Characteristics of anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic, extrinsic, and external electric-field induced spinben orbit couplings

The various competing contributions to the anomalous Hall effect in spin-polarized two-dimensional electron gases in the presence of both intrinsic, extrinsic and external electric-field induced spin-orbit coupling were investigated theoretically. Based on a unified semiclassical theoretical approach, it is shown that the total anomalous Hall conductivity can be expressed as the sum of three distinct contributions in the presence of these competing spin-orbit interactions, namely an intrinsic contribution determined by the Berry curvature in the momentum space, an extrinsic contribution determined by the modified Bloch band group velocity and an extrinsic contribution determined by spin-orbit-dependent impurity scattering. The characteristics of these competing contributions are discussed in detail in the paper.     

Anomalous Hall Effect in Spin-Polarized Two-Dimensional Hole Gas with Cubic-Rashbsa Spin-Orbit Interaction

Based on the Kubo formalism, the anomalous Hall effect in a magnetic two-dimensional hole gas with cubic-Rashba spin-orbit coupling is studied in the presence of δ-function scattering potential. When the weak, short-ranged disorder scattering is considered in the Born approximation, we find that the self-energy becomes diagonal in the helicity basis and its value is independent of the wave number, and the vertex correction to the anomalous Hall conductivity due to impurity scattering vanishes when both subbandsare occupied. That is to say, the anomalous Hall effect is not vanishing or influenced by the vertex correction for two-dimensional heavy-hole system, which is in sharp contrast to the case of linear-Rashba spin-orbit coupling in the electron band when the short-range disorder scattering is considered and the extrinsic mechanism as well as the effect of external electric field on the SO interaction are ignored.     

An Extended Extrinsic Mechanism for Anomalous Hall Effect

The extrinsic mechanism for anomalous Hall effect in ferromagnets is extended to include the contributions both from spin-orbit-dependent impurity scattering and from the spin-orbit coupling induced by external electric fields. The results obtained suggest that, within the framework of the extrinsic mechanisms, the anomalous Hall current in a ferromagnet may also contain a substantial amount of dissipationless contribution independent of impurity scattering. After the contribution from the spin-orbit coupling induced by external electric fields is included, the total anomalous Hall conductivity is about two times larger than that due to soin-orbit dependent impurity scatterings.     

Dissipationless spin-Hall current contribution in the extrinsic spin-Hall effect

This paper shows that a substantial amount of dissipationless spin-Hall current contribution may exist in the extrinsic spin-Hall effect, which originates from the spin-orbit coupling induced by the applied external electric field itself that drives the extrinsic spin-Hall effect in a nonmagnetic semiconductor (or metal). By assuming that the impurity density is in a moderate range such that the total scattering potential due to all randomly distributed impurities is a smooth function of the space coordinate, it is shown that this dissipationless contribution shall be of the same orders of magnitude as the usual extrinsic contribution from spin-orbit dependent impurity scatterings (or may even be larger than the latter one). The theoretical results obtained are in good agreement with recent relevant experimental results.     

Intrinsic spin hall effect induced by quantum phase transition in HgCdTe quantum wells

The spin Hall effect can be induced by both extrinsic impurity scattering and intrinsic spin-orbit coupling in the electronic structure. The HgTe/CdTe quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. By tuning the Cd content, the well width, or the bias electric field across the quantum well, the intrinsic spin Hall effect can be switched on or off and tuned into resonance under experimentally accessible conditions.     

Anomalous Hall effect in a two dimensional electron gas with magnetic impurities

Magnetic impurities play an important role in many spintronics-related materials. Motivated by this fact, we study the anomalous Hall effect in the presence of magnetic impurities, focusing on two-dimensional electron systems with Rashba spin-orbit coupling. We find a highly nonlinear dependence on the impurity polarization, including possible sign changes. At small impurity magnetizations, this is a consequence of the remarkable result that the linear term is independent of the spin-orbit coupling strength. Near saturation of the impurity spins, the anomalous Hall conductivity can be resonantly enhanced, due to interference between potential and magnetic scattering.     

Extrinsic spin Hall effect induced by iridium impurities in copper

We study the extrinsic spin Hall effect induced by Ir impurities in Cu by injecting a pure spin current into a CuIr wire from a lateral spin valve structure. While no spin Hall effect is observed without Ir impurity, the spin Hall resistivity of CuIr increases linearly with the impurity concentration. The spin Hall angle of CuIr, (2.1±0.6)% throughout the concentration range between 1% and 12%, is practically independent of temperature. These results represent a clear example of predominant skew scattering extrinsic contribution to the spin Hall effect in a nonmagnetic alloy.     

Orbitronics: the intrinsic orbital current in p-doped silicon

The spin Hall effect depends crucially on the intrinsic spin-orbit coupling of the energy band. Because of the smaller spin-orbit coupling in silicon, the spin Hall effect is expected to be much reduced. We show that an electric field in p-doped silicon can induce a dissipationless orbital current in a fashion reminiscent of the spin Hall effect. The vertex correction from impurity scattering vanishes and the effect is robust against disorder. The orbital Hall effect leads to accumulation of local orbital momentum at the edge of the sample, and can be detected by the Kerr effect.     

Electrically tunable quantum anomalous Hall effect in graphene decorated by 5d transition-metal adatoms

Based on first-principles calculations, we predict that 5d transition metals on graphene present a unique class of hybrid systems exhibiting topological transport effects that can be manipulated effectively by external electric fields. The origin of this phenomenon lies in the exceptional magnetic properties and the large spin-orbit interaction of the 5d metals leading to significant magnetic moments accompanied with colossal magnetocrystalline anisotropy energies. A strong magnetoelectric response is predicted that offers the possibility to switch the spontaneous magnetization direction by moderate electric fields, enabling an electrically tunable quantum anomalous Hall effect.     

Spin cloud induced around an elastic scatterer by the intrinsic spin hall effect

Similar to the Landauer electric dipole created around an impurity by the electric current, a spin polarized cloud of electrons can be induced by the intrinsic spin Hall effect near a spin independent elastic scatterer. It is shown that in the ballistic range around the impurity, such a cloud appears in the case of Rashba spin-orbit interaction, even though the bulk spin Hall current is absent.     

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.     

Hall effect induced by a spin-polarized current in superconductors

We propose a novel anomalous Hall effect caused by the spin-polarized current in superconductors (SC). The spin-polarized quasiparticles flowing in SC are deflected by spin-orbit scattering to yield a quasiparticle charge imbalance in the transverse direction. Overall charge neutrality gives rise to a compensating change in the number of Cooper pairs. A transverse electric field builds up as opposed to an acceleration of the Cooper pairs, producing the Hall voltage. It is found that the Hall voltages due to the side jump and skew scattering mechanisms have different temperature dependence in the superconducting state. A spin-injection Hall device to generate the ac Josephson effect is proposed.     

Absence of skew scattering in two-dimensional systems: testing the origins of the anomalous Hall effect

We study the anomalous Hall conductivity in spin-polarized, asymmetrically confined two-dimensional electron and hole systems, taking into account the intrinsic, side-jump, and skew-scattering contributions to the transport. We find that the skew scattering, principally responsible for the extrinsic contribution to the anomalous Hall effect, vanishes for the two-dimensional electron system if both chiral Rashba subbands are partially occupied, and vanishes always for the two-dimensional hole gas studied here, regardless of the band filling. Our prediction can be tested with the proposed coplanar two-dimensional electron-hole gas device and can be used as a benchmark to understand the crossover from the intrinsic to the extrinsic anomalous Hall effect.     

Intrinsic versus extrinsic anomalous Hall effect in ferromagnets

A unified theory of the anomalous Hall effect (AHE) is presented for multiband ferromagnetic metals with dilute impurities. In the clean limit, the AHE is mostly due to extrinsic skew scattering. When the Fermi level is located around anticrossing of band dispersions split by spin-orbit interaction, the intrinsic AHE to be calculated ab initio is resonantly enhanced by its nonperturbative nature, revealing the extrinsic-to-intrinsic crossover which occurs when the relaxation rate is comparable to the spin-orbit coupling.     

Spin-polarized transport through a time-periodic non-magnetic semiconductor heterostructure

Spin-dependent Floquet scattering theory is developed to investigate the photon-assisted spin-polarized electron transport through a semiconductor heterostructure in the presence of an external electric field. Spin-dependent Fano resonances and spin-polarized electron transport through a laser irradiated time-periodic non-magnetic heterostructure in the presence of Dresselhaus spin-orbit interaction and a gate-controlled Rashba spin-orbit interaction are investigated. The electric field due to laser along with the spin-orbit interactions help to get spin-dependent Fano resonances in the conductance, whereas the external bias can be appropriately adjusted to get a near 80% spin-polarized electron transmission through heterostructures. The resultant nature of the Floquet scattering depends on the relative strength of these two electric fields.     

Pure anomalous Hall effect in nonmagnetic zinc-blende semiconductors

We report the experimental observation of the pure anomalous Hall effect (AHE) in nonmagnetic zinc-blende semiconductors without application of the external magnetic fields. The AHE without any contribution from the ordinary Hall current originates from nonequilibrium magnetization induced by spin-polarized electrons generated by the circularly polarized light (σ). We measure the pure AHE as a function of the external bias, crystal temperature and pumping σ-photon energy. The results of their dependences are discussed.     

Out-of-plane spin polarization from in-plane electric and magnetic fields

We show that the joint effect of spin-orbit and magnetic fields leads to a spin polarization perpendicular to the plane of a homogeneous two-dimensional electron system with Rashba spin-orbit coupling and in-plane parallel dc magnetic and electric fields, for angle-dependent impurity scattering or nonparabolic energy spectrum, while only in-plane polarization persists for simplified models. We derive Bloch equations, describing the main features of recent experiments, including the magnetic field dependence of static and dynamic responses.     

Theory of spin Hall effect: extension of the Drude model

An extension of the Drude model is proposed that accounts for the spin and spin-orbit interaction of charge carriers. Spin currents appear due to the combined action of the external electric field, crystal field, and scattering of charge carriers. The expression for the spin Hall conductivity is derived for metals and semiconductors that is independent of the scattering mechanism. In cubic metals, the spin Hall conductivity sigma s and charge conductivity sigma c are related through sigma s=[2pi variant /(3mc2)]sigma2c with m being the bare electron mass. The theoretically computed value is in agreement with experiment.     

Anomalous Hall effect in ferromagnetic semiconductors in the hopping transport regime

We present a theory of the anomalous Hall effect in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conductivity sigma(AH)(xy). We show that sigma(AH)(xy) is proportional to the first derivative of the density of states varrho(epsilon) and thus can be expected to change sign as a function of impurity band filling. We also show that sigma(AH)(xy) depends on temperature as the longitudinal conductivity sigma(xx) within logarithmic accuracy.