Can Non-Equilibrium Spin Hall Accumulation be Induced in Ballistic Nanostructures?

We demonstrate that flow of longitudinal unpolarized current through a ballistic two-dimensional electron gas with Rashba spin-orbit coupling will induce nonequilibrium spin accumulation which has opposite sign for the two lateral edges and it is, therefore, the principal observable signature of the spin Hall effect in two-probe semiconductor nanostructures. The magnitude of its out-of-plane component is gradually diminished by static disorder, while it can be enhanced by an in-plane transverse magnetic field. Moreover, our prediction of the longitudinal component of the spin Hall accumulation, which is insensitive to the reversal of the bias voltage, offers a smoking gun to differentiate experimentally between the extrinsic, intrinsic, and mesoscopic spin Hall mechanisms.Comment: 5 pages, 3 color EPS figures; published versio

Modeling of diffusion of injected electron spins in spin-orbit coupled microchannels

We report on a theoretical study of spin dynamics of an ensemble of spin-polarized electrons injected in a diffusive microchannel with linear Rashba and Dresselhaus spin-orbit coupling. We explore the dependence of the spin-precession and spin-diffusion lengths on the strengths of spin-orbit interaction and external magnetic fields, microchannel width, and orientation. Our results are based on numerical Monte Carlo simulations and on approximate analytical formulas, both treating the spin dynamics quantum-mechanically. We conclude that spin-diffusion lengths comparable or larger than the precession-length occur i) in the vicinity of the persistent spin helix regime for arbitrary channel width, and ii) in channels of similar or smaller width than the precession length, independent of the ratio of Rashba and Dresselhaus fields. For similar strengths of the Rashba and Dresselhaus fields, the steady-state spin-density oscillates or remains constant along the channel for channels parallel to the in-plane diagonal crystal directions. An oscillatory spin-polarization pattern tilted by 45$^{\circ}$ with respect to the channel axis is predicted for channels along the main cubic crystal directions. For typical experimental system parameters, magnetic fields of the order of Tesla are required to affect the spin-diffusion and spin-precession lengths.Comment: Replaced with final version (some explanations and figures improved). 8 pages, 6 figure

Complementary operation.

<p>Schematic diagram of the MSET for different magnetization orientations. (a) <i>ϕ</i> = 0° the magnetization is in-plane and (b) <i>ϕ</i> = 90° the magnetization is out-of-plane. (c) Coulomb blockade oscillations as a function of the direction of the back-gate voltage <i>V</i>_<i>gs</i> and the applied magnetic field orientation <i>ϕ</i> for B = 0.7 T. The-dashed blue and red lines indicate the operating points. (d) MSET Ids-Vgs transfer function at <i>ϕ</i> = 0°. The logic 0 (1) has been selected at a low (high) current level, n-type SET. (e) MSET Ids-Vgs transfer function at <i>ϕ</i> = 90°. The logic outputs have been inverted, p-type SET.</p

Single-device logic.

<p>(a) <i>V</i>_<i>ds</i> − <i>V</i>_<i>gs</i> map of the drain current for <i>ϕ</i> = 0° showing the characteristic Coulomb diamonds. Red and blue frames sketch the implemented logic gates for <i>ϕ</i> = 0° and 90° respectively. (b-c) AND-OR set of reprogrammable logic gates. AND gate implemented at <i>ϕ</i> = 0° (b) and OR gate at <i>ϕ</i> = 90° (c) with <i>V</i>_<i>ds</i> (input A) 0(1) defined as −132(−220) <i>μ</i>V and <i>V</i>_<i>gs</i> (input B) 0(1) defined as −96(0) <i>μ</i>V. (d-e) NAND-NOR set of reprogrammable logic gates. NAND gate implemented at <i>ϕ</i> = 0° (d) and NOR gate at <i>ϕ</i> = 90° (e) with <i>V</i>_<i>sd</i> (input A) 0(1) defined as 220(132) <i>μ</i>V and <i>V</i>_<i>gs</i> (input B) 0(1) defined as 128(224) <i>μ</i>V.</p

Logic at the multiple device level considering identical SETs and the logic inputs defined in Fig 2.

<p>The inputs A and B are defined as taken as the SET gate values. (a) A series pull-down network performs the OR operation at <i>ϕ</i> = 0° and NAND at <i>ϕ</i> = 90°. (b) Parallel pull-down network performs the AND operation at <i>ϕ</i> = 0° and NOR at <i>ϕ</i> = 90°.</p

Device structure.

<p>(a) Schematic cross-section of the device sketching the magnetization orientation of the (Ga,Mn)As back-gate layer. (b) SEM image of the device. The aluminium island is separated from the source and drain leads by AlO_<i>x</i> tunnel junctions. Side gates were not used in this experiment. (c) Drain current (<i>I</i>_<i>ds</i>) oscillations as a function of the back gate voltage (<i>V</i>_<i>gs</i>).</p