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Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems

Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems. Tom as Jungwirth. Universit y of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds , Andrew Rushforth, et al. Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Ma š ek,

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Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems

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  1. Anisotropic magnetoresistance and spin-injection Hall effect in 2D spin-orbit coupled systems Tomas Jungwirth University of Nottingham Bryan Gallagher, Richard Campion, Kevin Edmonds, Andrew Rushforth, et al. Institute of Physics ASCR Karel Výborný, Jan Zemen, Jan Mašek, Vít Novák,Kamil Olejník, et al. Hitachi Cambridge, Univ. Cambridge Jorg Wunderlich, Andrew Irvine,Elisa de Ranieri, Byonguk Park, etal. Texas A&M Jairo Sinova, et al. University of Texas Allan MaDonald, et al.

  2. V Extraordinary magnetoresistance: AMR, AHE Ordinary magnetoresistance: response in normal metals to external magnetic field via classical Lorentz force Extraordinary magnetoresistance: response to internal spin polarization in ferromagnets via quantum-relativistic spin-orbit coupling B anisotropic magnetoresistance _ _ _ _ _ _ _ _ _ _ Lord Kelvin 1857 _ FL + + + + + + + + + + + + + I V _ _ FSO M _ I ordinary Hall effect 1879 anomalous Hall effect 1881

  3. Spin-orbit coupling nucleus rest frame electron rest frame 2 2 Lorentz transformation  Thomas precession

  4. From 1950’s microscopic model interpretations – often controversial AMR: Mott’s model of transport in metals ss sd ss sd Smit 1951 itinerant 4s: no exch.-split no SO localized 3d: exch. split SO coupled

  5. AHE Karplus&Luttinger 1954 (then partly forgotten till 2000’s) Berger 1970 Smit 1955

  6. From 1990’s numerics based on relativistic ab initio band strucrure & Kubo formula Scattering considered essential for both AMR and AHE  alloys like FeNi (treated in CPA) AMR AHE Numerically successful but difficult to connect with microscopic models due to complex bands in metals Banhart&Ebert EPL‘95 Khmelevskyi ‘PRB 03

  7. AMR sensors: dawn of spintronics in early 1990’s Magnetoresistive read element Inductive read/write element In mid 1990’s replaced in HDD by GMR or TMR but still extensively used in e.g. automotive industry

  8. From late 1990’s AMR and AHE studied in novel ferromagnets Ferromagnetic DMS GaMnAs with much simpler 3D band structure than metals Ga Bso As-p-like holes As Mn Mn-d-like local moments Bex + Bso Jungwirth et al. RMP’06 Dietl et al. Semicond. and Semimet. ‘08

  9. Semiquantitative numerical description of AMR and AHE in GaMnAs Jungwirth et al. RMP’06 Dietl et al. Semicond. and Semimet. ‘08

  10. M current  M  ) ) current [110]  ) AMR in GaMnAs DMS: from full numerics to microscopic mechanism Anisotropic scattering rate: non-crystalline and crystalline AMR Spherical model: non-crystalline AMR only Rushforth et al. PRL‘07

  11. AMR in GaMnAs DMS: from full numerics to microscopic mechanism Non-crystalline AMR mechanisms: 1) Polarized SO bands 2) Polarized impurities & SO bands M MGa current current Leading AMR mechanism in DMSs Rushforth et al. PRL‘07

  12. Microscopic mechanism of AHE in GaMnAs DMS Jungwirth et al PRL‘02 AHE explained by the revived intrinsic mechanism Note: Inspired to explain AHE in pure Fe,etcby intrinsic AHE Experiment sAH  1000 (W cm)-1 Theroy sAH  750 (W cm)-1 Yao et al PRL‘04

  13. 2D SO-coupled systems  simplest band-structures  offer most detailed and complete understanding of the AMR and AHE Rashba SO-coupled 2DEG

  14. AMR in 2D SO-coupled systems We will discuss a detailed theory analysis in Rashba-Dresselhaus 2D systems Experimentally not studied in 2D systems yet; we will comment on experiments in related 3D DMS systems Trushin, Vyborny et al PRB in press (arXiv:0904.3785)

  15. AHE in 2D SO-coupled systems Detailed theory analysis completed Nagaosa et al RMP ‘to be published (arXiv:0904.4154) We will discuss 2D AHE related experiment: Spin-injection Hall effect in a planar photo-diode

  16. Heuristic link between spin-texture of 2D SO bands, impurity potentials and AMR Short-range magnetic impurity potential Short-range electro-magnetic impurity potential

  17. Non-crystalline AMR>0 in Rashba 2D system Rashba Hamiltonian Eigenspinors

  18. current ( ) Non-crystalline AMR>0 in Rashba 2D system Scattering matrix elements

  19. ( ) Large non-crystalline AMR>0 in Rashba 2D system with electro-magnetic scatterrers Scattering matrix elementsof current current

  20. current current Negative and positive and crystalline AMR in Dresselhaus 2D system Dresselhaus Rashba

  21. AMR in (Ga,Mn)As modeled by j=3/2 Kohn-Luttinger Hamiltonian KL Hamiltonian Heavy holes Magnetic part of the impurity potential Scattering matrix elementsof Compare with spin-1/2

  22. Negative AMR in (Ga,Mn)As due to electro-magnetic MnGa impiruties Rashba Kohn-Luttinger current

  23. = const. for AMR in 2D Rashba system from exact solution to integral Boltzmann eq. or independent of averages to 0 over Fermi cont. quasiparticle life-time

  24. AMR in 2D Rashba system from exact solution to integral Boltzmann eq. transport life-time

  25. transport life-time is a good first approximation to AMR

  26. AMR in 2D Rashba system from exact solution to integral Boltzmann eq. contains only cos and sin harmonics analytical solution to the integral Boltzmann eq.

  27. 2DHG 2DEG Spintronic Hall effects in magnetic and non-magnetic (2D) systems Co/Pt Wunderlich et al. IEEE 01, PRL‘05

  28. jqs Spin-polarizer (e.g. ferromagnet,  light) nonmagnetic Spin-injection Hall effect: Hall measurement of spin-polarized electrical current injected into non-magnetic system + + + + – – – – – – – – + + + + Wunderlich et al. Nature Phys. in press, arXives:0811.3486

  29. Optical injection of spin-polarized charge currents into Hall bars  GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell p 2DHG i n 29

  30. Optical injection of spin-polarized charge currents into Hall bars  GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell - p 2DHG i n 30

  31. p i 2DHG n 2DEG Optical injection of spin-polarized charge currents into Hall bars  GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell 31

  32. VH h h h h h h e e e e e e Optical injection of spin-polarized charge currents into Hall bars  GaAs/AlGaAs planar 2DEG-2DHG photovoltaic cell 2DHG 2DEG 32

  33. Optical spin-generation area near the p-n junction Simulated band-profile p-n junction bulit-in potential (depletion length ) ~ 100 nm  self-focusing of the generation area of counter-propagating e- and h+ Hall probes further than 1m from the p-n junction  safely outside the spin-generation area and/or masked Hall probes

  34. Spin transport in a 2DEG with Rashba+Dresselhaus SO weak spin orbit coupling regime: System can be described by a set of spin-charge diff. Equation: Schliemann, et al., Phys. Rev. Lett. 94, 146801 (2003) Bernevig, et al., Phys. Rev. Lett. 97, 236601 (2006) Weber, et al., Phys. Rev. Lett. 98, 076604 (2007)

  35. Spin dynamics in a 2DEG with Rashba Dresselhaus SO Steady state solution for the out of plane spin-polarization component Spin-diffusion along the channel of injected spin- electrons SO-length ~1m

  36. ~10nm SO-length (~1m) >> mean-free-path (~10 nm) Local spin-dependent transverse deflection due to skew scattering Spin-diffusion along the channel of injected spin- electrons see also Bernevig et al., PRL‘06

  37. Skew-scattering Hall effect

  38. Spin injection Hall effect:theoretical estimate Local spin polarization  calculation of the Hall signal Weak SO coupling regime  extrinsic skew-scattering term is dominant A. Crepieux and P. Buno, PRB ’01 Large Hall angles – comparable to AHE in metals

  39. SIHE device realization n0: averaged-SIHE / AHE n3,n2,n1: local SIHE Spin-generation area 2 3 1 0

  40. Unmasked and masked SIHE devices 5.5m

  41. Vb= 0V Measured SIHE phenomenology Vb= -10V - 0+

  42. SIHE: spatially dependent, linear, strong H1 -+ H2

  43. (a) - - - 0 0 - 0 0 Vb=-5V Vb=+5V Vb=-0.5V Vb=+0.5V SIHE vs AHE

  44. SIHE survives to high temperatures - +

  45. Spin-detection in semiconductors • Magneto-optical imaging non-destructive  lacks nano-scale resolution and only an optical lab tool Datta-Das transistor • MR Ferromagnet  electrical  requires semiconductor/magnet hybrid design & B-field to orient the FM Ohno et al. Nature’99, others • spin-LED  all-semiconductor  requires further conversion of emitted light to electrical signal

  46. Spin-detection in semiconductors • Magneto-optical imaging non-destructive  lacks nano-scale resolution and only an optical lab tool Crooker et al. JAP’07, others • MR Ferromagnet  electrical  requires semiconductor/magnet hybrid design & B-field to orient the FM Ohno et al. Nature’99, others • spin-LED  all-semiconductor  requires further conversion of emitted light to electrical signal

  47. Spin-injection Hall effect  non-destructive  electrical  100-10nm resolution with current lithography in situ directly along the SC channel & all-SC requiring no magnetic elements in the structure or B-field

  48. Application of SIHE • Spin-photovoltaic cell: polarimeter on a SC chip requiring no magnetic elements, external magnetic field, or bias; form IR to visible light depending on the SC • Spin-detection tool for other device concepts (e.g. Datta-Das transistor) • Basic studies of quantum-relativistic spin-charge dynamics and AHE also in the intriguing strong SO regime in archetypal 2DEG systems

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