1. Research fueled by: Frontiers in Materials: Spintronics Strasboug, France May 13 th, 2012 Expecting the unexpected in the spin Hall effect: from fundamental to practical JAIRO SINOVA Vivek Amin Texas A&M University Institute of Physics ASCR Hitachi Cambridge Joerg W ü nderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, Karel Vyborny, et al

2. Expecting the unexpected in the spin Hall effect: from fundamental to practical! The spin Hall effects is a relativistic spin-orbit coupling phenomenon which can be used to electrically generate or detect spin currents in magnetic and non-magnetic systems. In spite of the short time since its discovery it has now become ubiquitous in the field of spintronics and its development has also sparked a renewed interest in the full understanding of all the relating effects, such as the anomalous Hall effect. Exploiting such effects fully requires a better understanding of the effects and their intricate connections. SHE has been used to create one of the first spin FETs, to measure spin-currents generated by magnetization dynamics, and even to generate spin-currents large enough to produce spin-torque effects! In this talk I attempt to give a short, brief, and possibly oversimplified overview of some of the critical developments of this vibrant subfield of spintronics, its present understanding, its present applications, and some of its future challenges.

3. 3 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Introduction: Basic AHE and SHE phenomenology Mechanism II. Spin Hall effect: the early days First proposals: from theory to experiment First observations of the extrinsic and intrinsic (optical) Inverse spin Hall effect Direct iSHE in metals Spin pumping and FMR SHE-FET Spin Hall injection and spin precession manipulation iSHE device with spin-accumulation modulation SHE as a spin current generator and detector Spin based FET: old and new paradigm in charge-spin transport Theory expectations and modeling Experimental results Conclusion Expecting the unexpected in the spin Hall effect: from fundamental to practical

4. 4 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 =

5. 5 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)

6. 6 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

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 #1 Internal communication between spin and charge:spin- orbit coupling interaction

8. 8 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

9. 9 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- ×

10. 10 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

11. 11 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Information and communication technology power consumption HAS consequences Relative electricity consumption of ICT equipment

12. 12 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

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 Topological transport effects Effects of spin-orbit coupling in multiband systems Caloritronics

14. 14 Caloritronics 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 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

15. 15 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!!!

16. 16 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

17. 17 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 Nature Physics 2010 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 Topological Insulators Kane and Mele PRL 05

18. 18 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Introduction: using the dual personality of the electron Internal coupling of charge and spin: origin and present use Control of material and transport properties through spin-orbit coupling Anomalous Hall effect: from the metallic to the insulating regime Anomalous Hall effect basics, history, progress in the metallic regime Spin injection Hall effect: a new paradigm in exploiting SO coupling Spin based FET: old and new paradigm in charge-spin transport Theory expectations and modeling Experimental results Topological thermoelectrics:Thermoelectric figure of merit Increase of ZT in topological insulators. Conclusion New twists in spintronics: anomalous Hall effect, spin-helix transistors, and topological thermoelectrics New twists in spintronics: anomalous Hall effect, spin-helix transistors, and topological thermoelectrics

19. 19 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 ⊗⊗⊗

20. 20 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

21. 21 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

22. 22 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?

23. 23 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?

24. 24 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]

25. 25 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] _ _

26. 26 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Persistent state spin helix verified by pump-probe experiments Similar wafer parameters to ours

27. 27 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!!!

28. 28 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) ✓

29. 29 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

30. 30 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 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 Use AHE to measure injected current polarization electrically ✓ ✓

31. 31 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

32. 32 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

33. 33 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

34. 34 Nanoelectronics, spintronics, and materials control by spin-orbit coupling T = 250K Further experimental tests of the observed SIHE (preliminary)

35. 35 Nanoelectronics, spintronics, and materials control by spin-orbit coupling V H2 I VbVb V H1 x V H2 VbVb V H1 x (a) (b) SiHE: new results Spin Hall effect transistor: Wunderlich, Irvine, Sinova, Jungwirth, et al, Science 2010 SiHE inverse SHE

36. 36 Nanoelectronics, spintronics, and materials control by spin-orbit coupling VHVH VgVg I VbVb VHVH VgVg VbVb x Δ x=1  m ++ SiHE transistor Spin Hall effect transitor: Wunderlich, Irvine, Sinova, Jungwirth, et al, Science 2010

37. 37 Nanoelectronics, spintronics, and materials control by spin-orbit coupling -- -- -- -- H1 H2 0 +0.1 -0.1 Vg2 [V] R H1 [ ] 0 12 R H2 [ ] 0 6 6 3 SHE transistor AND gate

38. 38 Nanoelectronics, spintronics, and materials control by spin-orbit coupling I. Introduction: using the dual personality of the electron Internal coupling of charge and spin: origin and present use Control of material and transport properties through spin-orbit coupling Anomalous Hall effect: from the metallic to the insulating regime Anomalous Hall effect basics, history, progress in the metallic regime Spin injection Hall effect: a new paradigm in exploiting SO coupling Spin based FET: old and new paradigm in charge-spin transport Theory expectations and modeling Experimental results Topological thermoelectrics:Thermoelectric figure of merit Increase of ZT in topological insulators. Conclusion New twists in spintronics: anomalous Hall effect, spin-helix transistors, and topological thermoelectrics New twists in spintronics: anomalous Hall effect, spin-helix transistors, and topological thermoelectrics

39. 39 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 Topological transport effects Effects of spin-orbit coupling in multiband systems Caloritronics Topological thermoelectrics

40. 40 Nanoelectronics, spintronics, and materials control by spin-orbit coupling From AHE to topological insulators to thermoelectrics Vishwanath et al Nature Physics 09 Dislocations have 1D channels which also protected Topological Insulators: edge (2D) or surface states (3D) survive disorder effects when the bulk gap is produced by spin-orbit coupling Kane, Zhang, Molenkamp, Moore, et al Zhang, Physics 1, 6 (2008) X X QSHE in HgTe

41. 41 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Thermoelectric generator

42. 42 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Courtesy of Saskia Fischer

43. 43 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Courtesy of Saskia Fischer

44. 44 Nanoelectronics, spintronics, and materials control by spin-orbit coupling From AHE to topological insulators to thermoelectrics Best thermoelectrics Can we obtain high ZT through the topological protected states; are they related to the high ZT of these materials? Vishwanath et al 09 Dislocations have 1D channels which also protected ? ? Seebeck coefficient electrical conductivity electric thermal conductivity phonon thermal conductivity

45. 45 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Bi 1−x Sb x (0.07 < x < 0.22) where the L’s are the linear Onsager dynamic coefficients Localized bulk states Possible large ZT through dislocation engineering Tretiakov, Abanov, Murakami, Sinova APL 2010

46. 46 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Possible large ZT through dislocation engineering Remains very speculative but simple theory gives large ZT for reasonable parameters Tretiakov, Abanov, Murakami, Sinova APL 2010

47. 47 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Beyond Bi 1−x Sb x (0.07 < x < 0.22) So far only one material is believed to have protected 1D states on dislocations: how to further exploit TI properties to increase ZT? Analogy to HolEy Silicon Tang et al Nano Letters 2010 Also phononic nanomesh structures (Yu, Mitrovic, et al Nature Nanotechnology 2010)

48. 48 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Extending the idea to the entire class of TI insulators The surface of the holes provide the needed anisotropic transport Similar theory analysis as in 1D protected states but not as robust Curvature of the holes can be critical for TI to remain protected (Ostrovsky et al PRL 10, Zhang and Vishwanath PRL 10) d=60 nm R=15 nm Tretiakov, Abanov, Sinova APL 2011

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 Topological transport effects Effects of spin-orbit coupling in multiband systems Caloritronics

50. 50 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Xin Liu Texas A&M U. Sinova’s group Oleg Tretiakov (main PI Abanov) Texas A&M U. H. Gao Texas A&M U. Vivek Amin Texas A&M U. Erin Vehstedt Texas A&M U. Jacob Gyles Texas A&M U. Jan Jacob U. Hamburg Tomas Jungwirth Texas A&M U. Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Principal Outside Collaborators