Spin-injection Hall Effect: A New Frontier in Spintronics Hall Family

1. Spin-injection Hall Effect: a new member of the spintronics Hall family Nanoelectronics, spintronics, and materials control in multiband complex systems JAIRO SINOVA Texas A&M University Institute of Physics ASCR Hitachi Cambridge Joerg Wünderlich, A. Irvine, et al University of Texas Allan MacDonald, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al University of Würzburg Laurens Molenkamp, E. Hankiewiecz, et al University of Nottingham Bryan Gallagher, Richard Campion, et al. University of Texas December 3rd, 2009 Research fueled by:

2. Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling • Technology motivation • Control of material and transport properties through spin-orbit coupling: • Ferromagnetic semiconductors • Tunneling anisotropic magnetoresistance • Anomalous Hall effect and spin-dependent Hall effects • Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE • SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

3. The need for basic research in technology development 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. Circuit heat generation is one key limiting factor for scaling device speed Nanoelectronics, spintronics, and materials control by spin-orbit coupling

4. Nanoelectronics Research Initiative • Advanced Micro Devices, Inc. • IBM Corporation • Intel Corporation • MICRON Technology, Inc. • Texas Instruments Incorporated New materials Nanoelectronics Strongly correlated systems Single electron systems (FETs) 1D systems Basic Research Inc. Spin dependent physics MIND SWAN INDEX WIN Molecular systems Ferromagnetic transport The need for basic research in technology development International Technology Roadmap for Semiconductors Nanoelectronics, spintronics, and materials control by spin-orbit coupling

5. International Technology Roadmap for Semiconductors 2005: EMERGING RESEARCH DEVICES Nanoelectronics, spintronics, and materials control by spin-orbit coupling

6. Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling • Technology motivation • Control of material and transport properties through spin-orbit coupling: • Ferromagnetic semiconductors • Tunneling anisotropic magnetoresistance • Anomalous Hall effect and spin-dependent Hall effects • Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE • SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

7. 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) Nanoelectronics, spintronics, and materials control by spin-orbit coupling

8. Topological transport effects Nano-transport Magneto-transport New magnetic materials As Ga Spintronic Hall effects Caloritronics Mn Control of materials and transport properties via spin-orbit coupling Effects of spin-orbit coupling in multiband systems Nanoelectronics, spintronics, and materials control by spin-orbit coupling

9. Topological transport effects Nano-transport Ga Magneto-transport Ferromagnetic Semiconductors Mn Spintronic Hall effects Caloritronics As Need true FSs not FM inclusions in SCs Mn GaAs - standard III-V semiconductor + Group-II Mn - dilute magnetic moments & holes (Ga,Mn)As - ferromagnetic semiconductor Control of materials and transport properties via spin-orbit coupling Effects of spin-orbit coupling in multiband systems Nanoelectronics, spintronics, and materials control by spin-orbit coupling

10. Topological transport effects Nano-transport Magneto-transport Ga New magnetic materials As EF Ga Spintronic Hall effects Transition to a ferromagnet when Mn concentration > 1.5-2 % Mn Caloritronics Mn As spin ↓ >2% Mn Mn DOS spin ↑ ferromagnetism onset near MIT when localization length is longer than Mn-Mn spacing. Zener type model valence band As-p-like holes Control of materials and transport properties via spin-orbit coupling Jungwirth, Sinova, et al RMP 06 Effects of spin-orbit coupling in multiband systems Nanoelectronics, spintronics, and materials control by spin-orbit coupling

11. Topological transport effects Nano-transport Magneto-transport Ga Ga New magnetic materials py As EF Ga Spintronic Hall effects p Transition to a ferromagnet when Mn concentration increases Mn Caloritronics Ferromagnetic Ga1-xMnxAs x>1.5% s Mn Mn As As ∇V spin ↓ >2% Mn Hso Mn px Mn • Ferromagnetism mediated by delocalized band states: • polarized carriers with large spin-orbit coupling DOS • Many useful properties • FM dependence on doping • Low saturation magnetization spin ↑ ferromagnetism onset near MIT when localization length is longer than Mn-Mn spacing. Zener type model valence band As-p-like holes Control of materials and transport properties via spin-orbit coupling Effects of spin-orbit coupling in multiband systems What are the consequences of the strong spin-orbit coupling of the carriers “gluing” the localized Mn moments ? Nanoelectronics, spintronics, and materials control by spin-orbit coupling

12. → Topological transport effects → Nano-transport Magneto-transport Ga New magnetic materials py As Ga Spintronic Hall effects p Control of magnetic anisotropy M M Caloritronics Ferromagnetic Ga1-xMnxAs x>1.5% s Mn Mn As ∇V Hso Mn px • Ferromagnetism mediated by delocalized band states: • polarized carriers with large spin-orbit coupling Strain & SO ↓ • Many useful properties • FM dependence on doping • Low saturation magnetization Strain induces changes in the band structure and, in turn, change the ferromagnetic easy axis. Piezoelectric devices: fast magnetization switching Wunderlich, Sinova, et al PRB 06 What are the consequences of the strong spin-orbit coupling of the carriers “gluing” the localized Mn moments ? Tensile strain Compressive strain Control of materials and transport properties via spin-orbit coupling Effects of spin-orbit coupling in multiband systems Effects of spin-orbit coupling in multiband systems Nanoelectronics, spintronics, and materials control by spin-orbit coupling

13. Topological transport effects G(T)MR Nano-transport Magneto-transport New magnetic materials As Ga Spintronic Hall effects ~ 100% MR effect Magneto-transport in GaMnAs Caloritronics Mn Control of materials and transport properties via spin-orbit coupling Effects of spin-orbit coupling in multiband systems Fert, Grunberg et al. 1988 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

14. Topological transport effects G(T)MR Nano-transport Magneto-transport New magnetic materials As Ga Spintronic Hall effects ~ 100% MR effect Magneto-transport in GaMnAs Caloritronics Mn Effects of spin-orbit coupling in multiband systems Exchange split bands: σ~ TDOS(↑↓) < TDOS(↑↑) Control of materials and transport properties via spin-orbit coupling Fert, Grunberg et al. 1988 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

15. TMR Au Topological transport effects Nano-transport Magneto-transport New magnetic materials As → Tunneling Anisotropic Magnetoresistance Ga Spintronic Hall effects ~ 100% MR effect Magneto-transport in GaMnAs Caloritronics σ ~ TDOS (M) Mn TAMR Effects of spin-orbit coupling in multiband systems discovered in (Ga,Mn)As Gold et al. PRL’04 Exchange split bands: σ~ TDOS(↑↓) < TDOS(↑↑) TAMR can be enormous depending on doping Now discovered in FM metals !! Control of materials and transport properties via spin-orbit coupling Ruster, JS, et al PRL05 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

16. Topological transport effects Au Nano-transport Magneto-transport New magnetic materials As → Tunneling Anisotropic Magnetoresistance Ga Spintronic Hall effects Magneto-transport in GaMnAs Caloritronics σ ~ TDOS (M) Mn TAMR Effects of spin-orbit coupling in multiband systems discovered in (Ga,Mn)As Gold et al. PRL’04 TAMR can be enormous depending on doping Ruster, JS, et al PRL05 Now discovered in FM metals !! Control of materials and transport properties via spin-orbit coupling Nanoelectronics, spintronics, and materials control by spin-orbit coupling

17. Topological transport effects Nano-transport Magneto-transport New magnetic materials As Ga Spintronic Hall effects Caloritronics Mn Effects of spin-orbit coupling in multiband systems Control of materials and transport properties via spin-orbit coupling Nanoelectronics, spintronics, and materials control by spin-orbit coupling

18. Topological transport effects Nano-transport Magneto-transport New magnetic materials As majority Ga Spintronic Hall effects Caloritronics Mn Anomalous Hall effects Effects of spin-orbit coupling in multiband systems FSO FSO I V minority Nagaosa, Sinova, Onoda, MacDonald, Ong, RMP 10 Control of materials and transport properties via spin-orbit coupling Nanoelectronics, spintronics, and materials control by spin-orbit coupling

19. majority _ _ _ FSO _ FSO I minority InMnAs V Anomalous Hall Effect: the basics Spin dependent “force” deflectslike-spin particles ρH=R0B ┴ +4π RsM┴ Simple electrical measurement of out of plane magnetization Nanoelectronics, spintronics, and materials control by spin-orbit coupling

20. Skew scattering independent of impurity density Vimp(r) (Δso>ħ/τ)or ∝ λ*∇Vimp(r) (Δso<ħ/τ) A ~σ~1/ni Intrinsic deflection B B Side jump scattering E Vimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ) 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) Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering. 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. SO coupled quasiparticles 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. Cartoon of the mechanisms contributing to AHE Nanoelectronics, spintronics, and materials control by spin-orbit coupling

21. Contributions understood in simple metallic 2D models 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 Semi-classical approach: Gauge invariant formulation Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08 Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

22. A high conductivity regime for σxx>106 (Ωcm)-1 in which AHE is skew dominated • A good metal regime for σxx ~104-106 (Ωcm) -1 in which σxyAH~ const • A bad metal/hopping regime for σxx<104 (Ωcm) -1 for which σxyAH~ σxyα with α>1 Skew dominated regime Scattering independent regime Q: is the scattering independent regime dominated by the intrinsic AHE? Phenomenological scaling regimes of AHE Review of AHE (to appear in RMP 2010), Nagaosa, Sinova, Onoda, MacDonald, Ong Nanoelectronics, spintronics, and materials control by spin-orbit coupling

23. n, q AHE in GaMnAs • DMS systems(Jungwirth et al PRL 2002, Jungwirth, Sinova, et al APL 03) • layered 2D ferromagnets e.g. SrRuO3 ferromagnets • (Taguchi et al, Science 01, Fang et al, Science 03) • CuCrSeBr compounds ( Lee et al, Science 04) • Fe(Yao et al PRL 04) n’≠n, q AHE in Fe Experiment: σAH ∼ 1000 (Ω cm)-1 Theory: σAH ∼ 750 (Ω cm)-1 Intrinsic AHE approach in comparing to experiment: phenomenological “proof” Nanoelectronics, spintronics, and materials control by spin-orbit coupling

24. V Anomalous Hall Effect Mesoscopic Spin Hall Effect Inverse SHE Spin Hall Effect Spin-injection Hall Effect majority _ _ _ _ _ FSO _ FSO FSO I FSO I minority V V Intrinsic Kato et al Science 03 Wunderlich, Kaestner, Sinova, Jungwirth PRL 04 Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Extrinsic Intrinsic Brune,Roth, Hankiewicz, Sinova, Molenkamp, et al 09 Valenzuela et al Nature 06 Anomalous Hall effect: more than meets the eye Nanoelectronics, spintronics, and materials control by spin-orbit coupling

25. Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling • Technology motivation • Control of material and transport properties through spin-orbit coupling: • Ferromagnetic semiconductors • Tunneling anisotropic magnetoresistance • Anomalous Hall effect and spin-dependent Hall effects • Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE • SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

26. Towards a realistic spin-based non-magnetic FET device 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) Nanoelectronics, spintronics, and materials control by spin-orbit coupling

27. 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) New paradigm using SO coupling: SO not so bad for dephasing 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). • Can we use SO coupling to manipulate spin AND increase spin-coherence? • Can we detect the spin in a non-destructive way electrically? Nanoelectronics, spintronics, and materials control by spin-orbit coupling

28. Device schematic - material p 2DHG i n

29. - Device schematic - trench p 2DHG i n

30. Device schematic – n-etch p i 2DHG n 2DEG

31. Vd Vs Device schematic – Hall measurement VH 2DHG 2DEG 22

32. e Vd e e h e e e h h h h h Vs VH 2DHG 2DEG Spin-injection Hall effect device schematics Nanoelectronics, spintronics, and materials control by spin-orbit coupling

33. VL Spin-injection Hall device measurements trans. signal σo σ- σ+ σo Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

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

36. An exact SU(2) symmetry The long lived spin-excitation: “spin-helix” • Finite wave-vector spin components • Shifting property essential Only Sz, zero wavevector U(1) symmetry previously known: J. Schliemann, J. C. Egues, and D. Loss, Phys. Rev. Lett. 90,146801 (2003). K. C. Hall et. al., Appl. Phys. Lett 83, 2937 (2003). 30 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

37. _ _ _ ky [010] ky [010] ky [010] α = -β α = 0, β < 0 [110] [110] α > 0, β = 0 [110] [110] [110] [110] kx [100] kx [100] kx [100] Effects of Rashba and Dresselhaus SO coupling Nanoelectronics, spintronics, and materials control by spin-orbit coupling

38. _ _ [110] [110] 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] Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

40. 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 Sx+ and Sz: For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004); Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004) 34 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

41. Spin-helix state when α ≠ β Spatial variation scale consistent with the one observed in SIHE Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

42. AHE contribution to Spin-injection Hall effect • Two types of contributions: • S.O. from band structure interacting with the field (external and internal) • Bloch electrons interacting with S.O. part of the disorder 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 Lower bound estimate of skew scatt. contribution Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

43. 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 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

44. Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling • Role of basic research in technology development • Control of material and transport properties through spin-orbit coupling: • Ferromagnetic semiconductors • Tunneling anisotropic magnetoresistance • Anomalous Hall effect and spin-dependent Hall effects • Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE • SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

46. Non public slides deleted. Please contact Sinova if interested Nanoelectronics, spintronics, and materials control by spin-orbit coupling

47. Non public slides deleted. Please contact Sinova if interested Nanoelectronics, spintronics, and materials control by spin-orbit coupling

48. 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 (μm). • Less computationally intensive than other methods (e.g. NEGF). Nanoelectronics, spintronics, and materials control by spin-orbit coupling

49. 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. Single Particle Monte Carlo Nanoelectronics, spintronics, and materials control by spin-orbit coupling

50. Effects of B field: current set-up Out-of plane magnetic field In-Plane magnetic field Nanoelectronics, spintronics, and materials control by spin-orbit coupling