Session P12: Focus Session: Spin-Orbit Coupling

Electrical manipulation of spin-orbit coupling in semiconductor heterostructures

Spin-orbit coupling provides a pathway for electrically initializing and manipulating electron spins. This coupling creates momentum-dependent spin-splittings related to the inversion asymmetries of the semiconductor heterostructure. We demonstrate that we can regulate these spin-splittings in semiconductor epilayers with strain\footnote{V. Sih, H. Knotz, J. Stephens, V. R. Horowitz, A. C. Gossard and D. D. Awschalom, \textit{Phys. Rev. B} \textbf{73}, 241316(R) (2006).} and in heterostructures using quantum confinement and orbital quantization\footnote{V. Sih, W. H. Lau, R. C. Myers, A. C. Gossard, M. E. Flatt\'{e} and D. D. Awschalom, \textit{Phys. Rev. B} \textbf{70}, 161313(R) (2004).}. These spin-splittings can provide a mechanism for electrically generating spin polarization without magnetic materials or magnetic fields. Using Kerr rotation microscopy, current-induced spin polarization and the spin Hall effect have been observed in bulk semiconductors and in a two-dimensional electron gas confined in (110) AlGaAs quantum wells\footnote{V. Sih, R. C. Myers, Y. K. Kato, W. H. Lau, A. C. Gossard and D. D. Awschalom, \textit{Nature Physics} \textbf{1}, 31 (2005).}. In contrast to measurements on bulk systems, the data for the quantum wells reveal that the spin Hall profile exhibits a complex structure and that the current-induced spin polarization is out-of-plane. The current-induced spin polarization is dependent on the direction along which the electric field is applied, reflecting the anisotropy of the spin-orbit interaction. More recently, we demonstrate that the observed spin accumulation due to the spin Hall effect is due to a bulk electron spin current\footnote{V. Sih, W. H. Lau, R. C. Myers, V. R. Horowitz, A. C. Gossard and D. D. Awschalom, \textit{Phys. Rev. Lett.} \textbf{97}, 096605 (2006).}. Channels with transverse arms allow us to observe that this spin current can drive spin transport over macroscopic distances in bulk GaAs.   

Spin generation by strong inhomogeneous electric fields

Motivated by recent experiments [1], we propose a model with extrinsic spin-orbit interaction, where an inhomogeneous electric field ${\bf E}$ in the x-y plane can give rise, through nonlinear effects, to a spin polarization with non-zero $s_z$, away from the sample boundaries. The field ${\bf E}$ induces a spin current ${\bf j}_s^z= \hat{z} \times(\alpha{\bf j}_c+\beta{\bf E})$, where ${\bf j}_c=\sigma {\bf E}$ is the charge current, and the two terms represent,respectively, the skew scattering and side-jump contributions. [2]. The coefficients $\alpha$ and $\beta$ are assumed to be $E$- independent, but conductivity $\sigma$ is field dependent. We find the spin density $s_z$ by solving the equation for spin diffusion and relaxation with a source term $\nabla \cdot {\bf j}_s^z$. For sufficiently low fields, $j_c$ is linear in $E$, and the source term vanishes, implying that $s_z=0$ away from the edges. However, for large fields, $\sigma$ varies with $E$. Solving the diffusion equation in a T-shaped geometry, where the electric current propagates along the main channel, we find spin accumulation near the entrance of the side channel, similar to experimental findings [1]. Also, we present a toy model where spin accumulation away from the boundary results from a nonlinear and anisotropic conductivity.\\{ }[1] V. Sih, et al, Phys.\ Rev.\ Lett. {\bf 97}, 096605 (2006).\\{ } [2] H.-A. Engel, B.I. Halperin, E.I.Rashba, Phys.\ Rev.\ Lett. {\bf 95}, 166605 (2005).   

Tuning of the spin-orbit interaction and resistance in two-dimensional GaAs holes via strain

We report direct measurements, via the Fourier analysis of the Shubnikov-de Hass oscillations, of the spin-orbit interaction induced spin-splitting in modulation-doped GaAs two-dimensional hole systems as a function of strain applied in the sample plane. The data reveal a remarkably strong dependence of the spin-splitting on strain, with up to about 20{\%} enhancement of the splitting upon the application of only about 2x10$^{-4}$ strain. The results are in very good agreement with our numerical calculations of the strain-induced spin-splitting. We also show a remarkable dependence of the anisotropy of the heavy hole band on strain. Its manifestation as a change of resistance with strain implies the use of GaAs 2D holes as a sensitive piezo-resistance sensor at low temperatures.   

Electron transport in semiconductor heterostructures with strong spin orbit coupling

GaAs/AlGaAs two dimensional electron gases (2DEGs) have been studied extensively in the context of mesoscopic transport through devices such as quantum point contacts and quantum dots. 2DEGs in heterostructures based on InGaAs or InAs instead of GaAs provide testbeds to study similar phenomena in systems with much larger intrinsic spin-orbit coupling. Stronger spin orbit coupling provides greater ease of control of the electron spin degree of freedom, leading to applications in spintronics as well as the possibility of observing novel quantum Hall states. We present some preliminary electronic transport data on gated InGaAs 2DEGs and discuss directions for possible further experiments on nanostructures in this material.   

Physical factors affecting Rashba Spin-orbit coupling

The Rashba Spin-orbital coupling plays a crucial role in charge and spin transport in semiconductor heterostructure. We study several physical parameters which may contribute to Rashba Spin-orbital coupling, including asymmetric potential barriers, quantum well inclination, effective mass, and band mixing. This may provide some insights in designing spintronic microdevices .   

Spin transport and the giant Zeeman effect in systems with spin-orbit interaction

Spin-orbit coupling in semiconductors provides a pathway for electrically initializing and manipulating electron spins for applications in spintronics and spin-based quantum information processing. This coupling can be regulated with quantum confinement, band structure engineering and applied fields. Here we investigate the spin-dependent transport properties of electrons in diluted magnetic two dimensional electron gas (2DEG) systems using a scattering matrix approach. We include the Rashba spin-orbit interaction and the role of realistic magnetic barriers produced by the deposition of ferromagnetic stripes on heterostructures [1]. We show that the quantum conductance in these systems depends on spin orientation of the incident carriers, the magnitude of spin-orbit coupling, and the giant Zeeman effect present in diluted magnetic semiconductors. We will describe how all effects can be employed in the efficient control of spin polarization via the application of moderate fields. \\ 1. A. Matulis, F. M. Peeters, P. Vasilopoulos, Phy. Rev. Lett. {\bf 72}, 1518 (1994).   

Spin-Orbit Coupling in AlGaN/AlN/GaN Heterostructures with a Polarization Induced Two-Dimensional Electron Gas

Spin-orbit coupling is investigated by weak antilocalization and Shubnikov-de Haas measurements in wurtzite Al$_{x}$Ga$_{1-x}$N/AlN/GaN heterostructures with a polarization induced two dimensional electron gas. By employing the persistent photoconductivity effect and by using five different heterostructures with different Al compositions, we cover a carrier density range extending from $0.8\times 10^{12}\mbox{ cm}^{-2}$ to $10.6\times 10^{12}\mbox{ cm}^{-2}$. We determine electron splitting energies for different carrier densities by analyzing the weak antilocalization measurements using the Iordanskii, Lyanda-Geller, and Pikus theory. We find the spin splitting energies do not scale linearly with the Fermi wavevector $k_{F}$ at high carrier densities. By fitting the spin splitting energies to a form $E_{SS}$=2($\alpha k_{F}+\gamma k_{F}^{3})$ we extract linear and cubic spin-orbit coupling parameters $\alpha $=5.13$\times $10$^{-13}$ eV m and $\gamma $=1.2$\times $10$^{-31}$eV m$^{3}$, respectively. The cubic spin-orbit coupling parameter is purely due to the bulk inversion asymmetry of the wurtzite crystal and has not been previously measured for the GaN system.   

A Study of Dresselhaus and Rashba Effects in InSb/InAlSb Heterostructures via Anti-Weak Localization Measurements

The InSb/InAlSb system has both the largest Dresselhaus effect (due to bulk inversion asymmetry) and Rashba effect (due to structural inversion asymmetry) of the III-V semiconductor family. Both mechanisms contribute to electronic spin splitting, even in zero applied field. While the Dresselhaus effect is purely materials specific, the Rashba interaction is less well understood with both the electric field at the interface and the discontinuity due to the barrier predicted to play significant roles. Standard measurements of the zero field spin splitting however, are usually performed at high field where Zeeman effects and higher subband occupancy become problematic. In this talk we will present our results in extremely low fields using anti-weak localization (AWL) measurements where these complications are absent. We report on systematic measurements of the Dresselhaus and Rashba interactions on a series of InSb/InAlSb heterostructures, where carrier density, dopant density and the Al concentration in the barrier have all been varied to extract the role of each in the strength of the spin-orbit coupling.   

Spin interference effect in a triangular loop array fabricated in (001)In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells

We report, for the first time, the spin interference (SI) effect in a triangular loop array fabricated in (001) In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells (QW). Previously [1], we studied the SI effect in a square loop array, where the sides of the squares are either parallel or perpendicular to the $<$110$>$ crystallographic axis. For an electron with a wave vector\textbf{ k} that is parallel or perpendicular to the $<$110$>$ direction, the magnitude of the effective magnetic field due to the all spin-orbit effects,$ B_{TOT}$, is given either by the sum ($B_{R}+B_{D})$ or by the difference ($B_{R}-B_{D})$ between the Rashba and Dresselhaus fields, which makes the analysis relatively simple. Though the situation is more complicated in a triangular loop array, theory including both the Rashba and Dresselhaus terms predicts clear difference in the SI patterns between the following two situations: the bases of the triangles in the array are placed parallel/perpendicular to the $<$110$>$ crystallographic axis. This finding is being confirmed experimentally. [1] T. Koga\textit{ et al.}, Phys. Rev. B \textbf{70}, 161302(R) (2004); \textit{ibid}. \textbf{74}, 041302(R) (2006).   

Spin and charge optical conductivities in spin-orbit coupled systems

Spin-orbit interaction (SOI) in systems lacking inversion symmetry is a phenomenon with great potential in the development of spintronic-based devices. Since the celebrated proposal by Datta and Das, of a spin-FET relying on the tunability of the Rashba SOI strength through electrical gating, there has been a remarkable attention in the search for new ways of manipulating electron spins without employing ferromagnetic materials and/or external magnetic fields. In this work we study the frequency dependent spin- and charge- conductivity tensors of a two-dimensional electron gas (2DEG) with both Rashba and Dresselhaus spin-orbit interaction. We show that the spectral behavior of the spin and charge response due to the angular anisotropy of the spin-splitting energy induced by the interplay between the Rashba and Dresselhaus couplings is much richer. The new spectral structures open the possibility for control of the optical response by applying an external bias and/or by adjusting the light frequency. In addition, we show that the relative strength of the spin-orbit coupling parameters can be obtained through optical probing.   

Spin interference effects in a 2D-hole ring with spin-orbit interaction.

We study the quantum interference effects in one-dimensional heavy hole (HH) rings with spin-orbit interaction realizable in HgTe quantum wells. The influence of the spin-orbit interaction strength on the transport is investigated analytically and numerically. The analytical results allow us to explain the interference effects as a signature of Berry phases. We compare our results with the previous studies on the electron Rashba systems and find more rapid oscillations as a function of the spin-orbit strength. The structures with stronger signature of the spin-orbit strength can lead to more sensitive spintronic devices that enable observation of quantum interference effects and control of spin at mesoscopic scales.   

Exchange energy and generalized polarization in the presence of spin-orbit coupling in two dimensions

We discuss the concomitant effects of the exchange energy and the spin-orbit interaction in a homogeneous system of interacting electrons in two spatial dimensions. This work extends the mean-field method originally developed in the case of Rashba spin-orbit to a more general form of spin-orbit interaction. The mean-field phase diagram and spin response for a number of representative cases are discussed. Our theory is rigorous in the high-density limit of the paramagnetic phase, where it can be expressed in terms of a generalized fractional electronic polarization. We show that in many cases, the effect of the exchange is to quench, rather than enhance, the generalized polarization induced by the spin-orbit coupling. Our results account qualitatively for the findings of recent experimental investigations.   

High density limit of the correlation energy of a two dimensional electron liquid in the presence of Rashba spin-orbit

We obtain analytic expressions for the high density limit of the correlation energy of a two dimensional electron liquid in the presence of Rashba spin-orbit. As a byproduct we have derived an analytic expression for the dependence of the ring diagrams contribution to this quantity on the fractional spin polarization of the system in the absence of spin-orbit. We will show that the latter is not properly represented by current standard interpolation formulas obtained from Monte-Carlo calculations.