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Optical transient-grating measurement of spin propagation in a two-dimensional electron gas

Optical transient-grating measurement of spin propagation in a two-dimensional electron gas. Chris Weber UC Berkeley and Lawrence Berkeley National Lab. LBNL, UC Berkeley, Stanford, and UCSB collaboration. CW, Nuh Gedik, Joel Moore, Joe Orenstein UC Berkeley and LBNL.

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Optical transient-grating measurement of spin propagation in a two-dimensional electron gas

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  1. Optical transient-grating measurement of spin propagation in a two-dimensional electron gas Chris Weber UC Berkeley and Lawrence Berkeley National Lab National High Magnetic Field Laboratory

  2. LBNL, UC Berkeley, Stanford, and UCSB collaboration CW, Nuh Gedik, Joel Moore, Joe Orenstein UC Berkeley and LBNL Andrei Bernevig and Shouchang Zhang Stanford Jason Stephens and David Awschalom Center for Spintronics and Quantum Computation UCSB National High Magnetic Field Laboratory

  3. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  4. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  5. Fast optics: time resolution and broad dynamic range 1 ns 10 ps 100 fs e-e collisons Electron-phonon int’n Spin lifetimes Quasiparticles (high-Tc) Excited states of biomolecules Spin-orbit splitting Electron-hole pairs 1 ueV 0.1 meV 10 meV Energy splittings or linewidths National High Magnetic Field Laboratory

  6. ħw =1.5 eV Example of pump-probe: spin dynamics in a GaAs quantum well Step 1: Optical orientation with a circular pump National High Magnetic Field Laboratory

  7. Pump ħw =1.5 eV GaAs QW (n-doped) Spin dynamics after circular excitation National High Magnetic Field Laboratory

  8. Detector Pump ħw =1.5 eV Parallel circular polarizations GaAs QW (n-doped) Anti-parallel circular polarizations Probe (variable delay) Measuring spin dynamics with a time-delayed probe DTspin(parallel) = -DTspin(antiparallel) National High Magnetic Field Laboratory

  9. Pump-probe schematic Delay stage Pump Probe Center wavelength 800 nm ~ 1.5 eV Pulse duration 100 fs Rep rate 80 MHz Avg. power at sample 20 mW Sample Detector National High Magnetic Field Laboratory

  10. n [1011 cm-2] TF [K] m [cm2/Vs] 7.8 400 230,000 4.3 220 93,000 1.9 100 70,000 Si in barrier layer Al0.3Ga0.7As GaAs (12nm) + + + + Samples: 10-layer, modulation-doped quantum wells National High Magnetic Field Laboratory

  11. } In this talk Spin dynamics at T = 50 K • You can learn most from pump-probe data when you have another “knob to turn”: • B field • T temperature • n doping • q wavevector • l disorder ts = 26 ps Why do we care about spin dynamics, anyway? National High Magnetic Field Laboratory

  12. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  13. Spin dynamics of Spin Coulomb drag Spin helix Spin dynamics: physics in, physics out H = H0 + He-e + HSO + Hdis + … Spin Hall effect Spin Coulomb drag Spin helix Weak (anti-) localization National High Magnetic Field Laboratory

  14. Spin-orbit coupling creates an effective magnetic field Dresselhaus term (from crystal structure) Rashba term (due to electric field) Typical field size ~ 2 T National High Magnetic Field Laboratory

  15. Tuning different contributions to spin-orbit interaction may provide an elegant solution. Spin-orbit coupling: hero and villain of spintronics Control over spin state via E field: good Non-conservation of spin angular momentum: bad Datta & Das Applied Physics Letters56, 665 (1990). …but National High Magnetic Field Laboratory

  16. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  17. Energy [meV] Jusserand et al., PRL 69, 848-51 (1992) Frequency shift [cm-1] How to measure spin dynamics & propagation? w-domain: Spin-flip Raman (low T) Neutron scattering Spin-flip Raman “motional narrowing” creates sharp peaks centered on zero frequency Time-domain: Transient spin gratings Low q (where the action is!) National High Magnetic Field Laboratory

  18. Creates a helicity wave… which generates a spin density wave. Transient spin gratings Cameron et al., Phys. Rev. Lett.76, 4793 (1996) Interference of two orthogonally polarized beams…. National High Magnetic Field Laboratory

  19. Probe beam q q transmitted diffracted Amplitude of diffracted beam Time delay Detecting the transient grating Pump beams National High Magnetic Field Laboratory

  20. Probe beam q q Detecting the transient grating Pump beams Amplitude of diffracted beam transmitted diffracted Time delay National High Magnetic Field Laboratory

  21. Probe beam q q transmitted diffracted Detecting the transient grating Pump beams Amplitude of diffracted beam Time delay National High Magnetic Field Laboratory

  22. Ordinary diffusion: higher-q gratings decay faster Low q High q National High Magnetic Field Laboratory

  23. Cameron et al., Phys. Rev. Lett.76, 4793 (1996) q2 [cm-2] Ordinary diffusion: higher-q gratings decay faster National High Magnetic Field Laboratory

  24. Rapid acquisition of data: more is different Points in (n,T,l)-space at which Ds has been measured. Before this work: In this work: • Technical innovations: • Rapid-scanned heterodyne detection of diffracted beam • Phase-mask for changing q 2 Hundreds National High Magnetic Field Laboratory

  25. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  26. Anomalous diffusion: Decay faster for finite q than for q = 0 ! T = 50 K q=0.6 x 104 cm-1 q=0 National High Magnetic Field Laboratory

  27. Decay time [ps] Wavevector [104 cm-1] Dispersion of double-exponential decay (50 K) Slow component Fast component q=0.6 x 104 cm-1 National High Magnetic Field Laboratory

  28. Decay time [ps] Wavevector [104 cm-1] Why the long lifetime? Imagine that the sample was one-dimensional … National High Magnetic Field Laboratory

  29. z x Spin-orbit precession: random walks in one-D Path (1) Motion along Path (2) These two paths have the same net precession. Spin precesses in x-z plane National High Magnetic Field Laboratory

  30. In one-D, spin helix has infinite lifetime! tq Sz+ iSx Sz- iSx 2pLs q 1/Ls At the resonant q,spin precesses by 2p as it propagates one period of the helix National High Magnetic Field Laboratory

  31. …back to two-dimensional reality. National High Magnetic Field Laboratory

  32. tq One-D Two-D q 1/Ls For spin diffusion in 2-D, Precession angle is path dependent… leading to weaker, but nonzero, spin/space correlations at the same critical wavevector. National High Magnetic Field Laboratory

  33. Froltsov PRB (2001) Burkov, Nunez, MacDonald PRB (2004) Mishchenko, Shytov, Halperin PRL (2004) Bernevig, Zhang PRL (2006) Rashba coupling only: Theoretical description in 2D National High Magnetic Field Laboratory

  34. tq Sz+ iSx Sz- iSx q 1/Ls Coupling of Sz and Sx… … leads to normal modes that are linear combinations of the two spin-components. At the resonant q, the normal modes are spin helices of opposite chirality National High Magnetic Field Laboratory

  35. Simple theory predicts two exponentials of equal weight Initial condition = + Sz One mode is fast, the other slow, depending on the sign of the internal field National High Magnetic Field Laboratory

  36. tq Decay time [ps] One-D Two-D q Wavevector [104 cm-1] 1/Ls Our spin lifetime is even longer than simple theories predict National High Magnetic Field Laboratory

  37. Decay time [ps] Wavevector [104 cm-1] Why the very long lifetime? Imagine that the Rashba and Dresselhaus couplings were equal … National High Magnetic Field Laboratory

  38. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  39. Equal contributions to SO coupling Rashba term (due to electric field) Dresselhaus term (from crystal structure) + = Spin-orbit field at every k points in the same direction National High Magnetic Field Laboratory

  40. All of these paths experience exactly the same net rotation! Perfect correlation of precession with displacement along x Precession in x-z plane: National High Magnetic Field Laboratory

  41. Test this prediction: design QW samples with Rashba = Dreselhaus, measure transient spin grating at q = 1/Ls (future work) Also predicts anisotropic spin transport: Precession notequal Precession equal So if Rashba = Dresselhaus • Persistent spin helix: in analogy with one-D, spin lifetime diverges at q = 1/Ls • There is an exact SU(2) symmetry (Bernevig & Zhang) • Can have strong spin-orbit without dephasing spins! National High Magnetic Field Laboratory

  42. …back to reality, where Rashba and Dressalhaus terms are unequal. National High Magnetic Field Laboratory

  43. Predictions are surprisingly robust Dresselhaus = Rashba Dresselhaus = 3 x Rashba • Spin-helix lifetime diverges • Spin-helix lifetime is long • Anisotropic spin transport • Anisotropic spin transport National High Magnetic Field Laboratory

  44. Sz t [ps] Anisotropic lifetimes at q = 1/Ls Precession equal Precession notequal National High Magnetic Field Laboratory

  45. Dispersion of double-exponential decay along the two directions: Theory for arbitrary Rashba, Dresselhaus (Bernevig & Zhang) National High Magnetic Field Laboratory

  46. Fits to Bernevig-Zhang theory Fits give: National High Magnetic Field Laboratory

  47. Outline • Introduction to fast optics • Spin physics in GaAs 2DEGs • Measuring spin propagation: the transient spin grating • Observation of anomalous diffusion • Prediction of the persistent spin helix, and preliminary observations • Observation of spin Coulomb drag: e-e collisions suppress spin diffusion National High Magnetic Field Laboratory

  48. n-GaAs QW n=7.81011 cm-2 Spin diffusion coefficient Nature 437, 1330-1333 (2005) National High Magnetic Field Laboratory

  49. Einstein relation (for charge) 7.8 E11 cm-2 4.3 E11 1.9 E11 where (non-interacting susceptibility) Compare Ds with charge diffusion coefficient, Dc0 Nature 437, 1330-1333 (2005) National High Magnetic Field Laboratory

  50. Spin Coulomb drag (D’Amico &Vignale) e-e collisions affect spin current, not charge current e-e collisions conserve total momentum, but exchange momentum between spin up and spin down populations. National High Magnetic Field Laboratory

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