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

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Optical transient-grating measurement of spin
propagation in a two-dimensional electron gas
Chris Weber UC Berkeley and Lawrence Berkeley
National Lab
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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
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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

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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

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Fast optics time resolution and broad dynamic
range
1 ns 10 ps
100 fs
e-e collisons
Electron-phonon intn
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
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Example of pump-probe spin dynamics in a GaAs
quantum well
Step 1 Optical orientation with a circular pump
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Spin dynamics after circular excitation
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Measuring spin dynamics with a time-delayed probe
DTspin(parallel) -DTspin(antiparallel)
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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
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Samples 10-layer, modulation-doped quantum wells
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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?
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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

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Spin dynamics physics in, physics out
H H0 He-e HSO Hdis
Spin Hall effect
Spin Coulomb drag
Spin helix
Weak (anti-) localization
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Spin-orbit coupling creates an effective magnetic
field
Dresselhaus term (from crystal structure)
Rashba term (due to electric field)
Typical field size 2 T
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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 Letters 56, 665
(1990).
but
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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

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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!)
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Transient spin gratings
Cameron et al., Phys. Rev. Lett. 76, 4793 (1996)
Interference of two orthogonally polarized beams.
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Detecting the transient grating
Pump beams
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Detecting the transient grating
Pump beams
Amplitude of diffracted beam
transmitted
diffracted
Time delay
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Detecting the transient grating
Pump beams
Amplitude of diffracted beam
Time delay
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Ordinary diffusion higher-q gratings decay faster
Low q
High q
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Ordinary diffusion higher-q gratings decay faster
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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
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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

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Anomalous diffusion Decay faster for finite q
than for q 0 !
T 50 K
q0.6 x 104 cm-1
q0
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Dispersion of double-exponential decay (50 K)
Slow component
Fast component
q0.6 x 104 cm-1
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Why the long lifetime?
Imagine that the sample was one-dimensional
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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
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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
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back to two-dimensional reality.
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For spin diffusion in 2-D,
Precession angle is path dependent
leading to weaker, but nonzero, spin/space
correlations at the same critical wavevector.
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Theoretical description in 2D
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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
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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
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Our spin lifetime is even longer than simple
theories predict
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Why the very long lifetime?
Imagine that the Rashba and Dresselhaus couplings
were equal
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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

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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
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Perfect correlation of precession with
displacement along x
Precession in x-z plane
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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!

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back to reality, where Rashba and Dressalhaus
terms are unequal.
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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

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Anisotropic lifetimes at q 1/Ls
Precession equal
Precession not equal
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Theory for arbitrary Rashba, Dresselhaus
(Bernevig Zhang)
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Fits to Bernevig-Zhang theory
Fits give
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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

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Spin diffusion coefficient
Nature 437, 1330-1333 (2005)
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Compare Ds with charge diffusion coefficient, Dc0
Nature 437, 1330-1333 (2005)
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e-e collisions affect spin current, not charge
current
Spin Coulomb drag (DAmico Vignale)
e-e collisions conserve total momentum, but
exchange momentum between spin up and spin down
populations.
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Drag damps diffusive spin current
Counter-propagation of spin populations
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Comparison of diffusion coefficients sCd theory
Nature 437, 1330-1333 (2005)
7.8 E11 cm-2
4.3 E11
1.9 E11
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Advantage of spin Coulomb drag how far can spin
packet drift in E-field before spreading?
Nature 437, 1330-1333 (2005)
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Future directions

• Tune a sample to Dressalhaus Rashba divergent
  lifetime at qc?
• Disordered sample weak (anti-) localization?

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Uses for a (high) magnetic field

• (Quasi-) infinite spin lifetimes (ordinary
  samples)
• Destroy persistent spin-helix
• (Dresselhaus Rashba sample)
• Spin-polarized 2DEG / QH ferromagnet
• Spin-waves?
• Skyrmions?
• Spin transport w/o charge transport?

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Conclusions

• Transient grating technique successfully probes
  spin transport in ps time regime
• Observed anomalous diffusion (fast slow modes
  maximum lifetime at nonzero q) due to spin-orbit
  coupling
• Exact mixing of Rashab Dresselhaus couplings
  should produce a persistent spin helix
• Spin Coulomb drag e-e collisions suppress spin
  diffusion to far below charge diffusion