Session L22: Focus Session: Spin-Orbit Effects in Semiconductors

Pure spin current pump in a quantum channel with both Rashba and Dresselhaus effects

We demonstrate a spin pump to generate pure spin current of tunable intensity and polarization in the absence of charge current. The system under consideration is a two-dimensional electron gas (2DEG) that is present at the interface of a heterostructure due to modulation doping and has intrinsic static Rashba and Dresselhaus spin-orbit interactions. The pumping functionality is achieved by means of an ac gate voltage that modulates the Rashba constant dynamically in a local region of a quantum channel in which both the static Rashba and Dresselhaus spin-orbit interactions are taken into account. The spin-resolved Floquet scattering matrix formalism is applied to our system. Based on the Floquet theorem, this formalism provides an exact and nonperturbative solution to the time-periodic Schrodinger equation in the mesoscopic system. Because the time-dependent spin-orbit interaction couples two spin polarizations and all sidebands together, analytic expression for the sideband dispersion is not feasible. Thus, we determine the sideband dispersion relation numerically by solving the Schrodinger equation in a nearly complete basis with the spatial inhomogeneity handled by matching boundary conditions region by region. The Floquet scattering matrix gives a coherent solution that goes beyond the adiabatic regime.   

Mesoscopic fluctuations in the spin-electric susceptibility due to Rashba spin-orbit interaction

Spin-orbit interaction enables the control of the spin with electric fields in non-magnetic semiconductors. The orbital transport processes generating the internal fields that are necessary for this control are typically described as classical diffusive drift. In contrast, when this orbital motion is phase coherent, typical mesoscopic effects occur not only in transport but also in the spin dynamics. We investigate mesoscopic fluctuations in the spin polarization generated by a static electric field and by Rashba spin-orbit interaction in a disordered 2D electron gas. In a diagrammatic approach we find that the out-of-plane polarization - while being zero for self-averaging systems - exhibits large sample-to- sample fluctuations which are shown to be within experimental reach. We evaluate the disorder-averaged variance of the susceptibility and find its dependence on magnetic field, spin-orbit interaction, dephasing, and chemical potential difference. [M. Duckheim and D. Loss, Phys. Rev. Lett.(in print), arXiv:0805.4143v1].   

Spin-orbit coupling effects and the angular dependence of the tunneling anisotropic magnetoresistance

We consider a tunnel junction in which one of the electrodes is ferromagnetic. Based on general properties and symmetry considerations, we develop a phenomenological model in which the anisotropy of the tunneling magnetoresistance with respect to the magnetization orientation of the ferromagnet originates from the spin-orbit interaction. The model reveals how the symmetry and angular dependence of the tunneling anisotropic magnetoresistance (TAMR) are determined by the form of the spin-orbit coupling field (SOCF), independently of the specific details of the system. We investigate the particularly important cases in which the SOCF is of Bychkov-Rashba and/or Dresselhaus type and obtain angular dependences which are in good agreement with available TAMR measurements. We also predict new forms of the angular dependence of the TAMR by exploring different geometric configurations.   

Magneto-transport in high mobility \textit{n}-InSb/InAlSb quantum wells

The inherent large spin-orbit (SO) coupling InSb quantum wells (QWs) is expected to result in sensitive tunability of the Rashba effect with electric field. The strength of the SO coupling can be extracted from measurements of weak anti-localisation (WAL) and from the beating of Shubnikov-de Haas (SdH) oscillations [1]. We have investigated these phenomena and report magneto transport measurements from a range of InSb/InAlSb QWs with varying carrier density $n$ and mobility \textit{$\mu $}. It is shown that the inherent large Zeeman splitting combined with inhomogeneous level broadening means that beating in the SdH oscillations in InSb QWs are rarely observed. However, her we show that in InSb/InAlSb QWs, $n$ can be modulated using a gate electric field from 1.15$ [Preview Abstract]

Diffusive spin-charge dynamics in an external electric field

We study the dynamics of a spin density injected into a two-dimensional electron system with generic spin-orbit interactions. We generalize the spin-charge diffusion equation formalism by including the effects of a uniform electric field. Within this approach, we study the coupling between spin and charge and we determine the charge (spin) profile induced by a non-uniform, periodic spin (charge) density in the presence of the external electric field. We determine the optimal range of parameters for observing the spin-charge coupling effects.   

Spin-orbit control of magnetization and electrical detection of current-induced spin polarization.

The success of future spintronic devices relies on the efficient control and detection of spin polarization. Extrinsically polarized currents, injected from ferromagnetic materials, can interact with magnetic domains and initiate domain rotation. Alternatively, spin polarization can be generated intrinsically via relativistic coupling of spin to the momentum of charge carriers, known as spin-orbit interaction (SO). While the use of SO for electrostatic control of polarization forms the basis of various theoretical device concepts, SO control of magnetization has not been realized experimentally. Here we demonstrate that magnetization can be reversibly manipulated by intrinsically polarized currents in ferromagnetic semiconductors with strong SO coupling. Magnetization direction is repeatedly switched between two orthogonal easy axes by SO effective magnetic field generated by the injection of unpolarized currents with densities $<$10$^{6}$ A/cm$^{2}$. We also show that current-induced SO field can be detected electrically. By monitoring magnetization direction in small external magnetic field we can measure both magnitude and direction of the SO field.   

Antilocalization in low dimensional InSb/InAlSb systems

Boundaries and a restricted phase space influence the spin coherence length in mesoscopic structures with strong spin-orbit coupling. We present mesoscopic transport experiments on the strongly spin-orbit coupled narrow gap semiconductor InSb. Low temperature magnetotransport measurements were performed on high mobility InSb/InAlSb two dimensional electron system (2DES) and quasi-1D wires fabricated from the 2DES. Antilocalization dominates the magnetoresistance in low applied magnetic fields; hence the magnetoresistance is sensitive to the electron spin and phase coherence lengths in the structures. Measurements of the low field magnetoresistance over temperature demonstrate that the antilocalization phenomena persists to temperatures above $\sim$20 K in the quasi-1D wires, whereas antilocalization is not observed above $\sim$15 K in the unpatterned 2DES. The extracted spin coherence lengths, obtained from fitting the magnetoresistance curves to localization theory, show only weak temperature dependence. Therefore, phase coherence appears to dominate the temperature dependence of antilocalization in the low dimensional InSb/InAlSb systems. (NSF DMR-0618235, DOE DE-FG02-08ER46532, NSF DMR-0520550)   

Full-zone spin-splitting for electrons and holes in bulk GaAs and GaSb

The spin-orbit interaction --- a fundamental electroweak force --- is equivalent to an effective magnetic field intrinsic to crystals, leading to band spin-splitting for certain k-points in sufficiently low-symmetry structures. This (Dresselhause) splitting has usually been calculated at restricted regions in the Brillouin-zone via small-wavevector approximations (e.g., ${\bf k\cdot p}$). We provide a full-zone description of the Dresselhaus splitting in zinc-blende semiconductors by using pseudopotentials, empirically corrected to rectify LDA errors by fitting GW results at a few firections. We find that (i) The largest spin-splitting occurs along the [210] direction, not the [110] direction as previously thought based on limited view of the Brillouin zone; (ii) The spin-splitting of the upper valence band VB1 is comparable to that of the next two valence bands VB2 and VB3. This has been previously overlooked due to the expectation that the largest spin-splitting will occur along the [110] direction; (iii) The spin-splitting pattern of each band is orthogonal to each other.   

Controlling the persistent spin helix with strain induced spin-orbit coupling

We use transient spin grating spectroscopy to study the persistent spin helix (PSH) state of the 2D electron gas. The PSH is a meta-stable helical spin density wave that emerges as a result of increased symmetry when the Rashba and Dresselhaus spin-orbit coupling terms are balanced, and which offers great promise as a means of controlling large ensembles of spins. We demonstrate that the spin-orbit symmetry, and the PSH dynamics, can be manipulated \textit{in-situ} by the application of uniaxial strain. This strain induces spin-orbit coupling with precisely the same symmetry as the Rashba term, allowing us to effectively tune the Rashba/Dresselhaus ratio in a single sample. This work is supported by DMSE office of BES-DOE, NSF, MARCO, ASEE and CNID.   

The precessing persistent spin helix in a magnetic field

While the spin-orbit interaction is useful for manipulating the electron spin, it could also cause spin decoherence. A Persistent Spin Helix (PSH) with infinite life time has been predicted [B. A. Bernevig et al., Phys. Rev. Lett. 97, 236601 (2006).] for 2D quantum wells with equal strength of Rashba and Dresselhaus spin-orbit coupling. This effect results from the spin SU(2) symmetry of electrons, which makes the spin density at a finite wave vector conserved. The PSH was later observed in the transient spin grating (TSG) experiment [C. P. Weber et al., Phys. Rev. Lett. 98, 076604 (2007).], where the spin density wave is pumped and its decay in the time domain is probed optically. In this work we propose measuring the PSH with an in-plane magnetic field and spin injection with alternating polarization. We derive and solve the drift-diffusion equation for the spin density and find that when the frequency of the spin injection is the same as the Larmor frequency, a great enhancement of the diffusion length and the amplitude of the spin oscillation should be observed, giving rise to a precessing PSH.   

Theory of Electron Spin Relaxation in ZnO

Doped ZnO is a promising material for spintronics applications. For such applications, it is important to understand the spin dynamics and particulary the spin relaxation times of this II-VI semiconductor. The transverse spin lifetime T$_{2}^{\ast}$ has been measured by optical orientation experiments, and it shows a surprising non-monotonic behavior with temperature. We explain this behavior by invoking spin exchange between localized and extended states. Interestingly, the effects of spin-orbit coupling are by no means negligible, in spite of the relatively small valence band splitting. This is due to the wurtzite crystal structure of ZnO. Detailed analysis allows us to characterize the impurity binding energies and densities, showing for the first time that optical orientation experiments can actually be used as a characterization tool for semiconductor samples. \newline [1] N.J. Harmon, W.O. Putikka, and R. Joynt, cond-mat/0808.2913 (2008)   

Effect of Induced Spin-orbit Coupling in Cold Atomic Gas

Spin-orbit (SO) coupling effect in semiconductors has emerged in the solid-state community as a very active field of research, fueled in part by the field of spintronics, e.g. spin current injection with spin Hall effect [1]. Recently, new schemes are developed to generate the SO interaction in cold atoms [2], which opens new possibilities in studying Spintronics in atomic systems. Here we shall report our recent proposal of SO coupling effects in Fermi atomic systems via optical method [3]. The induced SO coupling can be of the Dresselhaus and Rashba type with a Zeeman term. We show that the optically induced SO coupling can lead to a spin-dependent effective mass under proper condition, with one of them able to be tuned between positive and negative effective masses. As a direct observable we show that in the expansion dynamics of the atomic cloud the initial atomic cloud can split into two or four clouds depending on the effective mass regimes. Reference: [1] S. Murakami et al., Science 301, 1348 (2003); J. Sinova et al., Phys. Rev. Lett. 92, 126603 (2004). [2] X.-J. Liu et al., Phys. Rev. Lett. 98, 026602 (2007); S.-L. Zhu et al., ibid, 97, 240401 (2006); T. D. Stanescu et al., ibid, 99, 110403 (2007). [3] X.-J. Liu, M. F. Borunda, X. Liu, J. Sinova, submitted to PRL for publication, arxiv:0808.4137 (2008).