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JAIRO SINOVA

Anomalous and Spin-Hall effects in mesoscopic systems. JAIRO SINOVA. ICNM 2007, Istanbul, Turkey July 25 th 2007. Research fueled by:. NERC. Mario Borunda Texas A&M U. Alexey Kovalev Texas A&M U. Nikolai Sinitsyn Texas A&M U. U. of Texas. Ewelina Hankiewicz U. of Missouri

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JAIRO SINOVA

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  1. Anomalous and Spin-Hall effects in mesoscopic systems JAIRO SINOVA ICNM 2007, Istanbul, Turkey July 25th 2007 Research fueled by: NERC

  2. Mario Borunda Texas A&M U. Alexey Kovalev Texas A&M U. Nikolai Sinitsyn Texas A&M U. U. of Texas Ewelina Hankiewicz U. of Missouri Texas A&M U. Laurens Molenkamp Wuerzburg Kentaro Nomura U. Of Texas Branislav Nikolic U. of Delaware Tomas Jungwirth Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Allan MacDonald U of Texas Other collaborators: Bernd Kästner, Satofumi Souma, Liviu Zarbo, Dimitri Culcer , Qian Niu, S-Q Shen, Brian Gallagher, Tom Fox, Richard Campton, Winfried Teizer, Artem Abanov

  3. OUTLINE • The three spintronic Hall effects • Anomalous Hall effect and Spin Hall effect • AHE phenomenology and its long history • Three contributions to the AHE • Microscopic approach: focus on the intrinsic AHE • Application to the SHE • SHE in Rashba systems: a lesson from the past • Recent experimental results • Spin Hall spin accumulation: bulk and mesoscopic regime • Mesoscopic spin Hall effect: non-equilibrium Green’s function formalism and recent experiments • Summary

  4. The spintronics Hall effects SHE charge current gives spin current AHE SHE-1 polarized charge current gives charge-spin current spin current gives charge current

  5. Anomalous Hall transport • Commonalities: • Spin-orbit coupling is the key • Same basic (semiclassical) mechanisms • Differences: • Charge-current (AHE) well define, spin current (SHE) is not • Exchange field present (AHE) vs. non-exchange field present (SHE-1) • Difficulties: • Difficult to deal systematically with off-diagonal transport in multi-band system • Large SO coupling makes important length scales hard to pick • Conflicting results of supposedly equivalent theories • The Hall conductivities tend to be small

  6. Produces an electric field Ingredients: -“Impurity” potential V(r) - Motion of an electron In the rest frame of an electron the electric field generates and effective magnetic field This gives an effective interaction with the electron’s magnetic moment Spin-orbit coupling interaction(one of the few echoes of relativistic physics in the solid state) • CONSEQUENCES • If part of the full Hamiltonian quantization axis of the spin now depends on the momentum of the electron !! • If treated as scattering the electron gets scattered to the left or to the right depending on its spin!!

  7. majority _ _ _ FSO _ FSO I minority V Anomalous Hall effect: where things started, the long debate Spin-orbit coupling “force” deflects like-spin particles Simple electrical measurement of magnetization InMnAs controversial theoretically: semiclassical theory identifies three contributions (intrinsic deflection, skew scattering, side jump scattering)

  8. A history of controversy (thanks to P. Bruno– CESAM talk)

  9. Intrinsic deflection 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) Movie created by Mario Borunda 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.

  10. Skew scattering Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators. Movie created by Mario Borunda

  11. Side-jump scattering 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. Related to the intrinsic effect: analogy to refraction from an imbedded medium Movie created by Mario Borunda

  12. n’, k n, q m, p m, p n, q n, q = -1/0 n’n, q THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH Skew scattering Skew σHSkew (skew)-1 2~σ0 S where S = Q(k,p)/Q(p,k) – 1~ V0 Im[<k|q><q|p><p|k>] Averaging procedures: Side-jump scattering Vertex Corrections  σIntrinsic Intrinsic AHE = 0 Intrinsic σ0 /εF

  13. n, q n’n, q FOCUS ON INTRINSIC AHE: semiclassical and Kubo STRATEGY: compute this contribution in strongly SO coupled ferromagnets and compare to experimental results, does it work? Kubo: Semiclassical approach in the “clean limit” K. Ohgushi, et al PRB 62, R6065 (2000); T. Jungwirth et al PRL 88, 7208 (2002); T. Jungwirth et al. Appl. Phys. Lett. 83, 320 (2003); M. Onoda et al J. Phys. Soc. Jpn. 71, 19 (2002); Z. Fang, et al, Science 302, 92 (2003).

  14. Success of intrinsic AHE approach Experiment sAH  1000 (W cm)-1 Theroy sAH  750 (W cm)-1 • DMS systems (Jungwirth et al PRL 2002) • Fe (Yao et al PRL 04) • Layered 2D ferromagnets such as SrRuO3 and pyrochlore ferromagnets [Onoda and Nagaosa, J. Phys. Soc. Jap. 71, 19 (2001),Taguchi et al., Science 291, 2573 (2001), Fang et al Science 302, 92 (2003), Shindou and Nagaosa, Phys. Rev. Lett. 87, 116801 (2001)] • Colossal magnetoresistance of manganites, Ye et~al Phys. Rev. Lett. 83, 3737 (1999). • Ferromagnetic Spinel CuCrSeBr: Wei-Lee et al, Science (2004) Berry’s phase based AHE effect is quantitative-successful in many instances BUT still not a theory that treats systematically intrinsic and extrinsic contribution in an equal footing.

  15. _ _ _ FSO _ non-magnetic FSO I V=0 Spin Hall effect Take now a PARAMAGNET instead of a FERROMAGNET: Spin-orbit coupling “force” deflects like-spin particles Carriers with same charge but opposite spin are deflected by the spin-orbit coupling to opposite sides. Spin-current generation in non-magnetic systems without applying external magnetic fields Spin accumulation without charge accumulation excludes simple electrical detection

  16. Spin Hall Effect (Dyaknov and Perel) Interband Coherent Response  (EF) 0 • Occupation # • Response • `Skew Scattering‘ • (e2/h) kF (EF )1 X `Skewness’ [Hirsch, S.F. Zhang] • Intrinsic • `Berry Phase’ • (e2/h) kF [Murakami et al, Sinova et al] Influence of Disorder `Side Jump’’ [Inoue et al, Misckenko et al, Chalaev et al.] Paramagnets

  17. n, q n’n, q INTRINSIC SPIN-HALL EFFECT: Murakami et al Science 2003 (cond-mat/0308167)Sinova et al PRL 2004 (cont-mat/0307663) as there is an intrinsic AHE (e.g. Diluted magnetic semiconductors), there should be an intrinsic spin-Hall effect!!! (differences: spin is a non-conserved quantity, define spin current as the gradient term of the continuity equation. Spin-Hall conductivity: linear response of this operator) Inversion symmetry  no R-SO Broken inversion symmetry  R-SO Bychkov and Rashba (1984)

  18. n, q n’n, q = j = -e v = jz = {v,sz} SHE conductivity: Kubo formalism perturbation theory Skew σ0 S Intrinsic σ0 /εF Vertex Corrections  σIntrinsic

  19. n, q n’n, q Disorder effects: beyond the finite lifetime approximation for Rashba 2DEG Question: Are there any other major effects beyond the finite life time broadening? Does side jump contribute significantly? +…=0 + For the Rashba example the side jump contribution cancels the intrinsic contribution!! Inoue et al PRB 04 Raimondi et al PRB 04 Mishchenko et al PRL 04 Loss et al, PRB 05 Ladder partial sum vertex correction: the vertex corrections are zero for 3D hole systems (Murakami 04) and 2DHG (Bernevig and Zhang 05); verified numerically by Normura et al PRB 2006

  20. First experimentalobservations at the end of 2004 Wunderlich, Kästner, Sinova, Jungwirth, cond-mat/0410295 PRL 05 Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system Co-planar spin LED in GaAs 2D hole gas: ~1% polarization Kato, Myars, Gossard, Awschalom, Science Nov 04 Observation of the spin Hall effect bulk in semiconductors Local Kerr effect in n-type GaAs and InGaAs: ~0.03% polarization (weaker SO-coupling, stronger disorder)

  21. OTHER RECENT EXPERIMENTS Transport observation of the SHE by spin injection!! Valenzuela and Tinkham cond-mat/0605423, Nature 06 Saitoh et al APL 06 Sih et al, Nature 05, PRL 05 “demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current”

  22. The new challenge: understanding spin accumulation Spin is not conserved; analogy with e-h system Spin Accumulation – Weak SO Quasi-equilibrium Parallel conduction Spin diffusion length Burkov et al. PRB 70 (2004)

  23. Spin Accumulation – Strong SO ? Mean Free Path? Spin Precession Length

  24. SPIN ACCUMULATION IN 2DHG: EXACT DIAGONALIZATION STUDIES so>>ħ/ Width>>mean free path Nomura, Wundrelich et al PRB 06 Key length: spin precession length!! Independent of  !!

  25. n LED 1 p y m 1.5 m x n channel LED 2 z SHE experiment in GaAs/AlGaAs 2DHG Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05 10m channel - shows the basic SHE symmetries - edge polarizations can be separated over large distances with no significant effect on the magnitude - 1-2% polarization over detection length of ~100nm consistent with theory prediction (8% over 10nm accumulation length) Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '06

  26. SHE in the mesoscopic regime Non-equilibrium Green’s function formalism (Keldysh-LB) • Advantages: • No worries about spin-current definition. Defined in leads where SO=0 • Well established formalism valid in linear and nonlinear regime • Easy to see what is going on locally • Fermi surface transport

  27. Nonequilibrium Spin Hall Accumulation in Rashba 2DEG eV=0 -eV/2 +eV/2 Y. K. Kato, R. C. Myers, A. C. Gossard, and D.D. Awschalom, Science 306, 1910 (2004). PRL 95, 046601 (2005) • Spin density(Landauer –Keldysh):

  28. HgTe band structure semi-metal or semiconductor fundamental energy gap D.J. Chadi et al. PRB, 3058 (1972)

  29. HgTe-Quantum Well Structures QW Barrier VBO = 570 meV

  30. HgTe-Quantum Well Structures Typ-III QW conduction band QW < 55 Å G6 G6 HgTe HgTe HgCdTe HgCdTe HgCdTe E1 HH1 VBO = 570 meV G8 G8 valence band inverterted normal band structure

  31. High Electron Mobility

  32. H-bar for detection of Spin-Hall-Effect (electrical detection through inverse SHE) E.M. Hankiewicz et al ., PRB 70, R241301 (2004)

  33. Actual gated H-bar sample HgTe-QW DR = 5-15 meV 5 mm Gate- Contact ohmic Contacts

  34. First Data HgTe-QW DR = 5-15 meV Signal due to depletion?

  35. Results... Symmetric HgTe-QW DR = 0-5 meV Signal less than 10-4 Sample is diffusive: Vertex correction kills SHE (J. Inoue et al., Phys. Rev. B 70, 041303 (R) (2004)).

  36. New (smaller) sample sample layout 200 nm 1 mm

  37. SHE-Measurement insulating n-conducting p-conducting strong increase of the signal in the p-conducting regime, with pronounced features no signal in the n-conducting regime

  38. Mesoscopic electron SHE L/2 L/6 L calculated voltage signal for electrons (Hankiewicz and Sinova)

  39. Mesoscopic hole SHE L/2 L/6 L calculated voltage signal (Hankiweicz, Sinova, & Molenkamp) L more than 10 time larger!

  40. L/6 L Scaling of H-samples with the system size Oscillatory character of voltage difference with the system size.

  41. SUMMARY Extrinsic (1971,1999) and Intrinsic (2003) SHE predicted and observed (2004): back to the beginning on a higher level • Extrinsic + intrinsic AHE in graphene: • two approaches with the same answer Optical detection of current-induced polarization photoluminescence (bulk and edge 2DHG) Kerr/Faraday rotation (3D bulk and edge, 2DEG) Transport detection of the mesoscopic SHE in semiconducting systems: HgTe preliminary results agree with theoretical calculations

  42. WHERE WE ARE GOING (EXPERIMENTS) Experimental achievements Optical detection of current-induced polarization photoluminescence (bulk and edge 2DHG) Kerr/Faraday rotation (3D bulk and edge, 2DEG) Transport detection of the SHE Experimental (and experiment modeling) challenges: General edge electric field (Edelstein) vs. SHE induced spin accumulation Photoluminescence cross section edge electric field vs. SHE induced spin accumulation free vs. defect bound recombination spin accumulation vs. repopulation angle-dependent luminescence (top vs. side emission) hot electron theory of extrinsic experiments SHE detection at finite frequencies detection of the effect in the “clean” limit

  43. INTRINSIC+EXTRINSIC: STILL CONTROVERSIAL! AHE in Rashba systems with disorder: Dugaev et al PRB 05 Sinitsyn et al PRB 05 Inoue et al (PRL 06) Onoda et al (PRL 06) Borunda et al (cond-mat 07) All are done using same or equivalent linear response formulation–different or not obviously equivalent answers!!! The only way to create consensus is to show (IN DETAIL) agreement between the different equivalent linear response theories both in AHE and SHE

  44. Connecting Microscopic and Semiclassical approach Sinitsyn et al PRL 06, PRB 06 • Need to match the Kubo to the Boltzmann • Kubo: systematic formalism • Botzmann: easy physical interpretation of different contributions

  45. Kubo-Streda formula summary Semiclassical Boltzmann equation Golden rule: In metallic regime: J. Smit (1956): Skew Scattering

  46. Semiclassicalapproach II: Sinitsyn et al PRB 06 Golden Rule: Modified Boltzmann Equation: velocity: Sinitsyn et al PRB 06 current: Berry curvature: Coordinate shift:

  47. Some success in graphene EF Armchair edge Zigzag edge

  48. Single K-band with spin up Kubo-Streda formula: In metallic regime: Sinitsyn et al PRL 06, PRB 06 SAME RESULT OBTAINED USING BOLTMANN!!!

  49. Comparing Boltzmann to Kubo in the chiral basis

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