (ISGE-SOT) due to SOC-induced spin accumulation. The SOC produces an effective magnetic field at the interface, hence it modifies the angular momentum conservation expected for the SHE-STT. The SHE-induced spin voltage and the interface spin current are mutually dependent and, hence, are solved in a self-consistent manner. The result suggests that the SHE-STT and ISGE-SOT are of the same order of magnitude, and the spin transport mediated by the quantum well states may be an important mechanism for the experimentally observed rapid variation of the SOT with respect to the thickness of the ferromagnet.

Theory of Large Intrinsic Spin Hall Effect in Iridate Semimetals

We theoretically investigate the mechanism to generate large intrinsic spin Hall effect in iridates or more broadly in 5d transition metal oxides with strong spin-orbit coupling. We demonstrate such a possibility by taking the example of orthorhombic perovskite iridate with nonsymmorphic lattice symmetry, SrIrO₃, which is a three-dimensional semimetal with nodal line spectrum. It is shown that large intrinsic spin Hall effect arises in this system via the spin-Berry curvature originating from the nearly degenerate electronic spectra surrounding the nodal line. This effect exists even when the nodal line is gently gapped out, due to the persistent nearly degenerate electronic structure. The magnitude of the spin Hall conductivity is shown to be comparable to the best known example such as doped topological insulators and the biggest in any transition metal oxides. To gain further insight, we compute the intrinsic spin Hall conductivity in both bulk and thin film systems. We find that the geometric confinement in thin films leads to significant modifications of the electronic states, leading to even bigger spin Hall conductivity in certain cases. We compare our findings with the recent experimental report on the discovery of large spin Hall effect in SrIrO₃ thin films.

Spin Hall effect originated from fractal surface

The spin Hall effect (SHE) has shown promising impact in the field of spintronics and magnonics from fundamental and practical points of view. This effect originates from several mechanisms of spin scatterers based on spin-orbit coupling (SOC) and also can be manipulated through the surface roughness. Here, the effect of correlated surface roughness on the SHE in metallic thin films with small SOC is investigated theoretically. Toward this, the self-affine fractal surface in the framework of the Born approximation is exploited. The surface roughness is described by the k-correlation model and is characterized by the roughness exponent H [Formula: see text], the in-plane correlation length ξ and the rms roughness amplitude δ. It is found that the spin Hall angle in metallic thin film increases by two orders of magnitude when H decreases from H  =  1 to H  =  0. In addition, the source of SHE for surface roughness with Gaussian profile distribution function is found to be mainly the side jump scattering while that with a non-Gaussian profile suggests both of the side jump and skew scatterings are present. Our achievements address how details of the surface roughness profile can adjust the SHE in non-heavy metals.

Generation and detection of dissipationless spin current in a MgO/Si bilayer

Spintronics is an analogue to electronics where the spin of the electron rather than its charge is functionally controlled for devices. The generation and detection of spin current without ferromagnetic or exotic/scarce materials are two of the biggest challenges for spintronics devices. In this study, we report a solution to the two problems of spin current generation and detection in Si. Using non-local measurement, we experimentally demonstrate the generation of helical dissipationless spin current using the spin-Hall effect. Contrary to the theoretical prediction, we observe the spin-Hall effect in both n-doped and p-doped Si. The helical spin current is attributed to the site-inversion asymmetry of the diamond cubic lattice of Si and structure inversion asymmetry in a MgO/Si bilayer. The spin to charge conversion in Si is insignificant due to weak spin-orbit coupling. For the efficient detection of spin current, we report spin to charge conversion at the MgO (1 nm)/Si (2 µm) (p-doped and n-doped) thin film interface due to Rashba spin-orbit coupling. We detected the spin current at a distance of  >100 µm, which is an order of magnitude larger than the longest spin diffusion length measured using spin injection techniques. The existence of spin current in Si is verified from the coercivity reduction in a Co/Pd multilayer due to spin-orbit torque generated by spin current from Si.

Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system

We present a novel class of nonlinear dynamical systems-a hybrid of relativistic quantum and classical systems and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and an insulating ferromagnet, where the former possesses an insulating bulk with topologically protected, dissipationless, and conducting surface electronic states governed by the relativistic quantum Dirac Hamiltonian and the latter is described by the nonlinear classical evolution of its magnetization vector. The interactions between the two are essentially the spin transfer torque from the topological insulator to the ferromagnet and the local proximity induced exchange coupling in the opposite direction. The hybrid system exhibits a rich variety of nonlinear dynamical phenomena besides multistability such as bifurcations, chaos, and phase synchronization. The degree of multistability can be controlled by an external voltage. In the case of two coexisting states, the system is effectively binary, opening a door to exploitation for developing spintronic memory devices. Because of the dissipationless and spin-momentum locking nature of the surface currents of the topological insulator, little power is needed for generating a significant current, making the system appealing for potential applications in next generation of low power memory devices.

Orbital Edelstein Effect as a Condensed-Matter Analog of Solenoids

We theoretically study current-induced orbital magnetization in a chiral crystal. This phenomenon is an orbital version of the Edelstein effect. We propose an analogy between the current-induced orbital magnetization and an Ampère field in a solenoid in classical electrodynamics. To quantify this effect, we define a dimensionless parameter from the response coefficients relating a current density with an orbital magnetization. This dimensionless parameter can be regarded as a number of turns within a unit cell when the crystal is regarded as a solenoid, and it represents how "chiral" the crystal is. By focusing on the dimensionless parameter, one can design a band structure that realizes the induction of large orbital magnetization. In particular, a Weyl semimetal with all of the Weyl nodes close to the Fermi energy can have a large value for this dimensionless parameter, which can exceed that of a classical solenoid.

Tunable metal-insulator transition, Rashba effect and Weyl Fermions in a relativistic charge-ordered ferroelectric oxide

Controllable metal-insulator transitions (MIT), Rashba-Dresselhaus (RD) spin splitting, and Weyl semimetals are promising schemes for realizing processing devices. Complex oxides are a desirable materials platform for such devices, as they host delicate and tunable charge, spin, orbital, and lattice degrees of freedoms. Here, using first-principles calculations and symmetry analysis, we identify an electric-field tunable MIT, RD effect, and Weyl semimetal in a known, charge-ordered, and polar relativistic oxide Ag2BiO3 at room temperature. Remarkably, a centrosymmetric BiO6 octahedral-breathing distortion induces a sizable spontaneous ferroelectric polarization through Bi3+/Bi5+ charge disproportionation, which stabilizes simultaneously the insulating phase. The continuous attenuation of the Bi3+/Bi5+ disproportionation obtained by applying an external electric field reduces the band gap and RD spin splitting and drives the phase transition from a ferroelectric RD insulator to a paraelectric Dirac semimetal, through a topological Weyl semimetal intermediate state. These findings suggest that Ag2BiO3 is a promising material for spin-orbitonic applications.

Effect of spin relaxations on the spin mixing conductances for a bilayer structure

The spin current can result in a spin-transfer torque in the normal-metal(NM)—ferromagnetic-insulator(FMI) or normal-metal(NM)—ferromagnetic-metal(FMM) bilayer. In the earlier study on this issue, the spin relaxations were ignored or introduced phenomenologically. In this paper, considering the FMM or FMI with spin relaxations described by a non-Hermitian Hamiltonian, we derive an effective spin-transfer torque and an effective spin mixing conductance in the non-Hermitian bilayer. The dependence of the effective spin mixing conductance on the system parameters (such as insulating gap, s-d coupling, and layer thickness) as well as the relations between the real part and the imaginary part of the effective spin mixing conductance are given and discussed. We find that the effective spin mixing conductance can be enhanced in the non-Hermitian system. This provides us with the possibility to enhance the spin mixing conductance.

Magnetic Chern Insulators in a monolayer of Transition Metal Trichalcogenides

A monolayer of transition metal trichalcogenides has received a lot of attention as potential two dimensional magnetic materials. The system has a honeycomb structure of transition metal ions, where both spin-orbit coupling and electron correlation effect play an important role. Here, motivated by these transition metal series with effective doping or mixed valence case, we propose the possible realization of magnetic Chern insulators at quarter filled honeycomb lattice. We show that the interplay of intrinsic spin-orbit coupling and electron correlation opens a wide region of ferromagnetic Chern insulating phases in between metals and normal insulators. Within the mean field approximation, we present the phase diagram of a quarter filled Kane-Mele Hubbard model and also discuss the effects of Rashba spin-orbit coupling and nearest neighbor interactions on it.

Extraction of the Rashba spin-orbit coupling constant from scanning gate microscopy conductance maps for quantum point contacts

We study the possibility for the extraction of the Rashba spin-orbit coupling constant for a two-dimensional electron gas with the conductance microscopy technique. Due to the interplay between the effective magnetic field due to the Rashba spin-orbit coupling and the external magnetic field applied within the plane of confinement, the electron backscattering induced by a charged tip of an atomic force microscope located above the sample leads to the spin precession and spin mixing of the incident and reflected electron waves between the QPC and the tip-induced 2DEG depletion region. This mixing leads to a characteristic angle-dependent beating pattern visible in the conductance maps. We show that the structure of the Fermi level, bearing signatures of the spin-orbit coupling, can be extracted from the Fourier transform of the interference fringes in the conductance maps as a function of the magnetic field direction. We propose a simple analytical model which can be used to fit the experimental data in order to obtain the spin-orbit coupling constant.

Anisotropy and Suppression of Spin-Orbit Interaction in a GaAs Double Quantum Dot

The spin-flip tunneling rates are measured in GaAs-based double quantum dots by time-resolved charge detection. Such processes occur in the Pauli spin blockade regime with two electrons occupying the double quantum dot. Ways are presented for tuning the spin-flip tunneling rate, which on the one hand gives access to measuring the Rashba and Dresselhaus spin-orbit coefficients. On the other hand, they make it possible to turn on and off the effect of spin-orbit interaction with a high on/off ratio. The tuning is accomplished by choosing the alignment of the tunneling direction with respect to the crystallographic axes, as well as by choosing the orientation of the external magnetic field with respect to the spin-orbit magnetic field. Spin lifetimes of 10 s are achieved at a tunneling rate close to 1 kHz.

Atomically Abrupt Topological p-n Junction

Topological insulators (TI's) are a new class of quantum matter with extraordinary surface electronic states, which bear great potential for spintronics and error-tolerant quantum computing. In order to put a TI into any practical use, these materials need to be fabricated into devices whose basic units are often p-n junctions. Interesting electronic properties of a 'topological' p-n junction were proposed theoretically such as the junction electronic state and the spin rectification. However, the fabrication of a lateral topological p-n junction has been challenging because of materials, process, and fundamental reasons. Here, we demonstrate an innovative approach to realize a p-n junction of topological surface states (TSS's) of a three-dimensional (3D) topological insulator (TI) with an atomically abrupt interface. When a ultrathin Sb film is grown on a 3D TI of Bi₂Se₃ with a typical n-type TSS, the surface develops a strongly p-type TSS through the substantial hybridization between the 2D Sb film and the Bi₂Se₃ surface. Thus, the Bi₂Se₃ surface covered partially with Sb films bifurcates into areas of n- and p-type TSS's as separated by atomic step edges with a lateral electronic junction of as short as 2 nm. This approach opens a different avenue toward various electronic and spintronic devices based on well-defined topological p-n junctions with the scalability down to atomic dimensions.

Spin-orbit torques from interfacial spin-orbit coupling for various interfaces

We use a perturbative approach to study the effects of interfacial spin-orbit coupling in magnetic multilayers by treating the two-dimensional Rashba model in a fully three-dimensional description of electron transport near an interface. This formalism provides a compact analytic expression for current-induced spin-orbit torques in terms of unperturbed scattering coefficients, allowing computation of spin-orbit torques for various contexts, by simply substituting scattering coefficients into the formulas. It applies to calculations of spin-orbit torques for magnetic bilayers with bulk magnetism, those with interface magnetism, a normal metal/ferromagnetic insulator junction, and a topological insulator/ferromagnet junction. It predicts a dampinglike component of spin-orbit torque that is distinct from any intrinsic contribution or those that arise from particular spin relaxation mechanisms. We discuss the effects of proximity-induced magnetism and insertion of an additional layer and provide formulas for in-plane current, which is induced by a perpendicular bias, anisotropic magnetoresistance, and spin memory loss in the same formalism.

Rashba and Dresselhaus Couplings in Halide Perovskites: Accomplishments and Opportunities for Spintronics and Spin-Orbitronics

In halide hybrid organic-inorganic perovskites (HOPs), spin-orbit coupling (SOC) presents a well-documented large influence on band structure. However, SOC may also present more exotic effects, such as Rashba and Dresselhaus couplings. In this Perspective, we start by recalling the main features of this effect and what makes HOP materials ideal candidates for the generation and tuning of spin-states. Then, we detail the main spectroscopy techniques able to characterize these effects and their application to HOPs. Finally, we discuss potential applications in spintronics and in spin-orbitronics in those nonmagnetic systems, which would complete the skill set of HOPs and perpetuate their ride on the crest of the wave of popularity started with optoelectronics and photovoltaics.

Bulk Rashba Semiconductors and Related Quantum Phenomena

Bithmuth tellurohalides BiTeX (X = Cl, Br and I) are model examples of bulk Rashba semiconductors, exhibiting a giant Rashba-type spin splitting among their both valence and conduction bands. Extensive spectroscopic and transport experiments combined with the state-of-the-art first-principles calculations have revealed many unique quantum phenomena emerging from the bulk Rashba effect in these systems. The novel features such as the exotic inter- and intra-band optical transitions, enhanced magneto-optical response, divergent orbital dia-/para-magnetic susceptibility and helical spin textures with a nontrivial Berry's phase in the momentum space are among the salient discoveries, all arising from this effect. Also, it is theoretically proposed and indications have been experimentally reported that bulk Rashba semiconductors such as BiTeI have the capability of becoming a topological insulator under the application of a hydrostatic pressure. Here, we overview these studies and show that BiTeX are an ideal platform to explore the next aspects of quantum matter, which could ultimately be utilized to create spintronic devices with novel functionalities.

Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells

The concept of topology is becoming more and more relevant to the properties and functions of electronic materials including various transport phenomena and optical responses. A pedagogical introduction is given here to the basic ideas and their applications to optoelectronic processes in solids.

Bending strain engineering in quantum spin hall system for controlling spin currents

Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. Here the concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. We show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Furthermore, the curved quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.

Recent advances in the spin Hall effect of light

The spin Hall effect (SHE) of light, as an analogue of the SHE in electronic systems, is a promising candidate for investigating the SHE in semiconductor spintronics/valleytronics, high-energy physics and condensed matter physics, owing to their similar topological nature in the spin-orbit interaction. The SHE of light exhibits unique potential for exploring the physical properties of nanostructures, such as determining the optical thickness, and the material properties of metallic and magnetic thin films and even atomically thin two-dimensional materials. More importantly, it opens a possible pathway for controlling the spin states of photons and developing next-generation photonic spin Hall devices as a fundamental constituent of the emerging spinoptics. In this review, based on the viewpoint of the geometric phase gradient, we give a detailed presentation of the recent advances in the SHE of light and its applications in precision metrology and future spin-based photonics.

Toward surface orbitronics: giant orbital magnetism from the orbital Rashba effect at the surface of sp-metals

As the inversion symmetry is broken at a surface, spin-orbit interaction gives rise to spin-dependent energy shifts - a phenomenon which is known as the spin Rashba effect. Recently, it has been recognized that an orbital counterpart of the spin Rashba effect - the orbital Rashba effect - can be realized at surfaces even without spin-orbit coupling. Here, we propose a mechanism for the orbital Rashba effect based on sp orbital hybridization, which ultimately leads to the electric polarization of surface states. For the experimentally well-studied system of a BiAg₂ monolayer, as a proof of principle, we show from first principles that this effect leads to chiral orbital textures in k-space. In predicting the magnitude of the orbital moment arising from the orbital Rashba effect, we demonstrate the crucial role played by the Berry phase theory for the magnitude and variation of the orbital textures. As a result, we predict a pronounced manifestation of various orbital effects at surfaces, and proclaim the orbital Rashba effect to be a key platform for surface orbitronics.

Anomalous spin-orbit torque switching due to field-like torque-assisted domain wall reflection

Spin-orbit torques (SOTs) allow the electrical control of magnetic states. Current-induced SOT switching of the perpendicular magnetization is of particular technological importance. The SOT consists of damping-like and field-like torques, and understanding the combined effects of these two torque components is required for efficient SOT switching. Previous quasi-static measurements have reported an increased switching probability with the width of current pulses, as predicted considering the damping-like torque alone. We report a decreased switching probability at longer pulse widths, based on time-resolved measurements. Micromagnetic analysis reveals that this anomalous SOT switching results from domain wall reflections at sample edges. The domain wall reflection was found to strongly depend on the field-like torque and its relative sign to the damping-like torque. Our result demonstrates a key role of the field-like torque in deterministic SOT switching and the importance of the sign correlation of the two torque components, which may shed light on the SOT switching mechanism.

Interface-Induced Phenomena in Magnetism

This article reviews static and dynamic interfacial effects in magnetism, focusing on interfacially-driven magnetic effects and phenomena associated with spin-orbit coupling and intrinsic symmetry breaking at interfaces. It provides a historical background and literature survey, but focuses on recent progress, identifying the most exciting new scientific results and pointing to promising future research directions. It starts with an introduction and overview of how basic magnetic properties are affected by interfaces, then turns to a discussion of charge and spin transport through and near interfaces and how these can be used to control the properties of the magnetic layer. Important concepts include spin accumulation, spin currents, spin transfer torque, and spin pumping. An overview is provided to the current state of knowledge and existing review literature on interfacial effects such as exchange bias, exchange spring magnets, spin Hall effect, oxide heterostructures, and topological insulators. The article highlights recent discoveries of interface-induced magnetism and non-collinear spin textures, non-linear dynamics including spin torque transfer and magnetization reversal induced by interfaces, and interfacial effects in ultrafast magnetization processes.

Effect of quantum tunneling on spin Hall magnetoresistance

We present a formalism that simultaneously incorporates the effect of quantum tunneling and spin diffusion on the spin Hall magnetoresistance observed in normal metal/ferromagnetic insulator bilayers (such as Pt/Y₃Fe₅O₁₂) and normal metal/ferromagnetic metal bilayers (such as Pt/Co), in which the angle of magnetization influences the magnetoresistance of the normal metal. In the normal metal side the spin diffusion is known to affect the landscape of the spin accumulation caused by spin Hall effect and subsequently the magnetoresistance, while on the ferromagnet side the quantum tunneling effect is detrimental to the interface spin current which also affects the spin accumulation. The influence of generic material properties such as spin diffusion length, layer thickness, interface coupling, and insulating gap can be quantified in a unified manner, and experiments that reveal the quantum feature of the magnetoresistance are suggested.

Topological phase transition and evolution of edge states in In-rich InGaN/GaN quantum wells under hydrostatic pressure

Combining the k · p method with the third-order elasticity theory, we perform a theoretical study of the pressure-induced topological phase transition and the pressure evolution of topologically protected edge states in InN/GaN and In-rich InGaN/GaN quantum wells. We show that for a certain range of the quantum well parameters, thanks to a negative band gap pressure coefficient, it is possible to continuously drive the system from the normal insulator state through the topological insulator into the semimetal phase. The critical pressure for the topological phase transition depends not only on the quantum well thickness but also on the width of the Hall bar, which determines the coupling between the edge states localized at the opposite edges. We also find that in narrow Hall bar structures, near the topological phase transition, a significant Rashba-type spin splitting of the lower and upper branches of the edge state dispersion curve appears. This effect originates from the lack of the mirror symmetry of the quantum well potential caused by the built-in electric field, and can be suppressed by increasing the Hall bar width. When the pressure increases, the energy dispersion of the edge states becomes more parabolic-like and the spin splitting decreases. A further increase of pressure leads to the transition to a semimetal phase, which occurs due to the closure of the indirect 2D bulk band gap. The difference between the critical pressure at which the system becomes semimetallic, and the pressure for the topological phase transition, correlates with the variation of the pressure coefficient of the band gap in the normal insulator state.

Robust spin-orbit torque and spin-galvanic effect at the Fe/GaAs (001) interface at room temperature

Interfacial spin-orbit torques (SOTs) enable the manipulation of the magnetization through in-plane charge currents, which has drawn increasing attention for spintronic applications. The search for material systems providing efficient SOTs, has been focused on polycrystalline ferromagnetic metal/non-magnetic metal bilayers. In these systems, currents flowing in the non-magnetic layer generate—due to strong spin–orbit interaction—spin currents via the spin Hall effect and induce a torque at the interface to the ferromagnet. Here we report the observation of robust SOT occuring at a single crystalline Fe/GaAs (001) interface at room temperature. We find that the magnitude of the interfacial SOT, caused by the reduced symmetry at the interface, is comparably strong as in ferromagnetic metal/non-magnetic metal systems. The large spin-orbit fields at the interface also enable spin-to-charge current conversion at the interface, known as spin-galvanic effect. The results suggest that single crystalline Fe/GaAs interfaces may enable efficient electrical magnetization manipulation.

Interfacial spin-orbit torque allows electrical manipulation of magnetization, but this has been shown mostly in polycrystalline metal bilayers. Here the authors show robust spin-orbit torque in single crystalline Fe/GaAs interface at room temperature, observing conversion between spin and charge current.

Magnon Spin Nernst Effect in Antiferromagnets

We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with nontrivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.

Edge Plasmons in Two-Component Electron Liquids in the Presence of Pseudomagnetic Fields

We study the properties of edge plasmons in two-component electron liquids in the presence of pseudomagnetic fields, which have opposite signs for the two different electronic populations and therefore preserve the time-reversal symmetry. The physical realizations of such systems are many. We discuss the case of strained graphene, solving the problem with the Wiener-Hopf technique. We show (i) that two charged counterpropagating acoustic edge modes exist at the boundary and (ii) that, in the limit of large pseudomagnetic fields, each of them involves oscillations of only one of the two electronic components. We suggest that the edge pseudomagnetoplasmons of graphene can be used to selectively address the electrons of one specific valley, a feature relevant for the emerging field of valleytronics. Our solution highlights new features missing in previous (similar) results obtained with uncontrolled approximations, namely a logarithmic divergence of the plasmon velocity, and the absence of gapped edge modes inside the bulk-plasmon gap.

Perpendicular magnetic anisotropy of two-dimensional Rashba ferromagnets

We compute the magnetocrystalline anisotropy energy within two-dimensional Rashba models. For a ferromagnetic free-electron Rashba model, the magnetic anisotropy is exactly zero regardless of the strength of the Rashba coupling, unless only the lowest band is occupied. For this latter case, the model predicts in-plane anisotropy. For a more realistic Rashba model with finite band width, the magnetic anisotropy evolves from in-plane to perpendicular and back to in-plane as bands are progressively filled. This evolution agrees with first-principles calculations on the interfacial anisotropy, suggesting that the Rashba model captures energetics leading to anisotropy originating from the interface provided that the model takes account of the finite Brillouin zone. The results show that the electron density modulation by doping or an external voltage is more important for voltage-controlled magnetic anisotropy than the modulation of the Rashba parameter.

Quasiparticle Scattering in the Rashba Semiconductor BiTeBr: The Roles of Spin and Defect Lattice Site

Observations of quasiparticle interference have been used in recent years to examine exotic carrier behavior at the surfaces of emergent materials, connecting carrier dispersion and scattering dynamics to real-space features with atomic resolution. We observe quasiparticle interference in the strongly Rashba split 2DEG-like surface band found at the tellurium termination of BiTeBr and examine two mechanisms governing quasiparticle scattering: We confirm the suppression of spin-flip scattering by comparing measured quasiparticle interference with a spin-dependent elastic scattering model applied to the calculated spectral function. We also use atomically resolved STM maps to identify point defect lattice sites and spectro-microscopy imaging to discern their varying scattering strengths, which we understand in terms of the calculated orbital characteristics of the surface band. Defects on the Bi sublattice cause the strongest scattering of the predominantly Bi 6p derived surface band, with other defects causing nearly no scattering near the conduction band minimum.

Spin-torque generator engineered by natural oxidation of Cu

The spin Hall effect is a spin–orbit coupling phenomenon, which enables electric generation and detection of spin currents. This relativistic effect provides a way for realizing efficient spintronic devices based on electric manipulation of magnetization through spin torque. However, it has been believed that heavy metals are indispensable for the spin–torque generation. Here we show that the spin Hall effect in Cu, a light metal with weak spin–orbit coupling, is significantly enhanced through natural oxidation. We demonstrate that the spin–torque generation efficiency of a Cu/Ni₈₁Fe₁₉ bilayer is enhanced by over two orders of magnitude by tuning the surface oxidation, reaching the efficiency of Pt/ferromagnetic metal bilayers. This finding illustrates a crucial role of oxidation in the spin Hall effect, opening a route for engineering the spin–torque generator by oxygen control and manipulating magnetization without using heavy metals.

In thin film spintronic devices, heavy metals with strong spin-orbit coupling are required to achieve a sizeable spin Hall effect. Here, the authors demonstrate an enhancement of the spin Hall effect in Cu, a material with weak spin-orbit coupling, via natural oxidation.

Emergent spin-valley-orbital physics by spontaneous parity breaking

The spin-orbit coupling in the absence of spatial inversion symmetry plays an important role in realizing intriguing electronic states in solids, such as topological insulators and unconventional superconductivity. Usually, the inversion symmetry breaking is inherent in the lattice structures, and hence, it is not easy to control these interesting properties by external parameters. We here theoretically investigate the possibility of generating the spin-orbital entanglement by spontaneous electronic ordering caused by electron correlations. In particular, we focus on the centrosymmetric lattices with local asymmetry at the lattice sites, e.g. zigzag, honeycomb, and diamond structures. In such systems, conventional staggered orders, such as charge order and antiferromagnetic order, break the inversion symmetry and activate the antisymmetric spin-orbit coupling, which is hidden in a sublattice-dependent form in the paramagnetic state. Considering a minimal two-orbital model on a honeycomb structure, we scrutinize the explicit form of the antisymmetric spin-orbit coupling for all the possible staggered charge, spin, orbital, and spin-orbital orders. We show that the complete table is useful for understanding of spin-valley-orbital physics, such as spin and valley splitting in the electronic band structure and generalized magnetoelectric responses in not only spin but also orbital and spin-orbital channels, reflecting in peculiar magnetic, elastic, and optical properties in solids.

The theory of spin noise spectroscopy: a review

Direct measurements of spin fluctuations are becoming the mainstream approach for studies of complex condensed matter, molecular, nuclear, and atomic systems. This review covers recent progress in the field of optical spin noise spectroscopy (SNS) with an additional goal to establish an introduction into its theoretical foundations. Various theoretical techniques that have been recently used to interpret results of SNS measurements are explained alongside examples of their applications.

Magnetic gating of a 2D topological insulator

Deterministic control of transport properties through manipulation of spin states is one of the paradigms of spintronics. Topological insulators offer a new playground for exploring interesting spin-dependent phenomena. Here, we consider a ferromagnetic 'gate' representing a magnetic adatom coupled to the topologically protected edge state of a two-dimensional (2D) topological insulator to modulate the electron transmission of the edge state. Due to the locked spin and wave vector of the transport electrons the transmission across the magnetic gate depends on the mutual orientation of the adatom magnetic moment and the current. If the Fermi energy matches an exchange-split bound state of the adatom, the electron transmission can be blocked due to the full back scattering of the incident wave. This antiresonance behavior is controlled by the adatom magnetic moment orientation so that the transmission of the edge state can be changed from 1 to 0. Expanding this consideration to a ferromagnetic gate representing a 1D chain of atoms shows a possibility to control the spin-dependent current of a strip of a 2D topological insulator by magnetization orientation of the ferromagnetic gate.

Topological phase transition and quantum spin Hall edge states of antimony few layers

While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi₂Te₂Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition.

Rashba-Edelstein Magnetoresistance in Metallic Heterostructures

We report the observation of magnetoresistance originating from Rashba spin-orbit coupling (SOC) in a metallic heterostructure: the Rashba-Edelstein (RE) magnetoresistance. We show that the simultaneous action of the direct and inverse RE effects in a Bi/Ag/CoFeB trilayer couples current-induced spin accumulation to the electric resistance. The electric resistance changes with the magnetic-field angle, reminiscent of the spin Hall magnetoresistance, despite the fact that bulk SOC is not responsible for the magnetoresistance. We further found that, even when the magnetization is saturated, the resistance increases with increasing the magnetic-field strength, which is attributed to the Hanle magnetoresistance in this system.

Spin Transport at Interfaces with Spin-Orbit Coupling: Phenomenology

This paper presents the boundary conditions needed for drift-diffusion models to treat interfaces with spin-orbit coupling. Using these boundary conditions for heavy metal/ferromagnet bilayers, solutions of the drift-diffusion equations agree with solutions of the spin-dependent Boltzmann equation and allow for a much simpler interpretation of the results. A key feature of these boundary conditions is their ability to capture the role that in-plane electric fields have on the generation of spin currents that flow perpendicularly to the interface. The generation of these spin currents is a direct consequence of the effect of interfacial spin-orbit coupling on interfacial scattering. In heavy metal/ferromagnet bilayers, these spin currents provide an important mechanism for the creation of damping-like and field-like torques; they also lead to possible reinterpretations of experiments in which interfacial contributions to spin torques are thought to be suppressed.

Giant facet-dependent spin-orbit torque and spin Hall conductivity in the triangular antiferromagnet IrMn3

There has been considerable interest in spin-orbit torques for the purpose of manipulating the magnetization of ferromagnetic elements for spintronic technologies. Spin-orbit torques are derived from spin currents created from charge currents in materials with significant spin-orbit coupling that propagate into an adjacent ferromagnetic material. A key challenge is to identify materials that exhibit large spin Hall angles, that is, efficient charge-to-spin current conversion. Using spin torque ferromagnetic resonance, we report the observation of a giant spin Hall angle [Formula: see text] of up to ~0.35 in (001)-oriented single-crystalline antiferromagnetic IrMn₃ thin films, coupled to ferromagnetic permalloy layers, and a [Formula: see text] that is about three times smaller in (111)-oriented films. For (001)-oriented samples, we show that the magnitude of [Formula: see text] can be significantly changed by manipulating the populations of various antiferromagnetic domains through perpendicular field annealing. We identify two distinct mechanisms that contribute to [Formula: see text]: the first mechanism, which is facet-independent, arises from conventional bulk spin-dependent scattering within the IrMn₃ layer, and the second intrinsic mechanism is derived from the unconventional antiferromagnetic structure of IrMn₃. Using ab initio calculations, we show that the triangular magnetic structure of IrMn₃ gives rise to a substantial intrinsic spin Hall conductivity that is much larger for the (001) than for the (111) orientation, consistent with our experimental findings.

Spin-Swapping Transport and Torques in Ultrathin Magnetic Bilayers

Planar spin transport in disordered ultrathin magnetic bilayers comprising a ferromagnet and a normal metal (typically used for spin pumping, spin Seebeck and spin-orbit torque experiments) is investigated theoretically. Using a tight-binding model that puts the extrinsic spin Hall effect and spin swapping on equal footing, we show that the nature of spin-orbit coupled transport dramatically depends on the ratio between the layer thickness d and the mean free path λ. While the spin Hall effect dominates in the diffusive limit (d≫λ), spin swapping dominates in the Knudsen regime (d≲λ). A remarkable consequence is that spin swapping induces a substantial fieldlike torque in the Knudsen regime.

The induced nontrivial Z 2 topological phase in graphene sandwiched by pnictogen bilayers

By performing first-principles calculations, we find that graphene with nearly zero spin orbit coupling can be turned into a topological insulator after being sandwiched between pnictogen bilayers. It is found that a dipole field is induced between graphene and pnictogen bilayers, which will significantly pull down the Dirac point of graphene. Depending on the initial position of the Dirac point of graphene with respect to the energy gap of the pnictogen bilayers, Bi/graphene/Bi is found to be a metallic system while Sb/graphene/Sb a topological insulator. In Sb/graphene/Sb, a sizable gap is opened at the Dirac point of graphene. The strong spin-orbit coupling in Sb bilayers leads to a band inversion in the gapped Dirac cones of graphene via the proximity effect and the calculated Z 2 topological index further confirms that a nontrivial topological phase is induced in graphene. By applying longitudinal or lateral strains to Sb/graphene/Sb, topological phase transition occurs based on the change of the thickness of the Sb bilayer instead of the change of the separation between graphene and Sb bilayers.

Topological phases in two-dimensional materials: a review

Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.

Topological nature of nonlinear optical effects in solids

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Spin-Current and Spin-Splitting in Helicoidal Molecules Due to Spin-Orbit Coupling

The use of organic materials in spintronic devices has been seriously considered after recent experimental works have shown unexpected spin-dependent electrical properties. The basis for the confection of any spintronic device is ability of selecting the appropriated spin polarization. In this direction, DNA has been pointed out as a potential candidate for spin selection due to the spin-orbit coupling originating from the electric field generated by accumulated electrical charges along the helix. Here, we demonstrate that spin-orbit coupling is the minimum ingredient necessary to promote a spatial spin separation and the generation of spin-current. We show that the up and down spin components have different velocities that give rise to a spin-current. By using a simple situation where spin-orbit coupling is present, we provide qualitative justifications to our results that clearly point to helicoidal molecules as serious candidates to integrate spintronic devices.

Effects of Dephasing on Spin Lifetime in Ballistic Spin-Orbit Materials

We theoretically investigate spin dynamics in spin-orbit-coupled materials. In the ballistic limit, the spin lifetime is dictated by dephasing that arises from energy broadening plus a nonuniform spin precession. For the case of clean graphene, we find a strong anisotropy with spin lifetimes that can be short even for modest energy scales, on the order of a few ns. These results offer deeper insight into the nature of spin dynamics in graphene, and are also applicable to the investigation of other systems where spin-orbit coupling plays an important role.

Formation of Ideal Rashba States on Layered Semiconductor Surfaces Steered by Strain Engineering

Spin splitting of Rashba states in two-dimensional electron system provides a promising mechanism of spin manipulation for spintronics applications. However, Rashba states realized experimentally to date are often outnumbered by spin-degenerated substrate states at the same energy range, hindering their practical applications. Here, by density functional theory calculation, we show that Au one monolayer film deposition on a layered semiconductor surface β-InSe(0001) can possess "ideal" Rashba states with large spin splitting, which are completely situated inside the large band gap of the substrate. The position of the Rashba bands can be tuned over a wide range with respect to the substrate band edges by experimentally accessible strain. Furthermore, our nonequilibrium Green's function transport calculation shows that this system may give rise to the long-sought strong current modulation when made into a device of Datta-Das transistor. Similar systems may be identified with other metal ultrathin films and layered semiconductor substrates to realize ideal Rashba states.

Spin phase protection in interference of electron spin waves in lightly hydrogenated graphene

Here, we have realized the extremely light hydrogenation of a graphene surface on SiO₂ by precisely controlling the amount of electron beam (EB) irradiation to a specific EB resist including hydrogen atoms, treated on graphene.

Local currents in a 2D topological insulator

Symmetry protected edge states in 2D topological insulators are interesting both from the fundamental point of view as well as from the point of view of potential applications in nanoelectronics as perfectly conducting 1D channels and functional elements of circuits. Here using a simple tight-binding model and the Landauer-Büttiker formalism we explore local current distributions in a 2D topological insulator focusing on effects of non-magnetic impurities and vacancies as well as finite size effects. For an isolated edge state, we show that the local conductance decays into the bulk in an oscillatory fashion as explained by the complex band structure of the bulk topological insulator. We demonstrate that although the net conductance of the edge state is topologically protected, impurity scattering leads to intricate local current patterns. In the case of vacancies we observe vortex currents of certain chirality, originating from the scattering of current-carrying electrons into states localized at the edges of hollow regions. For finite size strips of a topological insulator we predict the formation of an oscillatory band gap in the spectrum of the edge states, the emergence of Friedel oscillations caused by an open channel for backscattering from an impurity and antiresonances in conductance when the Fermi energy matches the energy of the localized state created by an impurity.

Gauge Physics of Spin Hall Effect

Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. Our full treatment shows the Rashba 2DEG SHE conductivity to be instead of −, and Rashba heavy hole instead of −. This renewed treatment suggests a need to re-derive and re-calculate previously studied SHE conductivity.

Intrinsic spin torque without spin-orbit coupling

We derive an intrinsic contribution to the non-adiabatic spin torque for non-uniform magnetic textures. It differs from previously considered contributions in several ways and can be the dominant contribution in some models. It does not depend on the change in occupation of the electron states due to the current flow but rather is due to the perturbation of the electronic states when an electric field is applied. Therefore it should be viewed as electric-field-induced rather than current-induced. Unlike previously reported non-adiabatic spin torques, it does not originate from extrinsic relaxation mechanisms nor spin-orbit coupling. This intrinsic non-adiabatic spin torque is related by a chiral connection to the intrinsic spin-orbit torque that has been calculated from the Berry phase for Rashba systems.

Reduction of phase noise in nanowire spin orbit torque oscillators

Spin torque oscillators (STOs) are compact, tunable sources of microwave radiation that serve as a test bed for studies of nonlinear magnetization dynamics at the nanometer length scale. The spin torque in an STO can be created by spin-orbit interaction, but low spectral purity of the microwave signals generated by spin orbit torque oscillators hinders practical applications of these magnetic nanodevices. Here we demonstrate a method for decreasing the phase noise of spin orbit torque oscillators based on Pt/Ni80Fe20 nanowires. We experimentally demonstrate that tapering of the nanowire, which serves as the STO active region, significantly decreases the spectral linewidth of the generated signal. We explain the observed linewidth narrowing in the framework of the Ginzburg-Landau auto-oscillator model. The model reveals that spatial non-uniformity of the spin current density in the tapered nanowire geometry hinders the excitation of higher order spin-wave modes, thus stabilizing the single-mode generation regime. This non-uniformity also generates a restoring force acting on the excited self-oscillatory mode, which reduces thermal fluctuations of the mode spatial position along the wire. Both these effects improve the STO spectral purity.