1. Research fueled by: Instituto de Ciencia de Materiales de Madrid-CSIC November 19 th, 2010 JAIRO SINOVA Texas A&M University Institute of Physics ASCR Spin-helix-Hall transistors and topological thermoelectrics 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 Internal coupling of charge and spin: origin and present use Control of material and transport properties through spin-orbit coupling Overview of program II. Anomalous Hall effect: Anomalous Hall effect basics III.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. spin-helix-Hall transistors and topological thermoelectrics

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 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 In the rest frame of an electron the electric field generates an effective magnetic field Motion of an electron

5. 5 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: Spin or the band- structure Bloch states are linked to the momentum. Internal communication between spin and charge:spin- orbit coupling interaction

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 #2 Mott scattering Internal communication between spin and charge:spin- orbit coupling interaction

7. 7 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

8. 8 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

9. 9 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!!!

10. Nanoelectronics, spintronics, and materials control by spin-orbit coupling Anomalous Hall effect (scaling with ρ for metals) Material with dominant skew scattering mechanism Material with dominant scattering-independent mechanism σ xx >10 6 (Ωcm) -1 σ xx ~10 4 -10 6 (Ωcm) -1

11. Nanoelectronics, spintronics, and materials control by spin-orbit coupling Anomalous Hall effect (scaling for insulators) Diagonal hopping conductivity for most systems showing approximate scaling σ xy ~σ xx 1.4-1.7 over a few decades for σ xx <10 4 (Ωcm) -1

12. 12 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

13. 13 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

14. 14 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 Overview of program II. Anomalous Hall effect: Anomalous Hall effect basics III.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. spin-helix transistors and topological thermoelectrics

15. 15 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 ⊗⊗⊗

16. 16 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

17. 17 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

18. 18 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?

19. 19 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?

20. 20 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

21. 21 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]

22. 22 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] _ _

23. 23 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Persistent state spin helix verified by pump-probe experiments Similar wafer parameters to ours

24. 24 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!!!

25. 25 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) ✓

26. 26 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, Sinova, et al PRB 08 Non-Equilibrium Green’s Function (NEGF) microscopic approach Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08 Restriction to homogeneous magnetization. Magnetic textures lead to the so called topological AHE.

27. 27 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

28. 28 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 ✓ ✓

29. 29 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

30. 30 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

31. 31 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

32. 32 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Further experimental tests of the observed SIHE

33. 33 Nanoelectronics, spintronics, and materials control by spin-orbit coupling T = 250K Further experimental tests of the observed SIHE

34. 34 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 transitor: Wunderlich, Irvine, Sinova, Jungwirth, et al, arXiv:1008.2844 SiHE inverse SHE

35. 35 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, arXiv:1008.2844

36. 36 Nanoelectronics, spintronics, and materials control by spin-orbit coupling -- -- -- H1 H2 0 +0.1 -0.1 Vg2 [V] R H2 [ ] 0 6 3 SHE transistor AND gate R H1 [ ] -- 0 12 6

37. 37 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)

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 Overview of program Anomalous Hall effect: Anomalous Hall effect basics 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. 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 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

42. 42 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

43. 43 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

44. 44 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Anomalous Hall effect: from the metallic to the insulating regime I. Established a consistent theory of Anomalous Hall effect for metallic regime with homogeneous magnetization Spin injection Hall effect: a new paradigm in exploiting SO coupling I. Modeled and constructed a spin FET in the diffusive regime II. First spin AND gate with pure spin currents III. Topological thermoelectrics:Speculative theory of how to increase of ZT in topological insulators via line dislocations. spin-helix transistors and topological thermoelectrics Control of materials and transport properties via spin-orbit coupling A long list of challenges: DMSs, Antiferromagnetic semiconductors, current driven magnetization dynamics, pseudo-spintronics in double layer systems, spin-caloritronics (Spin Seebeck effect)

45. 45 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 Oleg Tretiakov Texas A&M U.