Transient grating measurements of spin diffusion. Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab

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1 Transient grating measurements of spin diffusion Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab

2 LBNL, UC Berkeley and UCSB collaboration Chris Weber, Nuh Gedik, Joel Moore, JO UC Berkeley and LBNL Jason Stephens and David Awschalom Center for Spintronics and Quantum Computation UCSB

3 Outline Spin diffusion in the presence of Rashba interaction Measuring spin diffusion optically: transient spin grating Experimental results in n-gaas QW: observation of spin Coulomb drag Anomalous wavevector dependent spin relaxation

4 Interest in spin transport Datta-Das transistor Datta, S. & Das, B. Applied Physics Letters 56, (1990). S B eff ( k ) k One-dimensional spin transport Burkov, A., Nunez, A., & MacDonald, A. Cond-mat (2003) perfect correlation of precession with spatial motion Spin-packet drift Kikkawa, J. M. & Awschalom, D. D. Nature 397, (1999). Δx (μm)

5 Interest in spin transport Spin-Hall effect Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Science 306, (2004). Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Physical Review Letters 94, /1-4 (2005).

6 Virtually no measurements of spin diffusion coefficients in doped semiconductors

7 Spin vs. charge currents Charge Spin j c = qv v j s = σ v z j s = σ v v z v

8 Spin diffusion and relaxation Spin diffusion can be defined when: τ s τ coll Usually modeled by diffusion eq. with loss term: 2 sz sz Ds sz + = t τ Decay rate of a fluctuation with wavevector q: s γ 2 q s s = Dq + 1/ τ This ignores spin-spatial correlations embodied in DP spin relaxation!

9 D yakonov-perel relaxation and spin-spatial correlations Δ S S =Ω int τ S B int ( k) Each scattering event changes precession axis of spin Interrupted precession about effective field Analogous to motional narrowing 2 DP regime: Ωintτ 1 = Ωintτ τ 1 s

10 Perfect spin-spatial correlation in 1D z Ω int V Drift L = Ω 2π vf int x Relaxation of S z and S x are now coupled for nonzero q q c =Ω int /v F is crossover wavevector

11 Dispersion of coupled S z and S x relaxation modes Spin fluctuation with wavevector Ω int /v F has infinite lifetime!

12 Anomalous relaxation in 2-dimensions γ q τ s Γ + Dq 2 Γ Freitsov Burkov, Nunez, MacDonald Relaxation rate predicted to slow at critical wavevector, but not to zero qv F /Ω SO

13 Transient spin gratings Ideal for measurement of wavevector dependence of spin relaxation rate Interference of two orthogonally polarized beams. Creates a helicity wave which generates a spin density wave. Cameron et al., Phys. Rev. Lett. 76, 4793 (1996)

14 Probing diffusion and relaxation: the transient grating technique Pump beams Probe beam transmitted Amplitude of diffracted beam diffracted Time delay

15 Probing diffusion and relaxation: the transient grating technique Pump beams Probe beam transmitted Amplitude of diffracted beam diffracted Time delay

16 Probing diffusion and relaxation: the transient grating technique Pump beams Probe beam transmitted Amplitude of diffracted beam diffracted Time delay

17 Technical innovations Phase mask array for rapid variation of q Phase-modulated heterodyne detection of diffracted wave N.Gedik and J. Orenstein, Optics Letters, 29, 2109 (2004).

18 Phase mask array

19 Heterodyne detection of the spin grating

20 Heterodyne detection of the spin grating Oscillating cover slip provides rapid scan of relative phase

21 Demonstration of coherent heterodyne detection

22 Quantum well samples 10-layer, modulationdoped quantum well Al 0.3 Ga 0.7 As GaAs (12nm) n [10 11 cm -2 ] T F [K] μ [cm 2 /Vs] , , ,000 Si in barrier layer

23 Grating decay for different wavevectors at room temperature Spin polarization 1 14 μm 4.8 μm 3.5 μm 2.5 μm n [10 11 cm -2 ] Time [ps]

24 Grating decay rate proportional to q 2 Dispersion shows no evidence of of spinspatial correlations at room temperature D s =120 cm 2 /s γ (ps -1 ) q 2 (x 10 8 cm -2 )

25 Grating decay rate vs. T (for different grating wavelengths) 10 0 γ (ps -1 ) μ 3.5 μ 4.8 μ 14 μ T (K)

26 Ballistic/diffusive crossover γ q 5 K q 295 K γ 2 q q

27 Ballistic regime: S z oscillates at low T At low T, the mean-free-path becomes comparable to the grating period 0.6 Spin polarization Time [ps]

28 T-dependence of ballistic oscillations From fit of theory (JEM) to data we obtain D s in the ballistic regime as well 5 K 13 K 29 K 1.8 μm 1.5 μm 1.5 μm TG (a.u.) 51 K 67 K 91 K 1.0 μm 0.7 μm 0.5 μm Time (ps)

29 Spin diffusion coefficient 3 D s (1000 cm 2 /s) 2 1 n-gaas QW n= cm T (K)

30 If scattering processes determining spin and charge conductivities are the same D = fd s c0 where f χ χ 0 s σ c, and Dc 0 2 e χ0 D c 0 = μe B F μ kt e e for T << T F for T >> T F

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

32 Comparison of spin and charge diffusion coefficients E11 cm E E D (cm 2 /s) D (cm 2 /s) D (cm 2 /s) T (K) T (K) T (K)

33 Spin Coulomb drag (D Amico &Vignale) e-e collisions affect spin current, not charge current J spin J c J spin e-e collisions conserve total momentum, but exchange momentum between spin up and spin down populations.

34 Drag leads to different D s for spin and charge n + n D = σ / χ c c c n n χ 0 Dc 0 Ds = 1+ χ ρ ρ s spin Drag resistance

35 Spin drag resistance is large for high mobility 2DEG s ρ (kω) ρ (scd theory) ρ c (measured) I. D Amico and G. Vignale, Phys. Rev. B 68, (2001) ρ depends only on n, T T (K)

36 Testing the D Amico Vignale prediction D = χ D 0 s c0 χs 1 1+ ρ ρ D D c0 s χ 0 or s = + χ ( 1 ρ ρ ) Zero-free parameter theory Directly from experiment

37 Direct comparison with theory 8 6 χ s > χ 0 D c 0 / D S ρ / ρ 7.8 E11 cm E E E11 (disordered)

38 Comparison of diffusion coefficients: no free parameters! E11 cm E E D (cm 2 /s) D (cm 2 /s) D (cm 2 /s) T (K) D s T (K) = χ 0 c0 χ 1 + ρ / ρ s D T (K)

39 Advantage of spin Coulomb drag: how far can spin packet drift in E- field before spreading? L D n n w L w D = eew D c εf Ds Enhancment due to spin Coulomb drag

40 L SO = 1.5 μm, independent of n, T L = Dτ S s s E11 cm -2 Spin relaxation rate (q=0) Diffusion coefficient L s (μ) E11 γ (ps -1 ) D (cm 2 /s) E T (K) T (K) T (K)

41 L SO as a function of n,t L S = D γ S S L s (μ) γ (ps -1 ) 10-2 D (cm 2 /s) T (K) T (K) T (K)

42 Disordered quantum well samples Quantum wells with varying fraction of dopant in the well Al 0.3 Ga 0.7 As GaAs n [10 11 cm -2 ] T F [K] μ [cm 2 /Vs] , , , ,000

43 Disordered sample at 295 K γ (ps -1 ) q 2 (10 8 cm -2 )

44 Ballistic/diffusive crossover γ q 5 K q 295 K γ 2 q q

45 Anomalous q-dependence at low T γ (ps -1 ) q 2 (10 8 cm -2 )

46 2D dispersion in presence of spin-orbit, but with adjustable parameter: D Ω τ v 2 2 s SO s F

47 Conclusions Heterodyne transient grating technique successfully probes spin transport in ps time regime spin Coulomb drag observed Anomalous (non-diffusive) relaxation at low T