1. Research fueled by: Ohio State University February 9 th, 2010 JAIRO SINOVA Texas A&M University Institute of Physics ASCR Exploiting the echoes of special relativity in condensed matter: new paradigms in spin-charge coupled physics Hitachi Cambridge Joerg W ü nderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al University of W ü rzburg Laurens Molenkamp, E. Hankiewiecz, et al University of Nottingham Bryan Gallagher, Richard Campion, et al.

2. 2 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Introduction: using the dual personality of the electron Electronics, ferromagnetism, and spintronics Internal coupling of charge and spin: origin and present use Motivation: ICT, energy consumption, roadblocks II. Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors: magnetic anisotropy control Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effect: a new paradigm in exploiting SO couplingSpin based FET: old and new paradigm in charge-spin transport Theory expectations and modeling Experimental results New experimental results, further checks, outlook Exploiting the echoes of special relativity in condensed matter: new paradigms in spin-charge coupled physics

3. 3 Nanoelectronics, spintronics, and materials control by spin-orbit coupling The electron: the key character with dual personalitiesCHARGE Easy to manipulate: Coulomb interaction SPIN 1/2 Makes the electron antisocial: a fermion quantum mechanics E=p 2 /2m E→ iħ d/dt p→ -iħ d/dr “Classical” external manipulation of charge & spin special relativity E 2 /c 2 =p 2 +m 2 c 2 (E=mc 2 for p=0) + particles/antiparticles & spin Dirac equation =

4. 4 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Using charge and spin in information technology HIGH tunablity of electronic transport properties the key to FET success in processing technology substrate semiconductor insulator SD gate Vg >0 Using charge to create a field effect transistor: work horse of information processing Using spin: Pauli exclusion principle and Coulomb repulsion →ferromagnetism work horse of information storage total wf antisymmetric = orbital wf antisymmetric × spin wf symmetric (aligned) Robust (can be as strong as bonding in solids) Robust (can be as strong as bonding in solids) Strong coupling to magnetic field Strong coupling to magnetic field (weak fields = anisotropy fields needed (weak fields = anisotropy fields needed only to reorient macroscopic moment) only to reorient macroscopic moment) e-e-e-e- What about the internal communication between charge & spin? (spintronics)

5. 5 e-e-e-e- Nanoelectronics, spintronics, and materials control by spin-orbit coupling Internal communication between spin and charge: 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 Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit) “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 an effective magnetic field Motion of an electron

6. 6 e-e-e-e- Nanoelectronics, spintronics, and materials control by spin-orbit coupling (one of the few echoes of relativistic physics in the solid state) This gives an effective interaction with the electron’s magnetic moment Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit) “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 an effective magnetic field Motion of an electron Consequence #1 Internal communication between spin and charge:spin- orbit coupling interaction

7. 7 e-e-e-e- Nanoelectronics, spintronics, and materials control by spin-orbit coupling (one of the few echoes of relativistic physics in the solid state) This gives an effective interaction with the electron’s magnetic moment Classical explanation (in reality it arises from a second order expansion of Dirac equation around the non-relativistic limit) “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 an effective magnetic field Motion of an electron Consequence #2 Mott scattering Internal communication between spin and charge:spin- orbit coupling interaction

8. 8 Nanoelectronics, spintronics, and materials control by spin-orbit coupling How spintronics has impacted your life: Metallic spintronics Appreciable sensitivity, simple design, cheap BUT only a 2-8 % effect Anisotropic magnetoresistance (AMR): In ferromagnets the current is sensitive to the relative direction of magnetization and current direction 1992 - dawn of (metallic) spintronics e-e-e-e- current magnetization Fert, Grünberg et al. 1998 Giant magnetoresistance (GMR) read head - 1997 High sensitivity, very large effect 30-100% ↑↑ and ↑↓ are almost on and off states: “1” and “0” & magnetic → memory bit Nobel Price 2007 Fert and Grünberg e-e-e-e- ×

9. 9 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. What next? The need for basic research

10. 10 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Information and communication technology power consumption HAS consequences Relative electricity consumption of ICT equipment

11. 11 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 Nanoelectronics Research Initiative SWAN MIND INDEX WIN Advanced Micro Devices, Inc. IBM Corporation Intel Corporationation MICRON Technology, Inc.MICRON Te Texas Instruments Incorporatedexas Instruments Advanced Micro Devices, Inc. IBM Corporation Intel Corporationation MICRON Technology, Inc.MICRON Te Texas Instruments Incorporatedexas Instruments

12. 12 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Introduction: using the dual personality of the electron Electronics, ferromagnetism, and spintronics Internal coupling of charge and spin: origin and present use Motivation: ICT, energy consumption, roadblocks II. Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors: magnetic anisotropy control Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effect: a new paradigm in exploiting SO couplingSpin based FET: old and new paradigm in charge-spin transport Theory expectations and modeling Experimental results New experimental results, further checks, outlook Exploiting the echoes of special relativity in condensed matter: new paradigms in spin-charge coupled physics

13. 13 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Control of materials and transport properties via spin-orbit couplingAs Ga Mn New magnetic materials Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems

14. 14 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems Ferromagnetic Semiconductors Need true FSs not FM inclusions in SCs Mn Ga As 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

15. 15 Nanoelectronics, spintronics, and materials control by spin-orbit coupling As Ga Mn New magnetic materials Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems Transition to a ferromagnet when Mn concentration > 1.5-2 % DOS spin ↓ spin ↑ valence band As-p-like holes Control of materials and transport properties via spin-orbit coupling Jungwirth, Sinova, et al RMP 06 Mn Ga As Mn >2% Mn EFEF ferromagnetism onset near MIT when localization length is longer than Mn-Mn spacing. Zener type model Energy

16. 16 Nanoelectronics, spintronics, and materials control by spin-orbit coupling As Ga Mn New magnetic materials Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems Transition to a ferromagnet when Mn concentration increases DOS spin ↓ spin ↑ valence band As-p-like holes Mn Ga As Mn >2% Mn EFEF ferromagnetism onset near MIT when localization length is longer than Mn-Mn spacing. Zener type model Mn Ga As Mn Ferromagnetic Ga 1-x Mn x As x>1.5% Ferromagnetism mediated by delocalized band states: polarized carriers with large spin-orbit coupling pxpx pypy ∇V∇V H so p s Many useful properties FM dependence on doping Low saturation magnetization What are the consequences of the strong spin-orbit coupling of the carriers “gluing” the localized Mn moments ? Control of materials and transport properties via spin-orbit coupling

17. 17 Effects of spin-orbit coupling in multiband systems Nanoelectronics, spintronics, and materials control by spin-orbit coupling As Ga Mn New magnetic materials Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems Mn Ga As Mn Ferromagnetic Ga 1-x Mn x As x>1.5% Ferromagnetism mediated by delocalized band states: polarized carriers with large spin-orbit coupling pxpx pypy ∇V∇V H so p s What are the consequences of the strong spin-orbit coupling of the carriers “gluing” the localized Mn moments ? Many useful properties FM dependence on doping Low saturation magnetization Control of magnetic anisotropy Strain & SO ↓ Strain induces changes in the band structure and, in turn, changes the ferromagnetic easy axis. Piezoelectric devices: fast magnetization switching Wunderlich, JS, et al PRB 06 Tensile strainCompressive strain M → M → Control of materials and transport properties via spin-orbit coupling

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

19. 19 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Simple electrical measurement of out of plane magnetization (or spin polarization ~ n ↑ -n ↓ ) InMnAs Spin dependent “force” deflects like-spin particles ρ H =R 0 B ┴ +4π R s M ┴ Anomalous Hall Effect: the basics I _ F SO _ _ _ majority minority V M⊥M⊥ AHE is does NOT originate from any internal magnetic field created by M ⊥ ; the field would have to be of the order of 100T!!!

20. 20 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

21. 21 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

22. 22 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Valenzuela et al Nature 06 Inverse SHE Anomalous Hall effect: more than meets the eye Wunderlich, Kaestner, Sinova, Jungwirth PRL 04 Kato et al Science 03 Intrinsic Extrinsic V Mesoscopic Spin Hall Effect Intrinsic Brune,Roth, Hankiewicz, Sinova, Molenkamp, et al 09 Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Spin-injection Hall Effect Anomalous Hall Effect I _ FSOFSO FSOFSO _ _ majority minority V Spin Hall Effect I _ FSOFSO FSOFSO _ _ V

23. 23 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Introduction: using the dual personality of the electron Electronics, ferromagnetism, and spintronics Internal coupling of charge and spin: origin and present use Motivation: ICT, energy consumption, roadblocks II. Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors: magnetic anisotropy control Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effect: a new paradigm in exploiting SO couplingSpin based FET: old and new paradigm in charge-spin transport Theory expectations and modeling Experimental results New experimental results, further checks, outlook Exploiting the echoes of special relativity in condensed matter: new paradigms in spin-charge coupled physics

24. 24 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Towards a realistic spin-based non-magnetic FET device [001] [100] [010] 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 (1990) Exploiting the large Rashba spin-orbit coupling in InAs Electrons are confined in the z-direction in the first quantum state of the asymmetric trap and free to move in the x-y plane. gate k y [010] k x [100] Rashba effective magnetic field ⊗⊗⊗

25. 25 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 (1990) Exploiting the large Rashba spin-orbit coupling in InAs Towards a realistic spin-based non-magnetic FET device High resistance “0” Low resistance “1” BUT l MF << L S-D at room temperature

26. 26 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Dephasing of the spin through the Dyakonov-Perel mechanism L SD ~ μm l MF ~ 10 nm

27. 27 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?

28. 28 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling a 2DEG is well described by the effective Hamiltonian:  > 0,  = 0 [110] _ k y [010] k x [100] Rashba: from the asymmetry of the confinement in the z-direction  = 0,  < 0 [110] _ k y [010] k x [100] Dresselhauss: from the broken inversion symmetry of the material, a bulk property 1) Can we use SO coupling to manipulate spin AND increase spin-coherence?

29. 29 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling 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

30. 30 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]

31. 31 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] _ _

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

33. 33 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-helix state when α ≠ β Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 For Rashba or Dresselhaus by themselves NO oscillations are present; only and over damped solution exists; i.e. the spin-orbit coupling destroys the phase coherence. There must be TWO competing spin-orbit interactions for the spin to survive!!!

34. 34 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? Use the persistent spin-Helix state and control of SO coupling strength (Bernevig et al 06, Weber et al 07, Wünderlich et al 09) ✓

35. 35 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 in a 2D gas Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

36. 36 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

37. 37 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? ✓ 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) ✓

38. i p n 2DHG material Device schematic - material

39. - 2DHG i p n trench Device schematic - trench

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

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

42. 42 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 For our 2DEG system: Hence α ≈ -β

43. 43 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

44. 44 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

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

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

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

48. 48 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 can be tuned electrically by external gate and combined with electrical spin-injection from a ferromagnet (e.g. Fe/Ga(Mn)As structures)

49. 49 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Control of materials and transport properties via spin-orbit couplingAs Ga Mn New magnetic materials Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems

50. 50 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 Sinova’s group Principal Collaborators Gerrit Bauer TU Delft Bryan Gallagher U. of Nottingham and many others