Spin-Hall field effect transistors

1. SemiSpinNet Spin-Hall field effect transistors University of Nottingham Tomas Jungwirth, Richard Campion, et al. Hitachi Cambridge Joerg Wünderlich, Andrew Irvine, et al Institute of Physics ASCR Kamil Olejnik, Tomas Jungwirth, Vít Novák, et al ASRC Workshop on Magnetic Materials and Nanostructures Tokai, Japan January 10th, 2012 Vivek Amin, JAIRO SINOVA Texas A&M University Institute of Physics ASCR Research fueled by:

2. spin-Hall field effect transistors • Optical injection spin-Hall FET • Spin based FET: old and new paradigm in charge-spin transport • Theory expectations and modeling • Experimental results • Spin-current AND-gate • Spin Hall and non-local spin valve detection of electrically injected and manipulated spins: • Spin amplifier and modulator • non-local spin accumulation measurements • Device and key issues • Modeling • Summary Nanoelectronics, spintronics, and materials control by spin-orbit coupling

3. This gives an effective interaction with the electron’s magnetic moment Classical explanation (in reality it is quantum mechanics + relativity ) p Produces an electric field In the rest frame of an electron the electric field generates and effective magnetic field s • “Impurity” potential V(r) • Motion of an electron ∇V Beff • 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” Spin-orbit coupling interaction (one of the few echoes of relativistic physics in the solid state)

4. Use the persistent spin-Helix state or quasi-1D-spin channels and control of SO coupling strength (Bernevig et al 06, Weber et al 07, Wünderlich et al 09, Zarbo et al 10) Use AHE to measure injected current polarization electrically (Wünderlich, et al Nature Physics. 09, PRL 04) Spin-Hall AND-gate device (Wünderlich, Jungwirth, et al Science 2010) From DD-FET to new paradigm using SO 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). DD-FET • 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 spin-FET logic device?

5. α > 0, β = 0 _ _ ky [010] Something interesting occurs when [110] For our 2DEG system: [110] α = 0, β < 0 [110] Hence α ≈ -β [110] kx [100] Spin-dynamics in 2D electron gas with Rashba and Dresselhauss SO coupling • Can we use SO coupling to manipulate spin AND increase spin-coherence? a 2DEG is well described by the effective Hamiltonian:

6. Use the persistent spin-Helix state or 1D-spin channels and control of SO coupling strength ✓ Use AHE to measure injected current polarization electrically ✓ Spin-injection Hall effect: theoretical expectations Local spin-polarization → calculation of AHE signal Weak SO coupling regime → extrinsic skew-scattering term is dominant Lower bound estimate • Can we use SO coupling to manipulate spin AND increase spin-coherence? • Can we detect the spin in a non-destructive way electrically?

7. SIHE ↔ Anomalous Hall VL Spin-injection Hall device measurements trans. signal σo σ- σ+ σo Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

8. T = 250K Further experimental tests of the observed SIHE

9. x Vb I VH1 VH1 VH2 Vb VH2 Spin injection Hall effect SiHE (a) x inverse SHE (b) Wunderlich, et al, Science 2010

10. SHE transistor AND gate Spin-FET with two gates → logic AND function Wunderlich et al., Science.‘10

11. spin-Hall field effect transistors • Optical injection spin-helix and spin-Hall FET • Spin based FET: old and new paradigm in charge-spin transport • Theory expectations and modeling • Experimental results • Spin-current AND-gate • Spin Hall and non-local spin valve detection of electrically injected and manipulated spins: • Spin amplifier and modulator • non-local spin accumulation measurements • Device and key issues • Modeling • Summary Nanoelectronics, spintronics, and materials control by spin-orbit coupling

12. ID Electrical injection, manipulation, and detection of spins in semiconductors Electrical injection spin-amplifier (modulator) in Fe/GaAs(3D) detection of spin polarization by FM detection of spin current by iSHE injection from a FM FM FM – + electrical manipulation of the spin profile by a drift current Huang et al 07 FM FM – +

13. VNL ID IB VSH Au Au Fe Fe n-GaAs Experimental device set-up Note: ID reminiscent of base current in the bipolar transistor amplifier IB↔ emitter current detected spin polarization (current) ↔ collector current

14. Electrical injection of a diffusive spin current from FM into a non-magnetic metal Electrical non-local spin valve detection by FM and by iSHE iSHE NL spin detection Valenzuela, S. O. & Tinkham, M, Nature‘06

15. z Bz y x Electrical injection of a diffusive spin current from FM into a non-magnetic metal Electrical non-local spin valve detection by FM and by iSHE NL spin detection iSHE Valenzuela, S. O. & Tinkham, M, Nature‘06

16. Electrical injection of a diffusive spin current from FM into a non-magnetic semiconductors Electrical non-local spin valve detection by FM and by iSHE very high-resitive spin-dependent tunnel contact ↓ low-resistive FM metal high-resitive semiconducor Fe/n-GaAs Schottky tunnel contacts Lou et al. Nature Phys.’07, Ciorga et al. PRB 09, Awo-Affouda et al. APL 09, Salis et al. PRB 09

17. Electrical injection of a diffusive spin current from FM into a non-magnetic semiconductors Electrical non-local spin valve detection by FM and by iSHE ... and by iSHE ? very high-resitive spin-dependent tunnel contact ↓ low-resistive FM metal high-resitive semiconducor Fe/n-GaAs Schottky tunnel contacts Lou et al. Nature Phys.’07, Ciorga et al. PRB 09, Awo-Affouda et al. APL 09, Salis et al. PRB 09

18. z z Bz y y x x Key is to experimentally remove the strong ordinary Hall effect in SCs Al Fe n-GaAs

19. z z y y x x Key is to experimentally remove the strong ordinary Hall effect in SCs Hanle + iSHE Al Fe n-GaAs BX

20. Epitaxial 2 nm Fe on n-GaAs grown in one MBE → large [110]/[1-10] in-plane anisotropy z y x BX x Baniso ≈ 200 mT >> BHanle≈ 50 mT

21. z y x Plus we know when each Fe electrode switches for a given φB B

22. z y x Hanle iSHE (ordinary Hall) iSHE BX x

23. Hard-axis Hanle NL spin-valve Hanle iSHE Easy-axis switching NL spin-valve

24. z z Bz y y x x Hanle curves affected by nuclear fields Bz,aniso ≈ 2 T Nuclear (Overhauser) field: Bx,aniso ≈ 200 mT BX

25. Hanle curves affected by nuclear fields

26. iSHE reverses sign upon reversing spin-current

27. Electrical spin modulator Bx=0

28. Bx=0 Drift-diffusion equations 1. sycontinuousat x=0 2. independent of vd(x)

29. Bx=0 Drift velocities Diffusion constant Spin lifetime Overall magnitude ( source term )

30. Experiment Theory

31. SHE analysis from calibrated spin-current Spin current Hall sensitivity function for a finite-size cross iSHE voltage (~ skew scattering Hall angle in GaAs)

32. Experiment Theory

33. Experiment Theory Theory - experiment comparison Summary of theory • DD-equation with non-constant vd analysis • Spin-lifetime from out of plane Hanle • Fit of DD to NL yields polarization at injection FM electrode • Use this injected spin-current estimate to calculate predicted spin Hall angle (because of geometry one needs to calculate the sensitivity function for the Hall cross bar). skew scattering Hall angle in GaAs:

34. Summary of spin-injection Hall FET optical-spin-injection Hall FET • 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 can be tuned electrically by external gate (e.g. Fe/Ga(Mn)As structures) all electrical Hall FET • Spin amplifier-modulator based on drift current • iSHE and NL in semiconductor device • Strongest theory-experiment comparison to date in SC