The spin-orbit interaction (SOI) in zincblende semiconductor quantum wells can be set to a symmetry point, in which spin decay is strongly suppressed for a helical spin mode. Signatures of such a persistent spin helix (PSH) have been probed using the transient spin grating technique, but it has not yet been possible to observe the formation and the helical nature of a PSH. Here we directly map the diffusive evolution of a local spin excitation into a helical spin mode by a timeand spatially resolved magneto-optical Kerr rotation technique. Depending on its in-plane direction, an external magnetic field interacts differently with the spin mode and either highlights its helical nature or destroys the SU(2) symmetry of the SOI and thus decreases the spin lifetime. All relevant SOI parameters are experimentally determined and confirmed with a numerical simulation of spin diffusion in the presence of SOI.Conduction-band electrons in semiconductors experience SOI from intrinsic [1] and extrinsic sources, leading to spin dephasing, current-induced spin polarization and spin Hall effects [2]. These physical mechanisms are of great fundamental and technological interest, recently also in the context of topolocial insulators [3] and Majorana fermions [4,5]. Intrinsic SOI arises from an inversion asymmetry of the bulk crystal (Dresselhaus term) and of the grown layer structure (Rashba term). In a quantum well (QW), these two components can be tailored by means of the confinement potential [6], and the Rashba SOI can be externally tuned by using gate electrodes [7,8]. In general, SOI leads to precession of electron spins. In the diffusive limit, in which the scattering length is much smaller than the spin-orbit (SO) length λ SO , a random walk of the spins on the Bloch sphere will dephase a non-equilibrium spin polarization [9].Of special interest is the situation in a two-dimensional electron gas (2DEG) with balanced Rashba and Dresselhaus contributions [6,[10][11][12][13]. There, the SOI attains SU(2) symmetry and the spin polarization of a helical mode is preserved. The reason for this conservation of the spin polarization is a unidirectional effective SO magnetic field B SO , which depends linearly on the component of the electron momentum along a specific in-plane direction. This causes the precession angle of a moving electron to vary linearly with the distance traveled along that direction, irrespective of whether the electron path is ballistic or diffusive [10,11]. In such a situation, a local spin excitation is predicted to evolve into a helical spin mode termed PSH [ Fig. 1(a)]. Transient spin grating measurements [6] showed that a spin excitation with a spatially modulated out-of-plane spin component decays with two characteristic lifetimes that correspond to two superposed spin modes of opposite helicity. * Electronic address: gsa@zurich.ibm.comHere we directly measure the diffusive evolution of a local spin excitation into a PSH by time-resolved Kerr rotation microscopy [ Fig. 1(b)]. We employ a pumpprobe appro...

We measured the Dresselhaus spin-orbit interaction coefficient β 1 for (001)-grown GaAs/Al 0.3 Ga 0.7 As quantum wells for six different well widths w between 6 and 30 nm. The varying size quantization of the electron wave vector z-component k 2 z ∼ (π/w) 2 influences β 1 = −γ k 2 z linearly. The value of the bulk Dresselhaus coefficient γ = (−11 ± 2) eVÅ 3 was determined. We discuss the absolute sign of the Landé g factors and the effective momentum scattering times.

The Dresselhaus spin-orbit interaction ͑SOI͒ of a series of two-dimensional electron gases hosted in GaAs/ AlGaAs and InGaAs/GaAs ͑001͒ quantum wells ͑QWs͒ is measured by monitoring the precession frequency of the spins as a function of an in-plane electric field. The measured spin-orbit-induced spin splitting is linear in the drift velocity, even in the regime where the cubic Dresselhaus SOI is important. We relate the measured splitting to the Dresselhaus coupling parameter ␥, the QW confinement, the Fermi wave number k F , and strain effects. From this, ␥ is determined quantitatively, including its sign.

The time evolution of a local spin excitation in a (001)-confined two-dimensional electron gas subjected to Rashba and Dresselhaus spin-orbit interactions of similar strength is investigated theoretically and compared with experimental data. Specifically, the consequences of the finite spatial extension of the initial spin polarization is studied for non-balanced Rashba and Dresselhaus terms and for finite cubic Dresselhaus spin-orbit interaction. We show that the initial out-of-plane spin polarization evolves into a helical spin pattern with a wave number that gradually approaches the value q0 of the persistent spin helix mode. In addition to an exponential decay of the spin polarization that is proportional to both the spin-orbit imbalance and the cubic Dresselhaus term, the finite width w of the spin excitation reduces the spin polarization by a factor that approaches exp(−q 2 0 w 2 /2) at longer times.

We experimentally investigate the dynamics of a persistent spin helix in etched GaAs wire structures of 2 to 80 um width. Using magneto-optical Kerr rotation with high spatial resolution, we determine the lifetime of the spin helix. A few nanoseconds after locally injecting spin polarization into the wire, the polarization is strongly enhanced as compared to the two-dimensional case. This is mostly attributed to a transition to one-dimensional diffusion, strongly suppressing diffusive dilution of spin polarization. The intrinsic lifetime of the helical mode is only weakly increased, which indicates that the channel confinement can only partially suppress the cubic Dresselhaus spin-orbit interaction

We have investigated the intrasubband spin-density excitation (SDE) in an asymmetrically doped GaAs-AlGaAs single quantum well with balanced Rashba and Dresselhaus spin-orbit interaction strengths by inelastic light scattering. For this unique symmetry, the combined spin-orbit field is either parallel or antiparallel to the [110] in-plane direction of the quantum well for all wave vectors of the two-dimensional reciprocal space. In backscattering geometry, the SDE is formed by spin-flip intrasubband transitions of the spin-split subband. Via the splitting of the intrasubband SDE, we have directly detected the spin splitting of the conduction band due to the anisotropic spin-orbit field. As expected, the splitting is nonzero if a wave vector is transferred perpendicular to the direction of the spin-orbit field and close to zero for a parallel wave-vector transfer. The extracted values for the spin-orbit strength and for the wavelength of a persistent spin helix compare well with results of previous experiments of direct spatial mapping of the spin helix.