1. Spin Injection Hall Effect: a new member of the spintronic Hall family and its implications in nano-spintronics Research fueled by: Optical Spintronics Meeting Hitachi-Cambridge, October 27 th, 2009 JAIRO SINOVA Texas A&M University Institute of Physics ASCR Hitachi Cambridge Joerg Wunderlich, X. Xu, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al Texas A&M L. Zarbo

2. 2 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system? Long standing paradigm: Datta-Das FET Unfortunately it has not worked : no reliable detection of spin-polarization in a diagonal transport configuration No long spin-coherence in a Rashba spin-orbit coupled system Towards a REALISTIC spin-based non-magnetic FET device

3. Ohno et al. Nature’99, others Crooker et al. JAP’07, others  Magneto-optical imaging  non-destructive  lacks nano-scale resolution and only an optical lab tool  MR Ferromagnet  electrical  destructive and requires semiconductor/magnet hybrid design & B-field to orient the FM  spin-LED  all-semiconductor  destructive and requires further conversion of emitted light to electrical signal Spin detection in semiconductors

4. 4 SHE B=0 charge current gives spin current Optical detection SHE -1 B=0 spin current gives charge current Electrical detection j s ––––––––––– + + + + + iSHE I _ F SO _ _ _ majority minority V The family of spintronic Hall effects AHE B=0 polarized charge current gives charge-spin current Electrical detection

5. J. Wunderlich, B. Kaestner, J. Sinova and T. Jungwirth, Phys. Rev. Lett. 94 047204 (2005) Spin-Hall Effect 5 B. Kaestner, et al, JPL 02; B. Kaestner, et al Microelec. J. 03; Xiulai Xu, et al APL 04, Wunderlich et al PRL 05 Proposed experiment/device: Coplanar photocell in reverse bias with Hall probes along the 2DEG channel Borunda, Wunderlich, Jungwirth, Sinova et al PRL 07 Utilize technology developed to detect SHE in 2DHG and measure polarization via Hall probes

6. i p n 2DHG Device schematics: materials

7. - 2DHG i p n Device schematics: trench

8. i p n 2DHG 2DEG Device schematics: n-etch

9. VdVd VHVH 2DHG 2DEG VsVs 9 Device schematics: materials

10. 2DHG 2DEG e h e e ee e h h h h h VsVs VdVd VHVH 10 Device schematics: SIHE measurement

11. 11 Nanoelectronics, spintronics, and materials control by spin-orbit coupling 2DHG 2DEG e h e e ee e h h h h h VsVs VdVd VHVH Spin-injection Hall effect device schematics

12. 12 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-injection Hall device measurements trans. signal σoσoσoσo σ+σ+σ+σ+ σ-σ-σ-σ- σoσoσoσo VLVL

13. 13 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-injection Hall device measurements trans. signal σoσoσoσo σ+σ+σ+σ+ σ-σ-σ-σ- σoσoσoσo VLVL SIHE ↔ Anomalous Hall Local Hall voltage changes sign and magnitude along a channel of 6 μm

14. and high temperature operation Zero bias- + + -- + + -- 14 Persistent Spin injection Hall effect

15. 15 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D electron gas with Rashba and Dresselhauss SO coupling The 2DEG is well described by the effective Hamiltonian: Hence For our 2DEG system:

16. 16 Nanoelectronics, spintronics, and materials control by spin-orbit coupling What is special about α≈β spin along the [110] direction is conserved long lived precessing spin wave for spin perpendicular to [110] The nesting property of the Fermi surface:

17. 17 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Effects of Rashba and Dresselhaus SO coupling  = -  [110] _ k y [010] k x [100]  > 0,  = 0 [110] _ k y [010] k x [100]  = 0,  < 0 [110] _ k y [010] k x [100]

18. 18 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D systems with Rashba and Dresselhauss SO coupling For the same distance traveled along [1-10], the spin precesses by exactly the same angle. [110] _ _

19. 19 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Similar wafer parameters to ours Persistent state spin helix verified by pump-probe experiments Weber et al. PRL 07

20. For arbitrary α, β spin-charge transport equation is obtained for diffusive regime For propagation on [1-10], the equations decouple in two blocks. Focus on the one coupling S x+ and S z : For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004); Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004) 20 The Spin-Charge Drift-Diffusion Transport Equations

21. 21 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spatial variation scale consistent with the one observed in SIHE Spin-helix state when α ≠ β

22. 22 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Simple electrical measurement of out of plane magnetization InMnAs I F SO majority minority V Spin dependent “force” deflects like-spin particles ρ H =R 0 B ┴ +4π R s M ┴ Understanding the Hall signal in SIHE: Anomalous Hall Effect

23. 23 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Anomalous Hall effect (scaling with ρ ) 37 Dyck et al PRB 2005 Material with dominant skew scattering mechanism Material with dominant scattering-independent mechanism Ohio State University 20096 GaMnAs Kotzler and Gil PRB 2005 Co films Edmonds et al APL 2003

24. 24 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Intrinsic deflection Electrons have an “anomalous” velocity perpendicular to the electric field related to their Berry’s phase curvature which is nonzero when they have spin-orbit coupling. ~τ 0 or independent of impurity density Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump. independent of impurity density Side jump scattering V imp (r) Skew scattering Asymmetric scattering due to the SO coupling of the electron or the impurity. Known as Mott scattering. ~1/n i V imp (r) Electrons deflect to the right or left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential E SO coupled quasiparticles STRONG SPIN-ORBIT COUPLED REGIME (Δ so >ħ/τ)

25. 25 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Side jump scattering from SO disorder Electrons deflect first to one side due to the field created by the impurity and deflect back when they leave the impurity since the field is opposite resulting in a side step. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump. independent of impurity density The terms/contributions dominant in the strong SO couple regime are strongly reduced (quasiparticles not well defined due to strong disorder broadening). Other terms, originating from the interaction of the quasiparticles with the SO-coupled part of the disorder potential dominate. Better understood than the strongly SO couple regime WEAK SPIN-ORBIT COUPLED REGIME (Δ so <ħ/τ) Skew scattering from SO disorder ~1/n i

26. 26 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Type (i) contribution much smaller in the weak SO coupled regime where the SO- coupled bands are not resolved, dominant contribution from type (ii) Crepieux et al PRB 01 Nozier et al J. Phys. 79 Two types of contributions: i)S.O. from band structure interacting with the field (external and internal) Bloch electrons interacting with S.O. part of the disorder Lower bound estimate of skew scatt. contribution AHE contribution to Spin-injection Hall effect

27. 27 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Local spin-polarization → calculation of AHE signal Weak SO coupling regime → extrinsic skew-scattering term is dominant Lower bound estimate Spin-injection Hall effect: theoretical expectations

28. 28 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Further experimental tests of the observed SIHE

29. S. Datta, B. Das, Appl. Phys. Lett. 56 665 (1990). … works only - if channel is 1dimensional - or under Spin Helix conditions for 2D channel Comment 1: Datta-Das type device

30. SIHE Field Effect Transistor

31. 31 Nanoelectronics, spintronics, and materials control by spin-orbit coupling SHE -1 B=0 spin current gives charge current Electrical detection AHE B=0 polarized charge current gives charge-spin current Electrical detection SHE B=0 charge current gives spin current Optical detection SIHE B=0 Optical injected polarized current gives charge current Electrical detection The spintronic Hall family

32. 32 - electrical detection method for Spin current - large signal (comparable to AHE in metallic ferromagnets) - high spatial resolution (~ < 50nm) - nondestructive detection of spin WITHOUT magnetic elements - linear with degree of spin polarization - high temperature operation - first electrical detection of the Spin Helix (coherently precessing spins) - all electrical polarimeter (transfers degree of light polarization into an electrical signal) SUMMARY

33. Drift-Diffusion eqs. with magnetic field perpendicular to 110 and time varying spin-injection Spin Currents 2009 σ + (t) B Similar to steady state B=0 case, solve above equations with appropriate boundary conditions: resonant behavior around ω L and small shift of oscillation period Jing Wang, Rundong Li, SC Zhang, et al

34. Semiclassical Monte Carlo of SIHE Numerical solution of Boltzmann equation Spin-independent scattering: Spin-dependent scattering: phonons, remote impurities, interface roughness, etc. side-jump, skew scattering. AHE Realistic system sizes (  m). Less computationally intensive than other methods (e.g. NEGF). Spin Currents 2009

35. Single Particle Monte Carlo Spin Currents 2009 Spin-Dependent Semiclassical Monte Carlo  Temperature effects, disorder, nonlinear effects, transient regimes.  Transparent inclusion of relevant microscopic mechanisms affecting spin transport (impurities, phonons, AHE contributions, etc.).  Less computationally intensive than other methods(NEGF).  Realistic size devices.

36. Effects of B field: current set-up Spin Currents 2009 In-Plane magnetic field Out-of plane magnetic field