Universal intrinsic spin Hall effect

Berry Phase Modification to the Energy Spectrum of Excitons

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and it highlights the importance of the Berry curvature in the effective mass approximation.

Light-Induced Exciton Spin Hall Effect in van der Waals Heterostructures

We propose a light-induced spin Hall effect for interlayer exciton gas in monolayer MoSe2-WSe2 van der Waals heterostructure. By applying two infrared, spatially varying laser beams coupled to the exciton internal states, a spin-dependent gauge potential on the exciton center-of-mass motion is induced. This gauge potential deflects excitons in different spin states towards opposite directions, leading to a finite spin current but vanishing mass current. In the Hall bar geometry, the spin-dependent deflection gives rise to spin-dependent chiral edge states with spin-velocity locking. The spin current and chiral edge states of the excitons can be detected by spatially resolved photoluminescence spectroscopy.

Quantum transport in Rashba spin-orbit materials: a review

In this review article we describe spin-dependent transport in materials with spin-orbit interaction of Rashba type. We mainly focus on semiconductor heterostructures, however we consider topological insulators, graphene and hybrid structures involving superconductors as well. We start from the Rashba Hamiltonian in a two dimensional electron gas and then describe transport properties of two- and quasi-one-dimensional systems. The problem of spin current generation and interference effects in mesoscopic devices is described in detail. We address also the role of Rashba interaction on localisation effects in lattices with nontrivial topology, as well as on the Ahronov-Casher effect in ring structures. A brief section, in the end, describes also some related topics including the spin-Hall effect, the transition from weak localisation to weak anti localisation and the physics of Majorana fermions in hybrid heterostructures involving Rashba materials in the presence of superconductivity.

Stacked bilayer phosphorene: strain-induced quantum spin Hall state and optical measurement

Bilayer phosphorene attracted considerable interest, giving a potential application in nanoelectronics owing to its natural bandgap and high carrier mobility. However, very little is known regarding the possible usefulness in spintronics as a quantum spin Hall (QSH) state of material characterized by a bulk energy gap and gapless spin-filtered edge states. Here, we report a strain-induced topological phase transition from normal to QSH state in bilayer phosphorene, accompanied by band-inversion that changes number from 0 to 1, which is highly dependent on interlayer stacking. When the bottom layer is shifted by 1/2 unit-cell along zigzag/armchair direction with respect to the top layer, the maximum topological bandgap 92.5 meV is sufficiently large to realize QSH effect even at room-temperature. An optical measurement of QSH effect is therefore suggested in view of the wide optical absorption spectrum extending to far infra-red, making bilayer phosphorene a promising candidate for opto-spintronic devices.

Controlling and probing non-abelian emergent gauge potentials in spinor Bose-Fermi mixtures

Gauge fields, typified by the electromagnetic field, often appear as emergent phenomena due to geometrical properties of a curved Hilbert subspace, and provide a key mechanism for understanding such exotic phenomena as the anomalous and topological Hall effects. Non-abelian gauge potentials serve as a source of non-singular magnetic monopoles. Here we show that unlike conventional solid materials, the non-abelianness of emergent gauge potentials in spinor Bose-Fermi atomic mixtures can be continuously varied by changing the relative particle-number densities of bosons and fermions. The non-abelian feature is captured by an explicit dependence of the measurable spin current density of fermions in the mixture on the variable coupling constant. Spinor mixtures also provide us with a method to coherently and spontaneously generate a pure spin current without relying on the spin Hall effect. Such a spin current is expected to have potential applications in the new generation of atomtronic devices.

Abelian and non-abelian emergent gauge fields govern the physics of many topological phenomena, such as Hall effects. Here the authors show theoretically that in a spinor Bose-Fermi mixture the non-abelianness of the gauge potential can be tuned, offering the chance to study the abelian-non-abelian crossover.

New perspectives for Rashba spin-orbit coupling

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

Spin Hall Effects Due to Phonon Skew Scattering

A diversity of spin Hall effects in metallic systems is known to rely on Mott skew scattering. In this work its high-temperature counterpart, phonon skew scattering, which is expected to be of foremost experimental relevance, is investigated. In particular, the phonon skew scattering spin Hall conductivity is found to be practically T independent for temperatures above the Debye temperature T_{D}. As a consequence, in Rashba-like systems a high-T linear behavior of the spin Hall angle demonstrates the dominance of extrinsic spin-orbit scattering only if the intrinsic spin splitting is smaller than the temperature.

OPTICS. Quantum spin Hall effect of light

Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.

Orthogonal Cherenkov sound in spin-orbit coupled systems

Conventionally the Cherenkov sound is governed by orbital degrees of freedom and is excited by supersonic particles. Additionally, it usually has a forward nature with a conic geometry known as the Cherenkov cone whose axis is oriented along the supersonic particle motion. Here we predict Cherenkov sound of a unique nature entirely resulting from the electronic spin degree of freedom and demonstrate a fundamentally distinct Cherenkov effect originating from essentially subsonic electrons in two-dimensional gases with both Bychkov-Rashba and Dresselhaus spin-orbit interactions. Specifically, we show that the axis of the conventional forward Cherenkov cone gets a nontrivial quarter-turn and at the same time the sound distribution strongly localizes around this rotated axis being now orthogonal to the subsonic particle motion. Apart from its fundamentally appealing nature, the orthogonal Cherenkov sound could have applications in planar semiconductor technology combining spin and acoustic phenomena to develop, e.g., acoustic amplifiers or sound sources with a flexible spin dependent orientation of the sound propagation.

Long-range spin-triplet correlations and edge spin currents in diffusive spin-orbit coupled SNS hybrids with a single spin-active interface

Utilizing a SU(2) gauge symmetry technique in the quasiclassical diffusive regime, we theoretically study finite-sized two-dimensional intrinsic spin-orbit coupled superconductor/normal-metal/superconductor (S/N/S) hybrid structures with a single spin-active interface. We consider intrinsic spin-orbit interactions (ISOIs) that are confined within the N wire and absent in the s-wave superconducting electrodes (S). Using experimentally feasible parameters, we demonstrate that the coupling of the ISOIs and spin moment of the spin-active interface results in maximum singlet-triplet conversion and accumulation of spin current density at the corners of the N wire nearest the spin-active interface. By solely modulating the superconducting phase difference, we show how the opposing parities of the charge and spin currents provide an effective venue to experimentally examine pure edge spin currents not accompanied by charge currents. These effects occur in the absence of externally imposed fields and moreover are insensitive to the arbitrary orientations of the interface spin moment. The experimental implementation of these robust edge phenomena are also discussed.

Magnon Hall effect on the Lieb lattice

Ferromagnetic insulators without inversion symmetry may show magnon Hall effect (MHE) in the presence of a temperature gradient due to the existence of Dzyaloshinskii-Moriya interaction (DMI). In this theoretical study, we investigate MHE on a lattice with inversion symmetry, namely the Lieb lattice, where the DMI is introduced by adding an external electric field. We show the nontrivial topology of this model by examining the existence of edge states and computing the topological phase diagram characterized by the Chern numbers of different bands. Together with the topological phase diagram, we can further determine the sign and magnitude of the transverse thermal conductivity. The impact of the flat band possessed by this model on the thermal conductivity is discussed by computing the Berry curvature analytically.

Chiral anomaly and transport in Weyl metals

We present an overview of our recent work on transport phenomena in Weyl metals, which may be connected to their nontrivial topological properties, particularly to chiral anomaly. We argue that there are two basic phenomena, which are related to chiral anomaly in Weyl metals: anomalous Hall effect (AHE) and chiral magnetic effect (CME). While AHE is in principle present in any ferromagnetic metal, we demonstrate that a magnetic Weyl metal is distinguished from an ordinary ferromagnetic metal by the absence of the extrinsic and the Fermi surface part of the intrinsic contributions to the AHE, as long as the Fermi energy is sufficiently close to the Weyl nodes. The AHE in a Weyl metal is thus shown to be a purely intrinsic, universal property, fully determined by the location of the Weyl nodes in the first Brillouin zone. In other words, a ferromagnetic Weyl metal may be thought of as the only example of a ferromagnetic metal with a purely intrinsic AHE. We further develop a fully microscopic theory of diffusive magnetotransport in Weyl metals. We derive coupled diffusion equations for the total and axial (i.e. node-antisymmetric) charge densities and show that chiral anomaly manifests as a magnetic-field-induced coupling between them. We demonstrate that an experimentally-observable consequence of CME in magnetotransport in Weyl metals is a quadratic negative magnetoresistance, which will dominate all other contributions to magnetoresistance under certain conditions and may be regarded as a smoking-gun transport characteristic, unique to Weyl metals.

Anomalous Hall effect in Weyl metals

We present a theory of the anomalous Hall effect (AHE) in a doped Weyl semimetal, or Weyl metal, including both intrinsic and extrinsic (impurity scattering) contributions. We demonstrate that a Weyl metal is distinguished from an ordinary ferromagnetic metal by the absence of the extrinsic and the Fermi surface part of the intrinsic contributions to the AHE, as long as the Fermi energy is sufficiently close to the Weyl nodes. The AHE in a Weyl metal is thus shown to be a purely intrinsic, universal property, fully determined by the location of the Weyl nodes in the first Brillouin zone.

Revisiting galvanomagnetic effects in conducting ferromagnets

The recently proposed coupling between the angular momentum density and magnetic moments is shown to provide a straightforward alternative explanation for galvanomagnetic effects, i.e. for both anisotropic magnetoresistance (AMR) and planar Hall effect (PHE). Such coupling naturally reproduces the general formula associated with AMR and PHE and allows for the occurrence of so-called 'negative AMR'. This coupling also provides a unifying link between AMR, PHE and the anomalous Hall effect (AHE) since this same coupling was previously found to give rise to AHE (Bellaiche et al 2013 Phys. Rev. B 88 161102).

Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals

The controlled flow of spin and valley pseudospin is key to future electronics exploiting these internal degrees of freedom of carriers. Here, we discover a universal possibility for generating spin and valley currents by electric bias or temperature gradient only, which arises from the anisotropy of Fermi pockets in crystalline solids. We find spin and valley currents to the second order in the electric field as well as their thermoelectric counterparts, i.e., the nonlinear spin and valley Seebeck effects. These second-order nonlinear responses allow two unprecedented possibilities to generate pure spin and valley flows without net charge current: (i) by an ac bias or (ii) by an arbitrary inhomogeneous temperature distribution. As examples, we predict appreciable nonlinear spin and valley currents in two-dimensional (2D) crystals including graphene, monolayer and trilayer transition-metal dichalcogenides, and monolayer gallium selenide. Our finding points to a new route towards electrical and thermal generations of spin and valley currents for spintronic and valleytronic applications based on 2D quantum materials.

Electric control of the spin Hall effect by intervalley transitions

Controlling spin-related material properties by electronic means is a key step towards future spintronic technologies. The spin Hall effect (SHE) has become increasingly important for generating, detecting and using spin currents, but its strength--quantified in terms of the SHE angle--is ultimately fixed by the magnitude of the spin-orbit coupling (SOC) present for any given material system. However, if the electrons generating the SHE can be controlled by populating different areas (valleys) of the electronic structure with different SOC characteristic the SHE angle can be tuned directly within a single sample. Here we report the manipulation of the SHE in bulk GaAs at room temperature by means of an electrical intervalley transition induced in the conduction band. The spin Hall angle was determined by measuring an electromotive force driven by photoexcited spin-polarized electrons drifting through GaAs Hall bars. By controlling electron populations in different (Γ and L) valleys, we manipulated the angle from 0.0005 to 0.02. This change by a factor of 40 is unprecedented in GaAs and the highest value achieved is comparable to that of the heavy metal Pt.

Prediction of novel interface-driven spintronic effects

The recently proposed coupling between the angular momentum density and magnetic moment (Raeliarijaona et al 2013 Phys. Rev. Lett. 110 137205) is shown here to result in the prediction of (i) novel spin currents generated by an electrical current and (ii) new electrical currents induced by a spin current in systems possessing specific interfaces between two different materials. Some of these spin (electrical) currents can be reversed near the interface by reversing the applied electrical (spin) current. Similarities and differences between these novel spintronic effects and the well-known spin Hall and inverse spin Hall effects are also discussed.

Valleytronics. The valley Hall effect in MoS₂ transistors

Electrons in two-dimensional crystals with a honeycomb lattice structure possess a valley degree of freedom (DOF) in addition to charge and spin. These systems are predicted to exhibit an anomalous Hall effect whose sign depends on the valley index. Here, we report the observation of this so-called valley Hall effect (VHE). Monolayer MoS2 transistors are illuminated with circularly polarized light, which preferentially excites electrons into a specific valley, causing a finite anomalous Hall voltage whose sign is controlled by the helicity of the light. No anomalous Hall effect is observed in bilayer devices, which have crystal inversion symmetry. Our observation of the VHE opens up new possibilities for using the valley DOF as an information carrier in next-generation electronics and optoelectronics.

Realization of tunable photonic spin Hall effect by tailoring the Pancharatnam-berry phase

Recent developments in the field of photonic spin Hall effect (SHE) offer new opportunities for advantageous measurement of the optical parameters (refractive index, thickness, etc.) of nanostructures and enable spin-based photonics applications in the future. However, it remains a challenge to develop a tunable photonic SHE with any desired spin-dependent splitting for generation and manipulation of spin-polarized photons. Here, we demonstrate experimentally a scheme to realize the photonic SHE tunably by tailoring the space-variant Pancharatnam-Berry phase (PBP). It is shown that light beams whose polarization with a tunable spatial inhomogeneity can contribute to steering the space-variant PBP which creates a spin-dependent geometric phase gradient, thereby possibly realizing a tunable photonic SHE with any desired spin-dependent splitting. Our scheme provides a convenient method to manipulate the spin photon. The results can be extrapolated to other physical system with similar topological origins.

Spin-orbit-coupled superconductivity

Superconductivity and spin-orbit (SO) interaction have been two separate emerging fields until very recently that the correlation between them seemed to be observed. However, previous experiments concerning SO coupling are performed far beyond the superconducting state and thus a direct demonstration of how SO coupling affects superconductivity remains elusive. Here we investigate the SO coupling in the critical region of superconducting transition on Al nanofilms, in which the strength of disorder and spin relaxation by SO coupling are changed by varying the film thickness. At temperatures T sufficiently above the superconducting critical temperature T(c), clear signature of SO coupling reveals itself in showing a magneto-resistivity peak. When T < T(c), the resistivity peak can still be observed; however, its line-shape is now affected by the onset of the quasi two-dimensional superconductivity. By studying such magneto-resistivity peaks under different strength of spin relaxation, we highlight the important effects of SO interaction on superconductivity.

Large spin splitting of metallic surface-state bands at adsorbate-modified gold/silicon surfaces

Finding appropriate systems with a large spin splitting of metallic surface-state band which can be fabricated on silicon using routine technique is an essential step in combining Rashba-effect based spintronics with silicon technology. We have found that originally poor structural and electronic properties of the Au/Si(111) √3 x √3 surface can be substantially improved by adsorbing small amounts of suitable species (e.g., Tl, In, Na, Cs). The resultant surfaces exhibit a highly-ordered atomic structure and spin-split metallic surface-state band with a momentum splitting of up to 0.052 Å(-1) and an energy splitting of up to 190 meV at the Fermi level. The family of adsorbate-modified Au/Si(111) √3 x √3 surfaces, on the one hand, is thought to be a fascinating playground for exploring spin-splitting effects in the metal monolayers on a semiconductor and, on the other hand, expands greatly the list of material systems prospective for spintronics applications.

Superfluid spin transport through easy-plane ferromagnetic insulators

Superfluid spin transport-dissipationless transport of spin-is theoretically studied in a ferromagnetic insulator with easy-plane anisotropy. We consider an open geometry where the spin current is injected into the ferromagnet from one side by a metallic reservoir with a nonequilibrium spin accumulation and ejected into another metallic reservoir located downstream. Spin transport is studied using a combination of magnetoelectric circuit theory, Landau-Lifshitz-Gilbert phenomenology, and microscopic linear-response theory. We discuss how spin superfluidity can be probed in a magnetically mediated negative electron-drag experiment.

Mapping polarization induced surface band bending on the Rashba semiconductor BiTeI

Surfaces of semiconductors with strong spin-orbit coupling are of great interest for use in spintronic devices exploiting the Rashba effect. BiTeI features large Rashba-type spin splitting in both valence and conduction bands. Either can be shifted towards the Fermi level by surface band bending induced by the two possible polar terminations, making Rashba spin-split electron or hole bands electronically accessible. Here we demonstrate the first real-space microscopic identification of each termination with a multi-technique experimental approach. Using spatially resolved tunnelling spectroscopy across the lateral boundary between the two terminations, a previously speculated on p-n junction-like discontinuity in electronic structure at the lateral boundary is confirmed experimentally. These findings realize an important step towards the exploitation of the unique behaviour of the Rashba semiconductor BiTeI for new device concepts in spintronics.

Microscopic theory of the inverse Edelstein effect

We provide a precise microscopic definition of the recently observed inverse Edelstein effect in which a nonequilibrium spin accumulation in the plane of a two-dimensional (interfacial) electron gas drives an electric current perpendicular to its own direction. The drift-diffusion equations that govern the effect are presented and applied to the interpretation of the experiments.

An antidamping spin-orbit torque originating from the Berry curvature

Magnetization switching at the interface between ferromagnetic and paramagnetic metals, controlled by current-induced torques, could be exploited in magnetic memory technologies. Compelling questions arise regarding the role played in the switching by the spin Hall effect in the paramagnet and by the spin-orbit torque originating from the broken inversion symmetry at the interface. Of particular importance are the antidamping components of these current-induced torques acting against the equilibrium-restoring Gilbert damping of the magnetization dynamics. Here, we report the observation of an antidamping spin-orbit torque that stems from the Berry curvature, in analogy to the origin of the intrinsic spin Hall effect. We chose the ferromagnetic semiconductor (Ga,Mn)As as a material system because its crystal inversion asymmetry allows us to measure bare ferromagnetic films, rather than ferromagnetic-paramagnetic heterostructures, eliminating by design any spin Hall effect contribution. We provide an intuitive picture of the Berry curvature origin of this antidamping spin-orbit torque as well as its microscopic modelling. We expect the Berry curvature spin-orbit torque to be of comparable strength to the spin-Hall-effect-driven antidamping torque in ferromagnets interfaced with paramagnets with strong intrinsic spin Hall effect.

The family of topological phases in condensed matter†

The discovery of topological insulators and superconductors is an important advance in condensed matter physics. Topological phases reflect global properties of the quantum states in materials, and the boundary states are the characteristic of the materials. Such phases constitute a new branch in condensed matter physics. Here a historic development is briefly introduced, and the known family of phases in condensed matter are summarized.

Ginzburg-Landau-type theory of spin superconductivity

Spin superconductivity is a recently proposed analogue of conventional charge superconductivity, in which spin currents flow without dissipation but charge currents do not. Here we derive a universal framework for describing the properties of a spin superconductor along similar lines to the Ginzburg-Landau equations that describe conventional superconductors, and show that the second of these Ginzburg-Landau-type equations is equivalent to a generalized London equation. Just as the GL equations enabled researchers to explore the behaviour of charge superconductors, our Ginzburg-Landau-type equations enable us to make a number of non-trivial predictions about the potential behaviour of putative spin superconductor. They enable us to calculate the super spin current in a spin superconductor under a uniform electric field or that induced by a thin conducting wire. Moreover, they allow us to predict the emergence of new phenomena, including the spin-current Josephson effect in which a time-independent magnetic field induces a time-dependent spin current.

Collective spin Hall effect for electron-hole gratings

We show that an electric field parallel to the wave fronts of an electron-hole grating in a GaAs quantum well generates, via the electronic spin Hall effect, a spin grating of the same wave vector and with an amplitude that can exceed 1% of the amplitude of the initial density grating. We refer to this phenomenon as the "collective spin Hall effect." A detailed study of the coupled spin-charge dynamics for quantum wells grown in different directions reveals rich features in the time evolution of the induced spin density, including the possibility of generating a helical spin grating.

Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light

Here, we investigate the spin-induced manipulation of orbitals using metasurfaces constructed from geometric phase elements. By carrying the spin effects to the orbital angular momentum, we show experimentally the transverse angular splitting between the two spins in the reciprocal space with metasurface, as a direct observation of the optical spin Hall effect, and an associated global orbital rotation through the effective orientations of the geometric phase elements. Such spin-orbit interaction from a metasurface with a definite topological charge can be geometrically interpreted using the recently developed high order Poincaré sphere picture. These investigations may give rise to an extra degree of freedom in manipulating optical vortex beams and orbitals using "spin-enabled" metasurfaces.

Spin currents in a coherent exciton gas

We report the observation of spin currents in a coherent gas of indirect excitons. The realized long-range spin currents originate from the formation of a coherent gas of bosonic pairs--a new mechanism to suppress the spin relaxation. The spin currents result in the appearance of a variety of polarization patterns, including helical patterns, four-leaf patterns, spiral patterns, bell patterns, and periodic patterns. We demonstrate control of the spin currents by a magnetic field. We also present a theory of coherent exciton spin transport that describes the observed exciton polarization patterns and indicates the trajectories of the spin currents.

The spin Hall effect in a quantum gas

Electronic properties such as current flow are generally independent of the electron's spin angular momentum, an internal degree of freedom possessed by quantum particles. The spin Hall effect, first proposed 40 years ago, is an unusual class of phenomena in which flowing particles experience orthogonally directed, spin-dependent forces--analogous to the conventional Lorentz force that gives the Hall effect, but opposite in sign for two spin states. Spin Hall effects have been observed for electrons flowing in spin-orbit-coupled materials such as GaAs and InGaAs (refs 2, 3) and for laser light traversing dielectric junctions. Here we observe the spin Hall effect in a quantum-degenerate Bose gas, and use the resulting spin-dependent Lorentz forces to realize a cold-atom spin transistor. By engineering a spatially inhomogeneous spin-orbit coupling field for our quantum gas, we explicitly introduce and measure the requisite spin-dependent Lorentz forces, finding them to be in excellent agreement with our calculations. This 'atomtronic' transistor behaves as a type of velocity-insensitive adiabatic spin selector, with potential application in devices such as magnetic or inertial sensors. In addition, such techniques for creating and measuring the spin Hall effect are clear prerequisites for engineering topological insulators and detecting their associated quantized spin Hall effects in quantum gases. As implemented, our system realizes a laser-actuated analogue to the archetypal semiconductor spintronic device, the Datta-Das spin transistor.

Spin backflow and ac voltage generation by spin pumping and the inverse spin Hall effect

The spin current pumped by a precessing ferromagnet into an adjacent normal metal has a constant polarization component parallel to the precession axis and a rotating one normal to the magnetization. The former is now routinely detected as a dc voltage induced by the inverse spin Hall effect (ISHE). Here we compute ac ISHE voltages much larger than the dc signals for various material combinations and discuss optimal conditions to observe the effect. The backflow of spin is shown to be essential to distill parameters from measured ISHE voltages for both dc and ac configurations.

Anisotropy of spin relaxation and transverse transport in metals

Using first-principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the real-space direction of the spin-quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit coupling the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distributions in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

Maximum intrinsic spin-Hall conductivity in two-dimensional systems with k-linear spin-orbit interaction

We analytically calculate the intrinsic spin-Hall conductivities (ISHCs) (σ(z)(xy) and σ(z)(yx)) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix β̃. We find that the determinant of the spin-orbit matrix detβ̃ describes the effective coupling of the spin sz and orbital motion Lz. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical (σ(z)(xy) ≠ -σ(z)(yx)), and it is governed by the asymmetric response function Δβ̃, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than e/8π, but has an upper bound value of e/4π. We will show that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature in the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that detβ̃ determines the field strength of the SU(2) non-Abelian gauge field.

Crystal growth and electronic properties of a 3D Rashba material, BiTeI, with adjusted carrier concentrations

3D Rashba materials can be a leading player in spin-related novel phenomena, ranging from the metallic extreme (unconventional superconductivity) to the transport intermediate (spin Hall effects) to the novel insulating variant (3D topological insulating states). As the essential backbone for both fundamental and applied research of such a 3D Rashba material, this study established the growth of sizeable single crystals of a candidate compound BiTeI with adjusted carrier concentrations. Three techniques (standard vertical Bridgman, modified horizontal Bridgman, and vapour transport) were employed, and BiTeI crystals (>1 × 1 × 0.2 mm(3)) with fundamentally different electronic states from metallic to insulating were successfully grown by the chosen technique. The 3D Rashba electronic states, including the Fermi surface topology, for the corresponding carrier concentrations of the obtained BiTeI crystals were revealed by relativistic first-principles calculations.

Strongly spin-orbit coupled two-dimensional electron gas emerging near the surface of polar semiconductors

We investigate the two-dimensional highly spin-polarized electron accumulation layers commonly appearing near the surface of n-type polar semiconductors BiTeX (X=I, Br, and Cl) by angular-resolved photoemission spectroscopy. Because of the polarity and the strong spin-orbit interaction built in the bulk atomic configurations, the quantized conduction-band subbands show giant Rashba-type spin splitting. The characteristic 2D confinement effect is clearly observed also in the valence bands down to the binding energy of 4 eV. The X-dependent Rashba spin-orbit coupling is directly estimated from the observed spin-split subbands, which roughly scales with the inverse of the band-gap size in BiTeX.

The limit spin current in a time-dependent Rashba spin-orbit coupling system

The generation of spin current in a one dimensional electron gas (1DEG) system is studied, where the Rashba spin-orbit coupling (RSOC) is modulated by a time-varying gate voltage. With a simple unitary transformation, we show the appearance of an additional spin-dependent potential which results in a spin-dependent effective electric field. We include the scattering interaction by taking a relaxation approximation. The formula for the induced spin current is derived, the limit value accessible by time-varying RSOC is obtained and the order of magnitude is estimated. We find that the maximum of a pulsed spin current can reach that limit value. The results in 1DEG are extended to 2DEG. In addition, we study the spin current in a metal-quantum dot-metal system.

Unconventional quantum Hall effect and tunable spin hall effect in Dirac materials: application to an isolated MoS2 trilayer

We analyze the Landau level (LL) structure in a MoS(2) trilayer and find a field-dependent unconventional Hall plateau sequence ν=…,-2M-6,-2M-4,-2M-2,-2M-1,…,-5,-3,-1,0,2,4,…. Because of orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with B, rather than with √[B]. Spin-orbital couplings break spin and valley degenerate LL's into two groups, with LL crossing effects present in the valence bands. In a p-n junction, spin-resolved fractionally quantized conductance appears in two-terminal measurements with a controllable spin-polarized current that can be probed at the interface. We also show the tunability of zero-field spin Hall conductivity.

Hall voltages without a magnetic field in a non-uniform two-dimensional electron system

We report on a measurement of giant second-harmonic Hall voltages which occur without a magnetic field and do not change their sign on current reversal in a two-dimensional electron system with a transverse density gradient. A quadratic dependence on the electric field, a strong temperature dependence, and both magnitude and directional dependence on the magnetic field are also observed. Such behavior points towards a plausible explanation based on a novel spin Hall effect with in-plane spin polarization.

Coherent propagation of spin helices in a quantum-well confined electron gas

We use phase-resolved transient grating spectroscopy to measure the propagation of spin helices in a high mobility n-GaAs/AlGaAs quantum well with an applied in-plane electric field. At relatively low fields helical modes crossover from overdamped excitations where the spin-precession period exceeds the spin lifetime, to a regime of coherent propagation where several spin-precession periods can be observed. We demonstrate that the envelope of a spin polarization packet reaches a current-driven velocity of 10(7) cm s(-1) in an applied field of 70 V cm(-1).

Fluctuation-induced magnetization dynamics and criticality at the interface of a topological insulator with a magnetically ordered layer

We consider a theory for a two-dimensional interacting conduction electron system with strong spin-orbit coupling on the interface between a topological insulator and the magnetic (ferromagnetic or antiferromagnetic) layer. For the ferromagnetic case we derive the Landau-Lifshitz equation, which features a contribution proportional to a fluctuation-induced electric field obtained by computing the topological (Chern-Simons) contribution from the vacuum polarization. We also show that fermionic quantum fluctuations reduce the critical temperature T[over ˜](c) at the interface relative to the critical temperature T(c) of the bulk, so that in the interval T[over ˜](c)≤T<T(c) it is possible to have a coexistence of gapless Dirac fermions at the interface with a ferromagnetically ordered layer. For the case of an antiferromagnetic layer on a topological insulator substrate, we show that a second-order quantum phase transition occurs at the interface, and compute the corresponding critical exponents. In particular, we show that the electrons at the interface acquire an anomalous dimension at criticality. The critical behavior of the Néel order parameter is anisotropic and features large anomalous dimensions for both the longitudinal and transversal fluctuations.

Nonlinear anomalous Hall effect and negative magnetoresistance in a system with random Rashba field

We predict two spin-dependent transport phenomena in two-dimensional electron systems, which are induced by a spatially fluctuating Rashba spin-orbit interaction. When the electron gas is magnetized, the random Rashba interaction leads to the anomalous Hall effect. An example of such a system is a narrow-gap magnetic semiconductor-based symmetric quantum well. We show that the anomalous Hall conductivity reveals a strongly nonlinear dependence on the magnetization, decreasing exponentially at large spin density. We also show that electron scattering from a fluctuating Rashba field in a two-dimensional nonmagnetic electron system leads to a negative magnetoresistance arising solely due to spin-dependent effects.

Magnetic oscillations driven by the spin Hall effect in 3-terminal magnetic tunnel junction devices

We show that a direct current in a tantalum microstrip can induce steady-state magnetic oscillations in an adjacent nanomagnet through spin torque from the spin Hall effect (SHE). The oscillations are detected electrically via a magnetic tunnel junction (MTJ) contacting the nanomagnet. The oscillation frequency can be controlled using the MTJ bias to tune the magnetic anisotropy. In this 3-terminal device, the SHE torque and the MTJ bias therefore provide independent controls of the oscillation amplitude and frequency, enabling new approaches for developing tunable spin torque nano-oscillators.

Current-induced switching of perpendicularly magnetized magnetic layers using spin torque from the spin Hall effect

We show that in a perpendicularly magnetized Pt/Co bilayer the spin-Hall effect (SHE) in Pt can produce a spin torque strong enough to efficiently rotate and switch the Co magnetization. We calculate the phase diagram of switching driven by this torque, finding quantitative agreement with experiments. When optimized, the SHE torque can enable memory and logic devices with similar critical currents and improved reliability compared to conventional spin-torque switching. We suggest that the SHE torque also affects current-driven magnetic domain wall motion in Pt/ferromagnet bilayers.

Detection of electrically modulated inverse spin hall effect in an Fe/GaAs microdevice

We report the detection of the inverse spin Hall effect (ISHE) in n-gallium arsenide (n-GaAs) combined with electrical injection and modulation of the spin current. We use epitaxial ultrathin-Fe/GaAs injection contacts with strong in-plane magnetic anisotropy. This allows us to simultaneously perform Hanle spin-precession measurements on an Fe detection electrode and ISHE measurements in an applied in-plane hard-axis magnetic field. In this geometry, we can experimentally separate the ordinary from the spin-Hall signals. Electrical spin injection and detection are combined in our microdevice with an applied electrical drift current to modulate the spin distribution and spin current in the channel. The magnitudes and external field dependencies of the signals are quantitatively modeled by solving drift-diffusion and Hall-cross response equations.