1. Research fueled by: JAIRO SINOVA Texas A&M University Institute of Physics ASCR Hitachi Cambridge Jörg Wunderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al Spin-injection Hall Effect: a new paradigm in using spin-orbit coupling to create a spin FET with pure spin-currents University of Utrecht Utrecht, January 8th 2010 SPIE conference Spintronics III August 1 st 2010 Sand Diego, CA

2. 2 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Technology motivation I. Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin- charge Dynamics iSHE FET Gating action of iSHEiSHE AND-gate with pure spin current Spin-injection Hall Effect: a new paradigm in using spin-orbit coupling to create a spin FET with pure spin-currents

3. 3 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Circuit heat generation is one key limiting factor for scaling device speed Industry has been successful in doubling of transistor numbers on a chip approximately every 18 months (Moore’s law). Although expected to continue for several decades several major challenges will need to be faced. The need for basic research in technology development

4. 4 Nanoelectronics, spintronics, and materials control by spin-orbit coupling International Technology Roadmap for Semiconductors Basic Research Inc. 1D systems Single electron systems (FETs) Spin dependent physics Ferromagnetic transport Molecular systems New materials Strongly correlated systems Nanoelectronics The need for basic research in technology development

5. 5 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-orbit coupling interaction (one of the few echoes of relativistic physics in the solid state) This gives an effective interaction with the electron’s magnetic moment Consequences Effective quantization axis of the spin depends on the momentum of the electron. Band structure (group velocities, scattering rates, etc.) mixed strongly in multi-band systems If treated as scattering the electron gets asymmetrically scattered to the left or to the right depending on its “spin” Classical explanation (in reality it is quantum mechanics + relativity ) “Impurity” potential V(r) Produces an electric field ∇V∇V B eff p s In the rest frame of an electron the electric field generates and effective magnetic field Motion of an electron

6. 6 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 (Dyakonov-Perel mechanism) Towards a realistic spin-based non-magnetic FET device

7. 7 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism). New paradigm using SO coupling: SO not so bad for dephasing 1) Can we use SO coupling to manipulate spin AND increase spin-coherence? Can we detect the spin in a non-destructive way electrically? 3) Can this effect be exploited to create a realistic spin-FET? Use the persistent spin-Helix state and control of SO coupling strength (Bernevig et al 06, Weber et al 07, Wünderlich et al 09) Use AHE to measure injected current polarization at the nano-scale electrically (Wünderlich, et al 09, 04) YES (Wünderlich, Irvin, JS, Jungwirth et al 2010)

8. VdVd VHVH 2DHG 2DEG VsVs 22 Hall measurement Device schematic – Hall measurement

9. 9 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

10. 10 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

11. 11 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

12. 12 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D electron gas with Rashba and Dresselhauss SO coupling a 2DEG is well described by the effective Hamiltonian: Something interesting occurs when spin along the [110] direction is conserved long lived precessing spin wave for spin perpendicular to [110] The nesting property of the Fermi surface: Bernevig et al PRL 06, Weber et al. PRL 07 Schliemann et al PRL 04 For our 2DEG system: Hence α ≈ -β

13. 13 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]

14. 14 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] _ _

15. Nanoelectronics, spintronics, and materials control by spin-orbit coupling 33 Persistent state spin helix verified by pump-probe experiments Similar wafer parameters to ours

16. 16 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 Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

17. 17 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Simple electrical measurement of out of plane magnetization InMnAs Spin dependent “force” deflects like-spin particles ρ H =R 0 B ┴ +4π R s M ┴ Understanding AHE in SIHE: AHE basics I _ F SO _ _ _ majority minority V

18. 18 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Cartoon of the mechanisms contributing to AHE independent of impurity density 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. Electrons deflect to the right or to the left as they are accelerated by an electric field ONLY because of the spin-orbit coupling in the periodic potential (electronics structure) E SO coupled quasiparticles Intrinsic deflection B 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) (Δso>ħ/τ)  ∝ λ* ∇ V imp (r) (Δso<ħ/τ) B Skew scattering Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering. ~σ~1/n i V imp (r) (Δso>ħ/τ)  ∝ λ* ∇ V imp (r) (Δso<ħ/τ) A

19. 19 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Contributions understood in simple metallic 2D models Semi-classical approach: Gauge invariant formulation Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07 Kubo microscopic approach: in agreement with semiclassical Borunda, Sinova, et al PRL 07, Nunner, JS, et al PRB 08 Non-Equilibrium Green’s Function (NEGF) microscopic approach Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08

20. 20 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 Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

21. 21 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

22. 22 Nanoelectronics, spintronics, and materials control by spin-orbit coupling SiHE: continuous shift of spin injection V H2 I VbVb V H1 ++ -- ++ -- ++ -- R[Ω] I ph [nA] Spin polarized charge current

23. 23 Nanoelectronics, spintronics, and materials control by spin-orbit coupling iSHE with spin-helix state B spin polarized charge current pure spin diffusive current: no particle current, no Joule heating generalized Boltzmann MC simulation

24. 24 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin Hall Transistor Manipulation 2  m long gate: reverse biased pn-junction Spin injector reverse biased pn-junction + light spot of 2  m diameter Detection Hall crosses 1 2

25. Nanoelectronics, spintronics, and materials control by spin-orbit coupling iSHE transistor: GATING Channel closed Channel opened Gating action of iSHE Spin polarized charge current Pure spin diffusive current

26. Nanoelectronics, spintronics, and materials control by spin-orbit coupling 2 Detectors and 1 Gate σ-σ-

27. 27 Nanoelectronics, spintronics, and materials control by spin-orbit coupling 2 Detectors and 2 Gates σ-σ-

28. Nanoelectronics, spintronics, and materials control by spin-orbit coupling SiHE AND spin logic gate charge current pure spin current: no particle current

29. 29 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Summary of spin-injection Hall effect  Basic studies of spin-charge dynamics and Hall effect in non-magnetic systems with SO coupling  Spin-photovoltaic cell: solid state polarimeter on a semiconductor chip requiring no magnetic elements, external magnetic field, or bias  SIHE-FET with pure spin currents in the active region  SiHE-AND gate

30. 30 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Next step.... Electrical injection through barrier from Fe Electrical detection by SIHE Schottky barrier: Kamil Olejnik (HCL, IOP Prague) MgO barrier: Sankara Rutala (CNRS, Thales, UPSUD, Orsay, France)

31. 31 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Allan MacDonald U of Texas Tomas Jungwirth Texas A&M U. Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Laurens Molenkamp Würzburg Xiong-Jun Liu Texas A&M U. Mario Borunda Texas A&M Univ. Harvard Univ. Nikolai Sinitsyn Texas A&M U. U. of Texas LANL Alexey Kovalev Texas A&M U. UCLA Liviu Zarbo Texas A&M Univ. Xin Liu Texas A&M U. Ewelina Hankiewicz (Texas A&M Univ.) Würzburg University Principal Collaborators Gerrit Bauer TU Delft Bryan Gallagher U. of Nottingham and many others

32. Nanoelectronics, spintronics, and materials control by spin-orbit coupling The Spin-Charge Drift-Diffusion Transport Equations 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) 34