Persistent spin helix in spin-orbit coupled system. Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab

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1 Persistent spin helix in spin-orbit coupled system Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab

2 Persistent spin helix in spin-orbit coupled system Jake Koralek, Chris Weber, Joe Orenstein Lawrence Berkeley National Lab Andrei Bernevig, Shoucheng Zhang Stanford University Shawn Mack, Jason Stevens, David Awschalom Center for Spintronics and Quantum Computation, University of California Santa Barbara

3 Motivation for studying spin propagation Correlated electrons separation of spin and charge Spintronics information carried by spin rather than charge One of the keys for spintronics is to achieve control over spin via E-fields; logic based on switching via B is not feasible. Spin-orbit coupling provides the potential mechanism, as exemplified in the Datta-Das transistor concept

4 but S-O coupling is a double-edged sword. Control over spin state via E fields: good Non-conservation of spin angular momentum: bad

5 This talk Spin-orbit as both advantage and obstacle. Schliemann, Egues, Loss proposal The significance of Rashba=Dresselhaus Spin propagation in the presence of spin-orbit coupling. Theory and experiment The quest for the Persistent Spin Helix. Measurement and control over Rashba, Dresselhaus coupling. Spin diffusion coefficient, violation of Einstein relation, and spin Coulomb drag. The future

6 Model 2D system: GaAs/AlGaAs quantum wells 2D electron gas parameters Free-electron-like Fermi surface n ~ cm -2 mean-free-time ~ 10 ps mean-free-path ~ 3 microns Trivial system except for the spin-orbit coupling

7 Spin-orbit Hamiltonian: Dresselhaus term (intrinsic) Rashba term ( asymmetry of well) k y k y ( M, N) k x ( M, N) k x

8 Length and frequency scale associated with spin-orbit coupling Spin precesses in Rashba field With frequency Ω = αk F Spin of ballistic electron

9 Datta-Das: spin transistor based on control of Rashba spin precession. =0 OFF ON

10 Datta-Das not robust with respect to disorder, which leads to Dyakanov-Perel spin relaxation. Interrupted spin precession

11 Spin diffusion length < spin precession length So this would seem to be the end of the road. However, Schliemann, Egues, and Loss proposed a way out

12 Rashba=Dresselhaus Rashba spin-orbit coupling Dresselhaus spin-orbit coupling + =

13 Special properties of Rashba equals Dresselhaus spin dynamics Spin rotation depends on displacement, independent of path y x All of these paths experience exactly the same net rotation!

14 Schliemann, Egues, Loss device x

15 Spin/displacement correlation via spin-orbit coupling leads to anomalous diffusion. Measuring spin diffusion can lead us to α=β

16 Models of spin propagation typically assume dynamics obey simple diffusion equation, with loss term to describe spin relaxation. which has solutions of the form: where,

17 Graph of spin polarization lifetime vs. q is simple Lorentzian 1/Γ q τ s 1/L s q

18 Perfect spin/displacement correlation at α=β leads to anomalous spin diffusion. Spin precesses in x -z plane like an arrow on a disk that rolls w/o slipping z x

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20 A helical polarization with the magic wavevector q=1/l s will never decay, even though the spin of each individual electron is rapidly randomized. Many electron system prepared with initial helical polarization

21 When α=β spin helix has infinite lifetime! τ q S z + is x πl s At the resonant q, spin precesses by 2π as it propagates one period of the helix 1/L s q

22 What about α β? Spin propagation Rashba only Burkov, Nunez, MacDonald, Phys. Rev. B 70 (2004) Precession angle is path dependent leading to weaker, but nonzero, spin/space correlations.

23 Summarizing predictions for spin helix lifetime τ q α=β α or β=0 No spin-orbit Prediction for 2D (Rashba only) Burkov, Nunez, MacDonald Phys. Rev. B 70 (2004) 1/L s q

24 Surprisingly, there are few direct measurements of spin diffusion in the presence of spin-orbit coupling D s =4 cm 2 /s at 1.6 K n ~ cm -3 in bulk GaAs

25 Collaborators at UCB and LBNL (Quantum well samples grown in Awschalom Lab by Jason Stephens) Chris Weber Joe Orenstein and Nuh Gedik

26 Optical probes of spin dynamics Injecting spin polarization: optical orientation effect Conduction band Left circular Valence band Right circular

27 Optical probes of spin dynamics Detecting spin polarization: Faraday rotation Δθ

28 Creating a spin polarization wave

29 Photon helicity wave creates a spin-density-wave in S z E x E y S z

30 Detecting a spin polarization wave

31 Heterodyne detection Modulate relative phase at 210 Hz Diffracted probe 2 Transmitted probe 1

32 Basic pump-probe set-up Ti:Sapphire laser Probe Sample Detector Pump Optical delay line

33 Coherent transient grating set-up Probe beams Sample Pump beams Detector

34 Oscillating cover-slip modulates reference phase

35 Quantum well samples Al 0.3 Ga 0.7 As Al 0.3 Ga 0.7 As GaAs 12nm Si δ-layers

36 Temperature dependence of spin polarization decay at fixed wavevector Double exponential decay appears below about 200 K

37 Direct demonstration of anomalous diffusion: Decay faster for q 0 than for q=0 q=0.6 x 10 4 cm -1 q=0

38 Two exponentials of equal weight Initial condition Normal modes = +

39 Wavevector dependence of lifetime Enhancement relative to q=0 larger than predicted for 2D Rashba model

40 Decay rate depends strongly on direction of wavevector in the plane

41 Dresselhaus+ε Rashba Dresselhaus spin-orbit coupling Rashba spin-orbit coupling + ε =

42 Bernevig-Zhang model: Graphs show dispersion of spin lifetime for different α/β Lifetime diverges as α β Fit parameters are α/β, α 2 +β 2, and D s Linear plot Log plot 4 10 Spin lifetime Wavevector Wavevector

43 Creation operator for spin density wave commutes with the Hamiltonian Fermi surface for α=β

44 Wavevector dependence of lifetime Fit to α=0.2β

45 The Holy Grail: α=β Tune Rashba coupling by varying doping asymmetry 4:1 Al 0.3 Ga 0.7 As Al 0.3 Ga 0.7 As GaAs 12nm Si δ-layers

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52 This plot emphasizes the contrast between grating decays on and off the peak of the PSH effect. At the magic wavector the spin polarization wave survives about x100 longer than it would in the absence of SO coupling

53 Where we are now in the search for α=β 600 S-O coupling [m/s] Rashba Dresselhaus Normalized E field

54 Measurements of spin diffusion coefficient in 2DEG s Observation of spin Coulomb drag Weber et al. Nature 437, (2005)

55 Direct measurement of spin diffusion coefficient, D s, in 2DEG Spin polarization Decay rate of a fluctuation with wavevector q 1 14 µm 4.8 µm 3.5 µm 2.5 µm! (ps -1 ) D s =120 cm 2 /s Time [ps] q 2 (x 10 8 cm -2 )

56 Comparison of spin and charge diffusion coefficients 6D (1000 cm2 /s) D s T (K)

57 Comparison of spin and charge diffusion coefficients 6 5 D (1000 cm 2 /s) D c D s 0.4 D s /D c T (K) T (K)

58 Spin Coulomb drag (D Amico &Vignale) J spin J spin J charge e-e collisions conserve total momentum, but exchange momentum between spin up and spin down populations creating spin drag resistance ρ

59 Direct comparison with theory 8 Dc0 /Ds cm cm cm -2 Spin Coulomb drag ρ /ρ Charge and spin diffuse at same rate

60 Future Continue the quest to infinity and beyond. Use the spin grating to study exotic effects such as spin Hall effect. Can we change spin polarization lifetime by orders of magnitude through a gate applied electric field? Is the Datta-Das device feasible under these conditions?

61 Datta-Das does not require point contacts