The generation and manipulation of carrier spin polarization in semiconductors solely by electric fields has garnered significant attention as both an interesting manifestation of spin-orbit physics as well as a valuable capability for potential spintronics devices. One realization of these spin-orbit phenomena, the spin Hall effect (SHE), has been studied as a means of all-electrical spin current generation and spin separation in both semiconductor and metallic systems. Previous measurements of the spin Hall effect have focused on steady-state generation and time-averaged detection, without directly addressing the accumulation dynamics on the timescale of the spin coherence time. Here, we demonstrate time-resolved measurement of the dynamics of spin accumulation generated by the extrinsic spin Hall effect in a doped GaAs semiconductor channel. Using electrically-pumped time-resolved Kerr rotation, we image the accumulation, precession, and decay dynamics near the channel boundary with spatial and temporal resolution and identify multiple evolution time constants. We model these processes using time-dependent diffusion analysis utilizing both exact and numerical solution techniques and find that the underlying physical spin coherence time differs from the dynamical rates of spin accumulation and decay observed near the sample edges.
Spin and electric Hall currents are calculated numerically in a two-dimensional mesoscopic system with Rashba and Dresselhaus spin-orbit coupling by means of the Landauer-Buttiker formalism. It is found that both electric and spin Hall currents circulate when two spin-orbit couplings coexist, while the electric Hall conductance vanishes if either one is absent. The electric and spin Hall conductances are suppressed in strong disorder, but survive in weak disorder. Physically it can be understood that the spinomotive transverse "force" generated by spin-orbit coupling is responsible for the for…
During the reconstruction of the edge of a quantum Hall liquid, Coulomb interaction energy is lowered through the change in the structure of the edge. We use theory developed earlier by one of the authors [K. Yang, Phys. Rev. Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a reconstructed edge, and study the consequences of the edge reconstruction for the momentum-resolved tunneling into the edge. It is found that additional excitation modes that appear after the reconstruction produce distinct features in the energy and momentum dependence of the spectral function, wh…
Tunneling from a two-dimensional contact into quantum-Hall edges is considered theoretically for a case where the barrier is extended, uniform, and parallel to the edge. In contrast to previously realized tunneling geometries, details of the microscopic edge structure are exhibited directly in the voltage and magnetic-field dependence of the differential tunneling conductance. In particular, it is possible to measure the dispersion of the edge-magnetoplasmon mode, and the existence of additional, sometimes counterpropagating, edge-excitation branches could be detected.
We report a magnetotransport study of the termination of the spin-resolved integer quantum Hall effect by controlled disorder in a gated GaAs/AlGaAs heterostructure. We have found that, for a given N^{th} Landau level, the difference in filling factors of a pair of spin-split resistivity peaks δν_{N}changes rapidly from one to zero near a critical density n_{c}. Scaling analysis shows that δν_{N} collapses onto a single curve independent of N when plotted against the parameter (n-n_{c})/n_{c} for five Landau levels. The effect of increasing the Zeeman energy is also examined by tilting the dir…
Momentum resolved magneto-tunnelling spectroscopy is performed at a single sharp quantum Hall edge. We directly probe the structure of individual integer quantum Hall (QH) edge modes, and find that an epitaxially overgrown cleaved edge realizes the sharp edge limit, where the Chklovskii picture relevant for soft etched or gated edges is no longer valid. The Fermi wavevector in the probe quantum well probes the real-space position of the QH edge modes, and reveals inter-channel distances smaller than both the magnetic length and the Bohr radius. We quantitatively describe the lineshape of princ…
Reentrant integer quantum Hall (RIQH) states are believed to be correlated electron solid phases, though their microscopic description remains unclear. As bias current increases, longitudinal and Hall resistivities measured for these states exhibit multiple sharp breakdown transitions, a signature unique to RIQH states. We present spatially-resolved measurements of RIQH breakdown that indicate these breakdown signatures can be ascribed to a phase boundary between broken-down and unbroken regions, spreading chirally from source and drain contacts as a function of bias current and passing voltag…
We realize a nanoscale-area Mach-Zehnder interferometer with co-propagating quantum Hall spin-resolved edge states and demonstrate the persistence of gate-controlled quantum interference oscillations, as a function of an applied magnetic field, at relatively large temperatures. Arrays of top-gate magnetic nanofingers are used to induce a resonant charge transfer between the pair of spin-resolved edge states. To account for the pattern of oscillations measured as a function of magnetic field and gate voltage, we have developed a simple theoretical model which satisfactorily reproduces the data.
A new kind of charge-Hall effect is shown. Unlike in the usual Hall effect, the driving force in the longitudinal direction is a spin force, which may originate from the gradient of a Zeeman field or a spin-dependent chemical potential. The transverse force is provided by a Berry curvature in a mixed position-momentum space. We can establish an Onsager relation between this effect and the spin-Hall effect provided the spin current in the latter is modified by a torque dipole contribution. This remarkable relation leads to new ways for experimental detection of spin accumulation predicted by th…
The spin Hall effect does not generally result in a charge Hall voltage. We predict that in systems with inhomogeneous electron density in the direction perpendicular to main current flow, the spin Hall effect is instead accompanied by a Hall voltage. Unlike the ordinary Hall effect, we find that this Hall voltage is quadratic in the longitudinal electric field for a wide range of parameters accessible experimentally. We also predict spin accumulation in the bulk and sharp peaks of spin-Hall induced charge accumulation near the edges. Our results can be readily tested experimentally, and would…
We have investigated spin-related effects on the electronic transport in a single antidot system in the vicinity of the $ν= 2$ quantum Hall state where two edge states with different spins of the lowest Landau level are formed around the antidot. The conductance exhibits the paired $h/2e$ Aharonov-Bohm (AB) oscillations. Using a tilted magnetic field technique, we have observed the evolution of the oscillations with the total magnetic field and a concomitant change in the source-drain bias dependence of the differential conductance. From the observation, we extract the effect of the Zeeman ene…
Electronic properties of bilayer graphene are distinct from both the conventional two dimensional electron gas and monolayer graphene due to its particular chiral properties and excitation charge carrier dispersions. We study the effect of strain on the electronic structure, the edge-states and charge transport of bilayer graphene nanoribbon at zero-temperature. We demonstrate a valley polarized quantum Hall effect in biased bilayer graphene when the system is subjected to a perpendicular magnetic field. In this system a topological phase transition from a quantum valley Hall to a valley polar…
Harmonic Hall voltage measurements are a wide-spread quantitative technique for the measurement of spin-orbit induced effective fields in heavy-metal / ferromagnet heterostructures. In the vicinity of the voltage pickup lines in the Hall bar, the current is inhomogeneous, which leads to a hitherto not quantified reduction of the effective fields and derived quantities, such as the spin Hall angle or the spin Hall conductivity. Here we present a thorough analysis of the influence of the aspect ratio of the voltage pickup lines to current channel widths on the apparent spin Hall angle. Experimen…
Spin Hall effect in a nonlocal spin-injection device is theoretically studied. Using a nonlocal spin-injection technique, a pure spin current is created in a nonmagnetic metal (N). The spin current flowing in N is deflected by spin-orbit scattering to induce the Hall current in the transverse direction and accumulate charge at the edges of N, yielding the spin-current induced Hall effect. We propose a method for extracting information for spin-orbit scattering in nonmagnetic metals.
It is proposed that the new generation of spintronics should be ideally massless and dissipationless for the realization of ultra-fast and ultra-low-power spintronic devices. We demonstrate that the spin-gapless materials with linear energy dispersion are unique materials that can realize these massless and dissipationless states. Furthermore, we propose four new types of spin Hall effects which consist of spin accumulation of equal numbers of electrons and holes having the same or opposite spin polarization at the sample edge in Hall effect measurements, but with vanishing Hall voltage. These…
The intrinsic spin Hall effect (SHE) originates from the topology of the Bloch bands in momentum space. The duality between real space and momentum space calls for a spin Hall effect induced from a real space topology in analogy to the topological Hall effect (THE) of skyrmions. We theoretically demonstrate the topological spin Hall effect (TSHE) in which a pure transverse spin current is generated from a skyrmion spin texture.
The spin Hall angle (SHA) is a measure of the efficiency with which a transverse spin current is generated from a charge current by the spin-orbit coupling and disorder in the spin Hall effect (SHE). In a study of the SHE for a Pt$|$Py (Py=Ni$_{80}$Fe$_{20}$) bilayer using a first-principles scattering approach, we find a SHA that increases monotonically with temperature and is proportional to the resistivity for bulk Pt. By decomposing the room temperature SHE and inverse SHE currents into bulk and interface terms, we discover a giant interface SHA that dominates the total inverse SHE current…
We propose a mechanism of intrinsic spin Hall effect (SHE). In this mechanism, local orbital angular momentum (OAM) induces electron position shift and couples with the bias electric field to generate orbital Hall effect (OHE). SHE then emerges as a concomitant effect of OHE through the atomic spin-orbit coupling. Spin Hall conductivity due to this mechanism is estimated to be comparable to experimental values for heavy metals. This mechanism predicts the sign change of the spin Hall conductivity as the spin-orbit polarization changes its sign, and also correlation between the spin Hall conduc…
Conceptual framework behind the intrinsic spin Hall effect in three-dimensional conductors is discussed. Theory suggests how the spin Hall current should depend on symmetry and orientation of the crystal.
Relativistic band theoretical calculations reveal that intrinsic spin Hall conductivity in hole-doped archetypical semiconductors Ge, GaAs and AlAs is large $[\sim 100 (\hbar/e)(Ωcm)^{-1}]$, showing the possibility of spin Hall effect beyond the four band Luttinger Hamiltonian. The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller, indicating no cancellation between the spin and orbital Hall effects in bulk semiconductors. Furthermore, it is found that the spin Hall effect can be strongly manipulated by strains, and that the $ac$ spin Hall conduc…
Spin pumping in ferromagnets provides a source of pure spin currents. Via the inverse spin Hall effect a spin current is converted into a charge current and a corresponding detectable DC-voltage. The ratio of injected spin current to resulting charge current is given by the spin Hall angle. However, the number of experiments more or less equals the number of different values for spin Hall angles, even for the most studied normal metal platinum. This publication provides a full study of inverse spin Hall effect and anisotropic magnetoresistance for different NiFe(Py) / normal metal bilayers usi…
In this review, we describe in detail two important spin-transport phenomena: the extrinsic spin-Hall effect (coming from spin-orbit interactions between electrons and impurities) and the spin-Coulomb drag. The interplay of these two phenomena is analyzed. In particular, we discuss the influence of scattering between electrons with opposite spins on the spin current and the spin accumulation produced by the spin-Hall effect. Future challenges and open questions are briefly discussed.
We show that the spin Hall conductivity in insulators is related with a magnetic susceptibility representing the strength of the spin-orbit coupling. We use this relationship as a guiding principle to search real materials showing quantum spin Hall effect. As a result, we theoretically predict that bismuth will show the quantum spin Hall effect, both by calculating the helical edge states, and by showing the non-triviality of the Z_2 topological number, and propose possible experiments.
We analyze the Landau level (LL) structure and spin Hall effect in a MoS2 trilayer. Due to orbital asymmetry, the low-energy Dirac fermions become heavily massive and the LL energies grow linearly with $B$, rather than with $\sqrt{B}$. Spin-orbital couplings break spin and valley degenerate LL's into two time reversal invariant groups, with LL crossing effects present in the valence bands. We find a field-dependent unconventional Hall plateau sequence $ν=...$ $-2M-6$, $-2M-4$, $-2M-2$, $-2M-1$, ..., -5, -3, -1, 0, 2, 4 .... In a p-n junction, spin-resolved fractionally quantized conductance ap…
We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account - the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.
While the helical character of the edge channels responsible for charge transport in the quantum spin Hall regime of a two-dimensional topological insulator is by now well established, an experimental confirmation that the transport in the edge channels is spin-polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin …
Spin Hall effects intermix spin and charge currents even in nonmagnetic materials and, therefore, ultimately may allow the use of spin transport without the need for ferromagnets. We show how spin Hall effects can be quantified by integrating permalloy/normal metal (N) bilayers into a coplanar waveguide. A dc spin current in N can be generated by spin pumping in a controllable way by ferromagnetic resonance. The transverse dc voltage detected along the permalloy/N has contributions from both the anisotropic magnetoresistance (AMR) and the spin Hall effect, which can be distinguished by their s…
The spin Hall effect and its inverse play key roles in spintronic devices since they allow conversion of charge currents to and from spin currents. The conversion efficiency strongly depends on material details, such as the electronic band structure and the nature of impurities. Here we show an anomaly in the inverse spin Hall effect in weak ferromagnetic NiPd alloys near their Curie temperatures with a shape independent of material details, such as Ni concentrations. By extending Kondo's model for the anomalous Hall effect, we explain the observed anomaly as originating from the second-order …
We predict spin Hall angles up to 80% for ultrathin noble metal films with substitutional Bi impurities. The colossal spin Hall effect is caused by enhancement of the spin Hall conductivity in reduced sample dimension and a strong reduction of the charge conductivity by resonant impurity scattering. These findings can be exploited to create materials with high efficiency of charge to spin current conversion by strain engineering.
We report the observation of negative nonlocal resistances in multiterminal mesoscopic gold Hall bar structures whose characteristic dimensions are larger than the electron mean-free path. Our results can only be partially explained by a classical diffusive model of the nonlocal transport, and are not consistent with a recently proposed model based on spin Hall effects. Instead, our analysis suggests that a quasiballistic transport mechanism is responsible for the observed negative nonlocal resistance. Based on the sensitivity of our measurements and the spin Hall effect model, we find an uppe…
Through combined ferromagnetic resonance, spin-pumping and inverse spin Hall effect experiments in Co|Pt bilayers and Co|Cu|Pt trilayers, we demonstrate consistent values of spin diffusion length $\ell_{\rm sf}^{\rm Pt}=3.4\pm0.4$ nm and of spin Hall angle $θ_{\rm SHE}^{\rm Pt}=0.051\pm0.004$ for Pt. Our data and model emphasize on the partial depolarization of the spin current at each interface due to spin-memory loss. Our model reconciles the previously published spin Hall angle values and explains the different scaling lengths for the ferromagnetic damping and the spin Hall effect induced v…
We measured the spin rectify effect and the inverse spin Hall effect in Nb-doped SrTiO$_3$ by injecting the spins from ferromagnetic thin films to SrTiO$_3$ using spin pumping. It was shown that the spin injection is increased when the doping level is increased. However, the spin Hall angle decreases when Nb occupies more than $\sim$2\% of the Ti sites, which is due to that beyond this concentration, the electron contributed the spin Hall effect is from the $d-$orbitals of Nb instead those from the Ti. Our work points to the importance of orbital occupations in the (inverse) spin Hall effect. …
We demonstrate an innovative quantum Hall circuit with variable geometry employing the moveable electrostatic potential induced by a biased atomic force microscope tip. We exploit this additional degree of freedom to identify the microscopic mechanisms that allow two co-propagating edge channels to equilibrate their charge imbalance. Experimental results are compared with tight-binding simulations based on a realistic model for the disorder potential. This work provides also an experimental realization of a beam mixer between co-propagating edge channels, a still elusive building block of a re…
Spin currents in ferromagnets afford diverse functionalities. We evaluate the extrinsic spin Hall effects of magnetic impurity scattering in ferromagnetic metals. We show that spin-dependent scattering can provide a high spin current polarized perpendicularly to the magnetization direction and is a dominant mechanism in the moderate-conductivity regime. We find that the superposition of the spin-conserve and spin-flip channels causes the spin currents. These findings suggest that optimizing alloy composition is an effective strategy to control the spin Hall effect.
We point out the existence of finite charge and spin Hall conductivities of graphene in the presence of a spin orbit interaction (SOI) and localized magnetic impurities. The SOI in graphene results in different transverse forces on the two spin channels yielding the spin Hall current. The magnetic scatterers act as spin-dependent barriers, and in combination with the SOI effect lead to a charge imbalance at the boundaries. As indicated here, the charge and spin Hall effects should be observable in graphene by changing the chemical potential close to the gap.
Voltages generated from inverse spin Hall and anisotropic magneto-resistance effects via spin pumping in ferromagnetic (F)/non-magnetic (N) bilayers are investigated by means of a broadband ferromagnetic resonance approach. Varying the non-magnetic layer thickness enables the determination of the spin diffusion length in Pd of 5.5 +/- 0.5 nm. We also observe a systematic change of the voltage lineshape when reversing the stacking order of the F/N bilayer, which is qualitatively consistent with expectations from spin Hall effects. However, even after independent calibration of the precession an…
The spin Hall effect of a Dirac Hamiltonian system is studied using semiclassical analyses and the Kubo formula. In this system, the spin Hall conductivity is dependent on the definition of spin current. All components of the spin Hall conductivity vanish when spin current is defined as the flow of spin angular momentum. In contrast, the off-diagonal components of the spin Hall conductivity are non-zero and scale with the carrier velocity (and the effective $g$-factor) when spin current consists of the flow of spin magnetic moment. We derive analytical formula of the conductivity, carrier mobi…
We study the dependence of the intrinsic spin Hall effect on the crystal symmetry and geometry of experiment. The spin current is obtained and the Hall voltage caused by the polarization of the electron spins is computed. The unique dependence of the effect on the crystal symmetry permits the choice of geometry in which the spin Hall effect can be unambiguously distinguished from the effects due to the orbital motion of charge carriers and due to the magnetic field generated by the transport current.
The spin Hall angle in Pt is evaluated in Pt/NiFe bilayers by spin torque ferromagnetic resonance (ST-FMR) measurements, and is found to increase with increasing the NiFe thickness. To extract the intrinsic spin Hall angle in Pt by estimating the total spin current injected into NiFe from Pt, the NiFe thickness dependent measurements are performed and the spin diffusion in the NiFe layer is taken into account. The intrinsic spin Hall angle of Pt is determined to be 0.068 at room temperature, and is found to be almost constant in the temperature range 13 - 300 K.
We develop a theoretical formula of spin Hall torque in the presence of two ferromagnets. While the direction of the conventional spin Hall torque always points to the in-plane direction, the present system enables to manipulate the torque direction acting on one magnetization by changing the direction of another magnetization. Based on the diffusion equation of the spin accumulation and the Landauer formula, we derive analytical formula of the spin Hall torque. The present model provides a solution to switch a perpendicular ferromagnet deterministically at zero field using the spin Hall effec…
A nonequilibrium Green's functions approach to spin-Hall effect is developed in a diffusive two-dimensional electron system with Rashba spin-orbit interaction. In the presence of long-range impurities, the coupled quantum kinetic equations are solved analytically in the self-consistent Born approximation. It is shown that the intrinsic spin-Hall effect stems from the dc-field-induced perturbation of the density of states. In addition, there is an additional disorder-mediated process, which involves the transition of nonequilibrium electrons between two spin-orbit-coupled bands. It results in a…
We address the question of how the time-resolved bulk Hall response of a two dimensional honeycomb lattice develops when driving the system with a pulsed perturbation. A simple toy model that switches a valley Hall signal by breaking inversion symmetry is studied in detail for slow quasi-adiabatic ramps and sudden quenches, obtaining an oscillating dynamical response that depends strongly on doping and time-averaged values that are determined both by the out of equilibrium occupations and the Berry curvature of the final states. On the other hand, the effect of irradiating the sample with a ci…
The discovery of the Quantum Spin Hall state, and topological insulators in general, has sparked strong experimental efforts. Transport studies of the Quantum Spin Hall state confirmed the presence of edge states, showed ballistic edge transport in micron-sized samples and demonstrated the spin polarization of the helical edge states. While these experiments have confirmed the broad theoretical model, the properties of the QSH edge states have not yet been investigated on a local scale. Using Scanning Gate Microscopy to perturb the QSH edge states on a sub-micron scale, we identify well-locali…
The nature of the fractional quantum Hall state with filling factor $ν=2/3$ and its edge modes continues to remain an open problem in low-dimensional condensed matter physics. Here, we suggest an experimental setting to probe the $ν=2/3$ edge by tunnel-coupling it to a $ν=1$ integer quantum Hall edge in another layer of a two-dimensional electron gas (2DEG). In this double-layer geometry, the momentum of tunneling electrons may be boosted by an auxiliary magnetic field parallel to the two planes of 2DEGs. We evaluate the current as a function of bias voltage and the boosting magnetic field. It…
Quantum Hall (QH) edge channels appear not only along the edge of the electron gas but also along an interface between two QH regions with different filling factors. However, the fundamental transport characteristics of such interface channels are not well understood, particularly in the high-frequency regime. In this study, we investigate the interface plasmon mode along the edge of a metal gate electrode with ungated and gated QH regions in both integer and fractional QH regimes using a time-resolved measurement scheme. The observed plasmon waveform was delayed and broadened due to the influ…
Topologically-protected edge states are dissipationless conducting surface states immune to impurity scattering and geometrical defects that occur in electronic systems characterized by a bulk insulating gap. One example can be found in a two-dimensional electron gas (2DEG) under high magnetic field in the quantum Hall regime. Based on the coherent control of the coupling between these protected states, several theoretical proposals for the implementation of information processing architectures were proposed. Here we introduce and experimentally demonstrate a new method that allows us to contr…
We have proposed a method to synchronize multiple spin-transfer torque oscillators based on spin pumping, inverse spin Hall, and spin Hall effects. The proposed oscillator system consists of a series of nano-magnets in junction with a normal metal with high spin-orbit coupling, and an accumulative feedback loop. We conduct simulations to demonstrate the effect of modulated charge currents in the normal metal due to spin pumping from each nano-magnet. We show that the interplay between the spin Hall effect and inverse spin Hall effect results in synchronization of the nano-magnets.
A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetry based classification of condensed matter. Exotic spin transport phenomena such as the dissipationless quantum spin Hall effect have been speculated to originate from a novel topological order whose identification requires a spin sensitive measurement, which does not exist to this date in any system (neither in Hg(Cd)Te quantum wells nor in the topological insulator BiSb). Using Mott polarimetry, we probe the spin degrees of freedom of these qu…
We study spin-resolved probability distributions for electrons in a multichannel waveguide in the presence of a spin-orbit interaction. For a spin-polarized electron injection, a zitterbewegung pattern is predicted in the probability distribution of electrons in the waveguide. For a spin-unpolarized injection, the spin-resolved electron probability in the waveguide shows spin accumulations. In addition to the spin Hall phenomenon, namely accumulations of opposite spins at the lateral edges of the waveguide, we predict the existence of a regular stripe pattern of spin accumulations in the inter…
Spin torque oscillators placed onto a nonmagnetic heavy metal show synchronized auto-oscillations due to the coupling originating from spin Hall magnetoresistance effect. Here, we study a system having two spin torque oscillators under the effect of the spin Hall torque, and show that switching the external current direction enables us to control the phase difference of the synchronization between in-phase and antiphase.
We study transport in normal metals in an external magnetic field. This system exhibits an interplay between a transverse spin imbalance (spin Hall effect) caused by the spin-orbit interaction, a Hall effect via the Lorentz force, and spin precession due to the Zeeman effect. Diffusion equations for spin and charge flow are derived. The spin and charge accumulations are computed numerically in experimentally relevant thin film geometries. The out-of-plane spin Hall potential is suppressed when the Larmor frequency is larger than the spin-flip scattering rate. The in-plane spin Hall potential v…
In ferromagnet/normal metal heterostructures, spin pumping and spin-transfer torques are two reciprocal processes that occur concomitantly. Their interplay introduces a dynamic feedback effect interconnecting energy dissipation channels of both magnetization and current. By solving the spin diffusion process in the presence of the spin Hall effect in the normal metal, we show that the dynamic feedback gives rise to: (i) a nonlinear magnetic damping that is crucial to sustain uniform steady-state oscillations of a spin Hall oscillator at large angles. (ii) a frequency dependent spin Hall magnet…
We derive the spin continuity equation by using the Noether's theorem. A new type of spin-tensor Hall current is found in the continuity equation. The spin-tensor Hall current is originating from the coupling of the spin-tensor and the momentum. The intrinsic spin Hall effect in the two-dimensional fermion model with the spin-orbit coupling and spin-tensor-momentum coupling is studied. The total spin Hall conductivity with the presence of the spin-tensor Hall current is calculated. The numerical results indicate that the total spin Hall conductivity is enhanced by the contribution of the spin-…
A self-consistent Thomas-Fermi-Poisson based calculation scheme is used to achieve spin resolved incompressible strips (ISs). The effect of exchange and correlation is incorporated by an empirically induced g factor. A local version of the Ohm's law describes the imposed fixed current, where the discrepancies of this model are resolved by a relevant spatial averaging process. The longitudinal resistance is obtained as a function of the perpendicular (strong) magnetic field at filling factor one and two plateaus. Interrelation between the ISs and the longitudinal zeros is explicitly shown.
We study the coupled dynamics of spin and charge currents in a two-dimensional electron gas in the transport diffusive regime. For systems with inversion symmetry there are established relations between the spin Hall effect, the anomalous Hall effect and the inverse spin Hall effect. However, in two-dimensional electron gases of semiconductors like GaAs, inversion symmetry is broken so that the standard arguments do not apply. We demonstrate that in the presence of a Rashba type of spin-orbit coupling (broken structural inversion symmetry) the anomalous Hall effect, the spin Hall and inverse s…
A theoretical formulation of magnetoresistance effect in a metallic ferromagnetic/nonmagnetic bilayer originated from the charge-spin conversion by the anomalous Hall effect is presented. Analytical expressions of the longitudinal and transverse resistivities in both nonmagnet and ferromagnet are obtained by solving the spin diffusion equation. The magnetoresistance generated from charge-spin conversion purely caused by the anomalous Hall effect in the ferromagnet is found to be proportional to the square of the spin polarizations in the ferromagnet and has fixed sign. We also find additional …
