Session P22: Focus Session: Spin Hall and other Spin-Orbit Effects in Semiconductors

Beller Lectureship Talk: Spin Hall Effect

The Spin Hall Effect (SHE) and related transport phenomena originating from the coupling of the charge and spin currents due to spin-orbit interaction were predicted [1] in 1971. Following the suggestion in [2], the first experiments in this domain were done at Ioffe Institute in Saint Petersburg [3], providing the first observation of what is now called the Inverse Spin Hall Effect. As to the SHE itself, it had to wait for 33 years before it was experimentally discovered by two groups [4] in Santa Barbara (US) and in Cambridge(UK). The phenomenon consists in spin accumulation at the lateral boundaries of a current-carrying non-magnetic conductor, the spin directions being opposite at the opposing boundaries. The boundary spin polarization is proportional to the current and changes sign when the direction of the current is reversed. It exists in relatively wide \textit{spin layers} determined by the spin diffusion length, typically on the order of 1 $\mu $m. I will discuss the phenomenology of spin-charge coupling, the underlying microscopic mechanisms, and the existing experimental results obtained in semiconductors and in metals at cryogenic, as well as at room temperatures. I will also address a related, but as yet unknown phenomenon, the \textit{swapping} of spin currents, which is due to the correlation between spin rotation during a scattering event and the direction of scattering. \\[4pt] [1] M.I. Dyakonov and V.I. Perel, JETP Lett. \textbf{13}, 467 (1971); , Phys. Lett. \textbf{A35}, 459 (1971)\\[0pt] [2] N.S. Averkiev and M.I. Dyakonov, JETP Lett. \textbf{35}, 196 (1983)\\[0pt] [3] A.A. Bakun et al., JETP Lett. \textbf{40}, 1293 (1984)\\[0pt] [4] Y.K. Kato et al., Science \textbf{306}, 1910 (2004); J. Wunderlich et al., Phys. Rev. Lett. \textbf{94}, 047204 (2005)   

Spin Hall frequency doubling and spin memristive effects

It is shown that when a time dependent voltage is applied to a system with inhomogeneous electron density in the direction perpendicular to main current flow, the spin Hall effect results in a transverse voltage containing a double frequency component. We demonstrate that there is a phase shift between applied and transverse voltage oscillations, related to memristive behavior of semiconductor spintronics systems. It is interesting that spin memristive effects in this system are manifested directly in the voltage response. A different method to achieve the second harmonic generation, based on the inverse spin Hall effect, is also discussed.   

Enhanced Spin Hall Effect by Single Antidot Potential

We theoretically investigate an extrinsic spin Hall effect in semiconductor heterostructures due to the scattering by an artificial potential created by a single antidot, STM tip, etc. The strength of the potential is electrically tunable. First, we formulate the spin Hall effect in terms of phase shifts in the partial wave expansion for two-dimensional electron gas. For scattered electrons in $\theta$ direction, we obtain a spin polarization $P(\theta)$ perpendicular to the two-dimensional plane [$P(-\theta)=-P (\theta)$]. The spin polarization $P(\theta)$ is significantly enhanced by an attractive potential when the resonant condition of a partial wave is satisfied by tuning the potential strength. Second, we study the spin Hall effect in a three-terminal device with an antidot at the junction. The conductance and spin polarization are evaluated numerically.\footnote{M.\ Yamamoto and B.\ Kramer, J.\ Appl.\ Phys.\ {\bf 103}, 123703 (2008), for repulsive potential.} We obtain a spin polarization of more than 50\% due to the resonant scattering when the attractive potential is properly tuned.   

Competiting interplay between Rashba and cubic-k Dresselhaus spin-orbit interaction in spin Hall effect

We study the interplay between the Rashba and cubic-$k$ Dresselhaus spin-orbit interactions (SOI) in a diffusive two-dimensional electron gas (2DEG). Within the spin Hall configuration, we perform a systematic calculation of the spin accumulation $S_{z}$ and the spin polarizations $S_{i}^{B}$ at the lateral edges and in the bulk of the 2DEG, respectively. Both the relative coupling strength of the Rashba and the Dresselhaus SOI, and the electron densities are varied. The spin accumulation exhibits strong competiting features, including in the Dresselhaus-dominant regime the sign change in $S_{z}$ when electron density is large enough, and in the Rashba-dominant regime the complete suppression of $S_{z}$. Most surprisingly is our finding that the Rashba-dominant regime occurs as early as $\alpha\approx 2\tilde{\beta}$, where $\alpha$, $\tilde{\beta}$ are the Rashba and the effective linear-$k$ Dresselhaus SOI coupling constant, respectively. Similar Rashba-dominant regime is found in the spin polarizations, when $\alpha\geq \tilde{\beta} $. Our results point out that decreasing $|\alpha|$ leads to the restoration of the spin accumulation.   

Monte Carlo Simulation of Spin-Injection Hall Effect

The spin-injection Hall effect,which is the newest addition to the spintronic Hall effect family, consists in the transversal deflection of a charge spin-polarized current injected in a spin-orbit coupled semiconductor channel which results in transverse Hall voltage whose magnitude varies along the channel direction. Just as in the case of spin Hall effect, the phenomenon is due to both intrinsic and extrinsic (impurity driven) spin-orbit scattering. We develop a semiclassical spin-dependent Monte Carlo simulation technique which enables us to quantitatively explain the mechanisms of spin-injection Hall effect in experimentally relevant systems. This is achieved by incorporating both intrinsic and extrinsic contributions to anomalous Hall effect (AHE) which are rigorously derived within the recently developed gauge invariant semiclassical theory of AHE. The advantage of this approach over a fully quantum mechanical treatment is that it enables us to investigate the spin-injection Hall effect in micrometer-size devices while still retaining the essential physics.   

Calculations of Spin-orbit Splittings in Two-Dimensional Heterostructures

We present calculations of the of the wave-vector dependent spin-orbit level splittings in GaAs/InGaAs and Si/SiGe quantum wells. We use both an effective mass approach and a numerical tight-binding approach (NEMO-3D) that includes the effects of the interfaces on atomic scales. We are able to separate the Rashba and Dresselhaus contributions. The calculations are done as a function of applied electric field and well width. We find good agreement of theory and experiment for the measurements of L. Meier {\it{et al.}}, (Nature Physics \textbf{3}, 650 (2007)) on GaAs/InGaAs. In Si/SiGe wells, we find significant valley- spin-orbit mixing and also that the Dresselhaus term is substantial, and can even be larger than the Rashba term for realistic parameters.   

Coherent ultrafast spin flip in a 2D electron gas

We report the experimental demonstration of ultrafast electron spin flip in a modulation doped CdTe quantum well. Complete spin flip is realized with an off-resonant laser pulse of 2 ps in duration. The effective pi-pulse flips the electron spins with respect to an axis that is orthogonal to both the external magnetic field (Voigt geometry) and the sample growth axis. The realization of the ultrafast pi-pulse opens up a new avenue for protecting electron spins from decoherence with dynamical decoupling.   

Analysis of Electron Spin Relaxation Momentum Time in Narrow Gap Semiconductor Quantum Well and Dots: Including Rashba and Dresselhaus Effects

A model of GaAs quantum dots embedded in a quantum wire is studied. We want to investigate how the electron spin relaxation momentum time (SRT) is varying with some physical parameters. We find that SRT decreases while the four parameters, external magnetic field, surrounding temperatures, both quantum wire width and thickness increase. The reason is caused by more and more phonons resulted in a higher scattering probability between electrons and phonons. Thus the SRT is reduced. Besides, Lommer and Silva showed that in narrow gap semiconductor bulk materials, the Rashba effect is larger than Dresselhaus effect. Our results show that Dresshaus effect is larger than Rashba effect for the quantum well under electric field, especially when the quantum well width is small. The authors are interested in studying whether the same characteristics exist in quantum dots. We are working on this line.   

Spin accumulation in a Rashba-type two-dimensional electron gas due to a nonuniform driving electric field

It is well understood that a Rashba-type two-dimensional electron gas (2DEG) does not support spin accumulation, or spin Hall effect, in the diffusive regime when the driving electric field is uniform. In this work we address the issue about a possible restoration of the spin Hall effect when the driving field is nonuniform. Toward this end, we consider the spin accumulation in the vicinity of a circular hole, with radius $R\sim l_{so}$, where the driving field becomes nonuniform. Here $l_{so}$ is the spin relaxation length, and $l_{so} \quad >> l_{e}$, the electron mean free path. Our result shows that the nonuniform driving field gives rise to nonuniform in-plane spin densities S$_{x}$ and S$_{y}$, which in turn contribute to a finite spin current via the combined processes of spin diffusion and spin-precession. The spin accumulation thus obtained is proportional to the Rashba coupling constant $\alpha $, and its spatial pattern is one of spin-dipole form, aligned perpendicular to the driving field.   

Scattering approach in calculating Rashba Spin-orbit coupling in asymmetric

The Rashba Spin-orbit coupling plays a crucial role in spin manipulation in semiconductor heterostructures. We study the underlying physics through scattering approach with the Kane model. Several physical parameters are considered, including potential barrier asymmetries, quantum well inclination, as well as band structure parameters. This may provide a better understanding in designing spintronic devices.   

2D Holstein polarons in the presence of spin-orbit interactions

The electron-phonon interaction in the presence of spin-orbit interactions (of either Rashba or Dresselhaus type) must be taken in account for GaAs quantum dots or for spintronic devices. The possibility of tuning the electron-phonon interaction by coupling to a substrate (e.g. in organic transistors) requires an accurate treatment of this problem in all coupling regimes. We apply a recently developed approximation (the Momentum Average Approximation) to this specific theoretical question. We have shown that this method is exact in various asymptotic regimes while being accurate for all coupling strengths. We calculate the self-energy at the MA(2) level of the approximation. From ground state properties (energy and effective mass) we conclude that in the presence of spin-orbit interactions, the polaron is harder to trap -- the crossover from large to small polarons is shifted to higher couplings. From the spectral function, we show that there are two distinct regimes, depending on relation between the phonon frequency and the strength of the spin-orbit interaction. When the latter is larger we find that the polaron character is dominated by only one band (the `-' band). We also show that the off-diagonal part of the self-energy plays an essential role in obtaining the polaron + one phonon continuum correctly.   

Full spin control in 2DEGs with no magnetic fields

A properly chosen closed spin transport path in the plane of a III-V semiconductor quantum well suffices for arbitrary spin manipulation of conduction electrons about any desired axis. This feature of spin transport relies on the non-commutativity of the precession matrices associated with non-colinear path segments. The electron spin rotation depends solely on the path geometry, not the speed of the spin along the path. Simple closed paths have been found which will perform arbitrary spin rotations along arbitrary axes with no net spatial displacement of the spins. The paths differ depending on the form of the internal effective magnetic fields induced by crystal asymmetry, growth asymmetry, and strain and electric fields. This work was supported by an ONR MURI.   

Many-body effects on $\rho_{xx}$ Ringlike Structures via SDFT

In the quantum Hall regime, the longitudinal resistivity $\rho_{xx}$ plotted in a density--magnetic-field diagram displays ringlike structures due to the crossings of spin split Landau levels of distinct subbands. We theoretically investigated the dependence of the magnetoresistance on the magnetic field tilt angle and on the temperature using Spin Density Functional Theory (SDFT). Assuming a temperature dependence of the Landau levels broadenings, we show that the ringlike structures are broken at sufficiently low temperatures due to a ferromagnetic quantum phase transition. Additionally, for tilt magnetic field, the momentum in the growth direction ($z$) also couples to the magnetic field $zP_x$ coupling, thus giving rise to anticrossings between consecutive Landau levels and subbands, collapsing the ring with increasing tilt angle. We find that the interplay of these anticrossings and many-body interactions (via SDFT) leads to a reduced $zP_x$ coupling, increasing the collapsing angle at which the ring fully disappears. Our results explain some of the physical mechanisms behind ring formation and collapse which have been experimentally observed.