Transient grating measurements of spin diffusion Joe Orenstein UC Berkeley and Lawrence Berkeley National Lab
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
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
Interest in spin transport Datta-Das transistor Datta, S. & Das, B. Applied Physics Letters 56, 665-7 (1990). S B eff ( k ) k One-dimensional spin transport Burkov, A., Nunez, A., & MacDonald, A. Cond-mat 0311328 (2003) perfect correlation of precession with spatial motion Spin-packet drift Kikkawa, J. M. & Awschalom, D. D. Nature 397, 139-41 (1999). Δx (μm)
Interest in spin transport Spin-Hall effect Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Science 306, 1910-13 (2004). Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Physical Review Letters 94, 047204/1-4 (2005).
Virtually no measurements of spin diffusion coefficients in doped semiconductors
Spin vs. charge currents Charge Spin j c = qv v j s = σ v z j s = σ v v z v
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!
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
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
Dispersion of coupled S z and S x relaxation modes Spin fluctuation with wavevector Ω int /v F has infinite lifetime!
Anomalous relaxation in 2-dimensions γ q τ s 10 8 6 4 2 Γ + Dq 2 Γ Freitsov Burkov, Nunez, MacDonald Relaxation rate predicted to slow at critical wavevector, but not to zero. 0 0 1 2 3 4 5 6 qv F /Ω SO
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)
Probing diffusion and relaxation: the transient grating technique Pump beams Probe beam transmitted Amplitude of diffracted beam diffracted Time delay
Probing diffusion and relaxation: the transient grating technique Pump beams Probe beam transmitted Amplitude of diffracted beam diffracted Time delay
Probing diffusion and relaxation: the transient grating technique Pump beams Probe beam transmitted Amplitude of diffracted beam diffracted Time delay
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).
Phase mask array
Heterodyne detection of the spin grating
Heterodyne detection of the spin grating Oscillating cover slip provides rapid scan of relative phase
Demonstration of coherent heterodyne detection
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] 7.8 400 230,000 4.3 220 93,000 1.9 100 70,000 Si in barrier layer
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 ] 7.8 4.3 1.9 0.1 0 20 40 60 80 Time [ps]
Grating decay rate proportional to q 2 Dispersion shows no evidence of of spinspatial correlations at room temperature 0.12 0.10 0.08 D s =120 cm 2 /s γ (ps -1 ) 0.06 0.04 0.02 0.00 0 1 2 3 4 5 6 7 q 2 (x 10 8 cm -2 )
Grating decay rate vs. T (for different grating wavelengths) 10 0 γ (ps -1 ) 10-1 2.5 μ 3.5 μ 4.8 μ 14 μ 10-2 0 100 200 300 T (K)
Ballistic/diffusive crossover γ q 5 K q 295 K γ 2 q q
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 0.4 0.2 0.0 0 10 20 30 Time [ps]
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 0 5 10 0 5 10 0 5 10 Time (ps)
Spin diffusion coefficient 3 D s (1000 cm 2 /s) 2 1 n-gaas QW n=7.8 10 11 cm -2 0 0 50 100 150 200 250 300 T (K)
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
Comparison of spin and charge diffusion coefficients 6 D (1000 cm 2 /s) 5 4 3 2 1 D s /D c 0.4 0.2 0.0 0 100 200 T (K) 0 0 50 100 150 200 250 300 T (K)
Comparison of spin and charge diffusion coefficients 6000 1500 7.8 E11 cm -2 4.3 E11 1.9 E11 600 D (cm 2 /s) 4000 2000 D (cm 2 /s) 1000 500 D (cm 2 /s) 400 200 0 0 100 200 300 T (K) 0 0 100 200 300 T (K) 0 0 100 200 300 T (K)
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.
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
Spin drag resistance is large for high mobility 2DEG s ρ (kω) 1.5 1.0 0.5 ρ (scd theory) ρ c (measured) I. D Amico and G. Vignale, Phys. Rev. B 68, 45307 (2001) ρ depends only on n, T 0.0 0 100 200 300 T (K)
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
Direct comparison with theory 8 6 χ s > χ 0 D c 0 / D S 4 2 0 0 1 2 3 4 5 ρ / ρ 7.8 E11 cm -2 4.3 E11 1.9 E11 7.8 E11 (disordered)
Comparison of diffusion coefficients: no free parameters! 6000 1500 7.8 E11 cm -2 4.3 E11 1.9 E11 600 D (cm 2 /s) 4000 2000 D (cm 2 /s) 1000 500 D (cm 2 /s) 400 200 0 0 100 200 300 T (K) D s 0 0 100 200 300 T (K) = χ 0 c0 χ 1 + ρ / ρ s D 0 0 100 200 300 T (K)
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
L SO = 1.5 μm, independent of n, T 1.5 1.0 L = Dτ S s s 0.5 0.0 1.5 7.8 E11 cm -2 Spin relaxation rate (q=0) Diffusion coefficient L s (μ) 1.0 0.5 0.0 1.5 1.0 4.3 E11 γ (ps -1 ) 10-1 10-2 D (cm 2 /s) 10 3 10 2 0.5 1.9 E11 0.0 0 100 200 300 T (K) 0 100 200 300 T (K) 0 100 200 300 T (K)
L SO as a function of n,t L S = D γ S S 10-1 10 3 L s (μ) γ (ps -1 ) 10-2 D (cm 2 /s) 10 2 0 100 200 300 T (K) 0 100 200 300 T (K) 0 100 200 300 T (K)
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] 7.8 400 230,000 4.3 220 93,000 1.9 100 70,000 7.8 400 3,000
Disordered sample at 295 K 0.15 0.10 γ (ps -1 ) 0.05 0.00 0 2 4 6 8 10 q 2 (10 8 cm -2 )
Ballistic/diffusive crossover γ q 5 K q 295 K γ 2 q q
Anomalous q-dependence at low T 0.15 0.10 γ (ps -1 ) 0.05 0.00 0 2 4 6 8 10 q 2 (10 8 cm -2 )
2D dispersion in presence of spin-orbit, but with adjustable parameter: D Ω τ v 2 2 s SO s F
Conclusions Heterodyne transient grating technique successfully probes spin transport in ps time regime spin Coulomb drag observed Anomalous (non-diffusive) relaxation at low T