Universal intrinsic spin Hall effect

We describe a new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems. We argue that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current is intrinsic. In the usual case where both spin-orbit split bands are occupied, the intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening.     

Phase diagram of the spin Hall effect

We obtain analytic formulas for the frequency-dependent spin-Hall conductivity of a two-dimensional electron gas (2DEG) in the presence of impurities, linear spin-orbit Rashba interaction, and external magnetic field perpendicular to the 2DEG. We show how different mechanisms (skew scattering, side jump, and spin precession) can be brought in or out of focus by changing controllable parameters such as frequency, magnetic field, and temperature. We find, in particular, that the dc spin-Hall conductivity vanishes in the absence of a magnetic field, while a magnetic field restores the skew-scattering and side jump contributions proportionally to the ratio of magnetic and Rashba fields.     

Conserved spin current with a perpendicular magnetic field

Previous theoretical studies show that the spin current in spin-orbit coupled systems can be effectively conserved. In this study, we show that in the presence of an external magnetic field B perpendicular to the surface without causing Landau levels, the spin-Hall conductivity, including the conventional spin and spin-torque Hall currents exhibit an interesting symmetry, ${\sigma }_{xy}^c(B)={\sigma }_{xy}^c(-B)$ valid for k-linear and k-cubic Rashba systems. The phenomenon where the electric field generated spin z component is unaltered under $B\to -B$ is attributed to the fact that the spin precession is locked in spin-orbit coupled systems. The perpendicular magnetic field generates spin x and y components, which are linear to B, and thus, there is no time-reversal symmetry. This result provides evidence for the detection of the bulk spin-Hall current. Furthermore, the applied magnetic field breaks the degenerate point of the two-band model, and the resulting spin-Hall conductivity does not vanish even for systems with linear momentum, which implies that the Berry phase is not the principal mechanism in k-linear systems. The non-zero charge-Hall conductivity generated by the perpendicular magnetic field is discussed here.     

Spin Hall effect and Nernst effect in FePt/Au multi-terminal devices with different Au thicknesses

The spin-Hall effect and the Nernst effect were investigated in multi-terminal devices consisting of an FePt perpendicular spin polarizer and a Au Hall cross with different Au thicknesses. As the thickness of the Au Hall cross increased from 10 nm to 20 nm, the spin-Hall angle (${\alpha }_H$) was significantly reduced. The significant reduction of the spin-Hall angle indicates that the interface and/or surface scattering of the electron spins play a crucial role for the large ${\alpha }_H$. The voltage change due to the Nernst effect also decreased with increasing the thickness of the Au Hall cross.     

Influence of spin-orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a Rashba two-dimensional electron gas

We study theoretically the influence of spin--orbit coupling induced by in-plane external electric field on the intrinsic spin-Hall effect in a two-dimensional electron gas with Rashba spin--orbit coupling. We show that, after such an influence is taken into account, the static intrinsic spin-Hall effect can be stabilized in a disordered Rashba two-dimensional electron gas, and the static intrinsic spin-Hall conductivity shall exhibit some interesting characteristics as conceived in some original theoretical proposals.     

Orbital ac spin-Hall effect in the hopping regime

The Rashba and Dresselhaus spin-orbit interactions are both shown to yield the low temperature spin-Hall effect for strongly localized electrons coupled to phonons. A frequency-dependent electric field E(omega) generates a spin-polarization current, normal to E, due to interference of hopping paths. At zero temperature the corresponding spin-Hall conductivity is real and is proportional to omega2. At nonzero temperatures the coupling to the phonons yields an imaginary term proportional to omega. The interference also yields persistent spin currents at thermal equilibrium, at E=0. The contributions from the Dresselhaus and Rashba interactions to the interference oppose each other.     

Spin transverse force on spin current in an electric field

As a relativistic quantum mechanical effect, it is shown that the electron field exerts a transverse force on an electron spin 1/2 only if the electron is moving. The spin force, analogue to the Lorentz for an electron charge in a magnetic field, is perpendicular to the electric field and the spin current whose spin polarization is projected along the electric field. This spin-dependent force can be used to understand the Zitterbewegung of the electron wave packet with spin-orbit coupling and is relevant to the generation of the charge Hall effect driven by the spin current in semiconductors.     

Experimental observation of the spin-Hall effect in a spin–orbit coupled two-dimensional hole gas

Electrically induced ordering and manipulation of electron spins in semiconductors has a number of practical advantages over the established techniques using circularly polarized light sources, external magnetic fields and spin injection from a ferromagnet. The spin-Hall effect utilizes spin–orbit coupling to induce edge spin accumulation in response to a longitudinal electric field which can be applied locally and lead to low energy consumption devices. We study spin accumulation near the edge of a weakly disordered two-dimensional hole gas (2DHG) in a GaAs/AlGaAs heterostructure where the magnitude of the transverse spin current approaches the intrinsic, disorder independent value, in contrast to the impurity dominated regime observed in 3D electron doped systems. In our experiment, the induced spin polarization is detected by the electroluminescence resulting from two p–n junctions bordering the 2DHG channel. When an electric field is applied across the 2DHG channel, a non-zero out-of-plane component of the spin is optically detected. The sign of the spin depends on the direction of the field and is opposite for the two edges, consistent with theory predictions. We also report and analyze an in-plane spin-polarization effect induced in the device by asymmetric electron–hole recombination.     

Electron spin precession in two-dimensional electron gas with Rashba spin-orbit coupling

Using the time-dependent Schrödinger equation, we present the analytical result of the expectation value of spin injected into a two-dimensional electron gas with respect to an arbitrarily spin-polarized electron state and monitor the spin time-evolution. We demonstrate that the expectation value of spin operator Sx is the time-independent, and only the expectation values in the Sy-Sz plane are time-dependent. A detailed study of spin precession in the spin-valve and spin-transistor geometry is presented, in which the initial spin-polarized electron state point perpendicular and parallel to the current direction, respectively. We put forward the possible reason that the resistance change is independent of gate voltage in the spin-valve geometry. Furthermore, it has been shown that the effective magnetic field generated by the spin-orbit interaction is not same with the truly magnetic field. The main effect of the truly magnetic field is to align the spin along the field direction, but the effective magnetic field generated by the spin-orbit interaction does not.     

Spin-Hall insulator

Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin-Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum-Hall effect in that all the states below the gap contribute and there occurs no dissipation. However, the spin-Hall conductance is not quantized even in two dimensions. This is the first example of a nontrivial topological structure in a band insulator without any magnetic field.     

Spin-Seebeck effects in Ni81Fe19/Pt films

The spin-Seebeck effect (SSE) converts a heat current into a spin current, a flow of spin angular momentum, and spin voltage, the driving force for nonequilibrium spin currents, in a ferromagnetic metal. In this study, the SSE in a ferromagnetic Ni₈₁Fe₁₉ film has been investigated by means of the inverse spin-Hall effect (ISHE) in a Pt film at room temperature. The experimental results measured in the Ni₈₁Fe₁₉/Pt system show that the sign of the thermally induced spin voltage is reversed between the higher- and lower-temperature ends of the Ni₈₁Fe₁₉ film. The ISHE in the Pt film allows us to detect the SSE signal with high sensitivity and to separate it from extrinsic thermoelectric effects.     

The observation of inherent spin Seebeck effect in Rh/YIG hybrid structure

Rhodium (Rh) is a 4d metal possessing a large spin orbit coupling strength and spin-Hall conductivity with a very small magnetic susceptibility, implying an insignificant magnetic proximity effect (MPE). We report here the observation of longitudinal spin Seebeck effect (LSSE) using Rh as a normal metal. A Rh film was sputtered on nanometer thick YIG films of highly crystalline nature and extremely low magnetic damping to obtain Rh/YIG hybrid structure. A clear thermal voltage V_th (SSE voltage) was obtained when a temperature gradient was applied on the Rh/YIG hybrid. The Rh film showed a very weak anomalous Hall resistance and the magneto-resistive testing clearly ruled out the magnetization of the Rh films via MPE. The anisotropic magnetoresistance (AMR) revealed a clear spin hall magnetoresistance (SMR) signal in Rh film implying a purely intrinsic spin current generation, free from any parasitic magnetic effects. The work can open a new window in the study of pure and uncontaminated spin current, generated in ferromagnetic insulators, using Rh as spin current detector.     

Quantum theory of high-electric-field magnetotransport for a two-dimensional electron gas in microstructures

Summary Nonlinear response to an electric field applied in the plane of a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field is expressed in terms of an electric-field (F)-dependent magnetoconductivity in which the effect of the electric field is incorporated in the resolvent of the Liouville operator. This electric-field-dependent Kubo-type formula is calculated in the presence of the simultaneous scattering by disorder and phonons and is expressed in terms of the electric-field-dependent broadening and shifting of the Landau levels. It is found to be essential to treat the two interactions simultaneously and self-consistently at low temperatures. High-field effects such as ?collisional broadening? and ?intracollisional field effects? as manifested through the electric-field-dependent tetradic self-energy of 2DEG in a perpendicular magnetic field are calculated and shown to be much more pronounced in 2DEG as compared to the same phenomenon in three-dimensional semiconductors. The present results are found to be useful in the calculation of the effects of the temperature (T), magnetic field (B) and the electric field (F) as well as the interplay of the two interactions on the quantum effects as manifested in the Landau level broadening due to the relaxation and acceleration of the electrons in an applied electric field. In the limitF→0 the present results reduce to the usual formulae as known from the linear response theory.     

Spin Hall current driven by quantum interferences in mesoscopic Rashba rings

We propose an all-electrical nanostructure where pure spin current is induced in the transverse voltage probes attached to a quantum-coherent ballistic one-dimensional ring when unpolarized charge current is injected through its longitudinal leads. Tuning of the Rashba spin-orbit coupling in a semiconductor heterostructure hosting the ring generates quasiperiodic oscillations of the predicted spin-Hall current due to spin-sensitive quantum-interference effects caused by the difference in the Aharonov-Casher phase accumulated by opposite spin states. Its amplitude is comparable to that of the spin-Hall current predicted for finite-size (simply connected) two-dimensional electron gases, while it gets reduced gradually in wide two-dimensional rings or due to spin-independent disorder.     

Semiclassical spin transport in spin-orbit-coupled bands

Motivated by recent interest in novel spintronics effects, we develop a semiclassical theory of spin transport that is valid for spin-orbit coupled bands. Aside from the obvious convective term in which the average spin is transported at the wave packet group velocity, the spin current has additional contributions from the wave packet's spin and torque dipole moments. Electric field corrections to the group velocity and carrier spin contribute to the convective term. Summing all terms we obtain an expression for the intrinsic spin-Hall conductivity of a hole-doped semiconductor, which agrees with the Kubo formula prediction for the same quantity. We discuss the calculation of spin accumulation, which illustrates the importance of the torque dipole near the boundary of the system.     

Intrinsic spin-Hall effect: topological transitions in two-dimensional systems

Topological transitions are the discontinuous changes of the Berry phase caused by continuous variation of parameters. These transitions can be detected by investigating the spin-Hall effect in two-dimensional electron and hole systems with a spin-obrit interaction when the density of carriers or the structural asymmetry are varied. The discontinuous behavior and the universality features of the spin-Hall conductivity are determined by the topological properties of the spin-orbit field.     

Photodetachment of H- near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H near an elastic wall in a magnetic field.The magnetic field confines the perpendicular motion of the electron,which results in a real three-dimensional well for the detached electron.The analytical formulas for the cross section of the photodetachment in the threedimensional quantum well are derived based on both the quantum approach and closed-orbit theory.The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment.The oscillation amplitude depends on the strength of the magnetic field,the ion-wall distance and the photon polarization as well.Specially,for the circularly polarized photon-induced photodetachment,the cross sections display a suppressed(E E th) 1/2 threshold law with energy E in the vicinity above Landau energy E th,contrasting with the(E E th) 1/2 threshold law in the presence of only the magnetic field.The semiclassical calculation fits the quantum result quite well,although there are still small deviations.The difference is attributed to the failure of semiclassical mechanics.     

Spin–orbit coupling and spin transport

Recent achievements in semiconductor spintronics are discussed. Special attention is paid to spin–orbit interaction, coupling of electron spins to external electric fields, and spin transport in media with spin–orbit coupling, including the mechanisms of spin-Hall effect. Importance of spin-transport parameters at spin-precession wave vector k_so is emphasized, and existence of an universal relation between spin currents and spin accumulation at the spatial scale of is conjectured.     

自旋轨道耦合系统中的自旋流与自旋霍尔效应

作为自旋电子学的重要研究内容,如何在固态系统中产生、操控以及探测自旋流引起了研究人员的广泛兴趣。基于自旋轨道耦合的自旋霍尔效应为在非磁性半导体中产生自旋流提供了一种有效途径。然而,在具有自旋轨道耦合的系统中,自旋流并不守恒。如何理解这点并恰当地表述相应的连续性方程,成为自旋输运研究的基本问题之一。本文主要综述自旋轨道耦合系统中自旋流与自旋霍尔效应方面的研究进展。引入SU(2)规范势后,自旋流满足协变形式的连续性方程,该方程保证了SU(2)Kubo公式在不同规范固定下的自洽性。利用SU(2)场强张量,可以直接得到自旋密度和自旋流在SU(2)外场中受到的自旋力,该力在只有U(1)磁场时对应于Stern-Gerlach力。由于依赖杂质散射的外在自旋霍尔效应很难被利用,内在自旋霍尔效应的概念被提出:在非磁半导体中,U(1)电场会诱导出自旋流并导致系统边缘处的自旋积累。自旋霍尔效应已经在半导体和金属材料中被观察到。虽然在干净的二维电子气中自旋霍尔电导率是一普适常数e/8π,但杂质对它的影响却引起了人们的高度关注。通过引入退相干效应,自旋霍尔效应中杂质效应的一些令人困惑的理论结果,则得到清晰的解释。此外,本文还将介绍具有层间隧穿的双层二维电子气中的自旋输运现象。在能量简并点附近,自旋霍尔电导率和隧穿自旋电导率均会出现共振现象。当两层间的杂质势强度存在差异时,隧穿自旋电导率随门压的变化曲线呈现出非对称性,显示出自旋二极管效应。     

自旋轨道耦合系统中的自旋流与自旋霍尔效应

作为自旋电子学的重要研究内容,如何在固态系统中产生、操控以及探测自旋流引起了研究人员的广泛兴趣.基于自旋轨道耦合的自旋霍尔效应为在非磁性半导体中产生自旋流提供了一种有效途径.然而,在具有自旋轨道耦合的系统中,自旋流并不守恒.如何理解这点并恰当地表述相应的连续性方程,成为自旋输运研究的基本问题之一.本文主要综述自旋轨道耦合系统中自旋流与自旋霍尔效应方面的研究进展.引入SU(2)规范势后,自旋流满足协变形式的连续性方程,该方程保证了SU(2)Kubo公式在不同规范固定下的自洽性.利用SU(2)场强张量,可以直接得到自旋密度和自旋流在SU(2)外场中受到的白旋力,该力在只有U(1)磁场时对应于Stern-Gerlach力.由于依赖杂质散射的外在自旋霍尔效应很难被利用,内在自旋霍尔效应的概念被提出:在非磁半导体中,U(1)电场会诱导出自旋流并导致系统边缘处的自旋积累.自旋霍尔效应已经在半导体和金属材料中被观察到.虽然在干净的二维电子气中自旋霍尔电导率是一普适常数e/8π,但杂质对它的影响却引起了人们的高度关注.通过引入退相干效应,自旋霍尔效应中杂质效应的一些令人困惑的理论结果,则得到清晰的解释.此外,本文还将介绍具有层间隧穿的双层二维电子气中的自旋输运现象.在能量简并点附近,自旋霍尔电导率和隧穿白旋电导率均会出现共振现象.当两层间的杂质势强度存在差异时,隧穿自旋电导率随门压的变化曲线呈现出非对称性,显示出自旋二极管效应.