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SPIN-HALL EFFECT a new adventure in condensed matter physics

SPIN-HALL EFFECT a new adventure in condensed matter physics. JAIRO SINOVA. San Houston State University, January 22 th 2008. Research fueled by:. NERC. Mario Borunda Texas A&M U. Sergio Rodriguez Texas A&M U. Xin Liu Texas A&M U. Alexey Kovalev Texas A&M U. Nikolai Sinitsyn

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SPIN-HALL EFFECT a new adventure in condensed matter physics

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  1. SPIN-HALL EFFECT a new adventure in condensed matter physics JAIRO SINOVA San Houston State University, January 22th 2008 Research fueled by: NERC

  2. Mario Borunda Texas A&M U. Sergio Rodriguez Texas A&M U. Xin Liu 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 • From electronics to spintronics: • Electron multipersonality: using the charge and using the spin • Success stories of metal based spintronics • Why semiconductor spintronics may be better • Spin-orbit coupling: the necessary evil • The usual example: Das-Datta transistor • Spin-Hall effect: • Normal and anomalous Hall effect and Spin Hall effect • Three contributions to the AHE • Turbulent history of the AHE • Recent focus on the intrinsic AHE • Application to the SHE • Short but turbulent history of the SHE • SHE experiments • Resolution of some of the controversy • Spin Hall spin accumulation • Theory challenges • Experimental challenges

  4. CHARGE Two parts to his personality ! SPIN What is spintronics? ELECTRONICS Mr. Electron UP TO NOW: all electronics are mostly based on the manipulation of the charge of the electron so perhaps we should say “charge electronics” SPINTRONICS: manipulate spin and charge simultaneously

  5. Vg >0 gate S D - - - - - - thin free charge carrier channel induced by electric field from gate Using the charge the field effect transistor:work horse of information processing ALL computers have these transistors in one form or another insulator semiconductor substrate HIGH tunablity of electronic transport properties the key to FET success in processing technology High mobility 2DEG: IQHE, FQHE, MIT, etc.

  6. Using the spin ferromagnetism:work horse of information storing

  7. GMR allowed read-out heads in hard drives to be MUCH smaller 1st generation spintronic devices based on ferromagnetic metals: GMR– already in every computer Magnetic tunneling junction (MTJ) or “spin valve”  Nonvolatile MRAM: “Microchips that never forget” Compatibility with Si and GaAs  next phase:semiconductor spintronics, a marriage of convenience!!!

  8. A brighter future with semiconductor spintronics • Can do what metals do • - GMR, TMR in diluted magnetic semi-cond., spin transfer, etc. • Easy integration with semiconductor devices • - possible way around impedance mismatch for spin injection. • More tunable systems • - transport properties: carrier concentration is tuned by gates and chemical doping • - ferromagnetic state affected by carrier concentration (DMS) - optical control of non-equilibrium populations • Possibility of new physical regimes/effects • - TAMR • - tunable spin-orbit coupling MORE KNOBS = MORE PHYSICS

  9. Necessities in performing spintronics in semiconductors Spin-generation: “spin battery” - injection (conventional) - optical, via selection rules (excitation with circular polarized light) - via SO coupling (e.g., occupation-asymmetry in k-space, Spin Hall effect) Spin-manipulation - external magnetic field - via SO coupling (e.g. Datta Das Spin-transistor) Spin-detection: “spin meter” - Magnetoresistive measurement (conventional) - optical, via selection rules (Spin LED) - via SO coupling(e.g., anomalous Hall effect)

  10. 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!!

  11. Beff Beff Beff - - - v v v Using SO: Datta-Das spin FET V/2 V

  12. Datta-Das spin FET: the movie Movie created by Mario Borunda

  13. OUTLINE • From electronics to spintronics: • Electron multipersonality: using the charge and using the spin • Success stories of metal based spintronics • Why semiconductor spintronics may be better • Spin-orbit coupling: the necessary evil • The usual example: Das-Datta transistor • Spin-Hall effect: • Normal and anomalous Hall effect and Spin Hall effect • Three contributions to the AHE • Turbulent history of the AHE • Recent focus on the intrinsic AHE • Application to the SHE • Short but turbulent history of the SHE • SHE experiments • Resolution of some of the controversy • Spin Hall spin accumulation • Theory challenges • Experimental challenges

  14. SPIN HALL EFFECTA NEW TWIST ON AN OLD HAT References: N. A. Sinitsyn, J.E. Hill, Hongki Ming, Jairo Sinova, and A. H. MacDonald, Phys. Rev. Lett. 97, 106804 (2006)Jairo Sinova, Shuichi Murakami, S.-Q. Shen, Mahn-Soo Choi, Solid State Comm. 138, 214 (2006).K. Nomura, J. Wunderlich, Jairo Sinova, B. Kaestner, A.H. MacDonald, T. Jungwirth, Phys. Rev. B 96, 076804 (2006).B. Kaestner, J. Wunderlich, Jairo Sinova, T. Jungwirth, Appl. Phys. Lett. 88, 091106 (2006).K. Nomura, Jairo Sinova, N.A. Sinitsyn, and A. H. MacDonald,Phys. Rev. B. 72, 165316 (2005).E. M. Hankiewicz, Tomas Jungwirth, Qian Niu, Shun-Qing Shen, and Jairo Sinova, Phys. Rev. B.72, 155305 (2005).N.A. Sinitsyn, Qian Niu, Jairo Sinova, K. Nomura, Phys. Rev. B 72, 045346 (2005).Branislav K. Nikolic, Satofumi Souma, Liviu P. Zarbo, Jairo Sinova,Phys. Rev. Lett. 95, 046601 (2005). Joerg Wunderlich, Bernd Kaestner, Jairo Sinova, Tomas Jungwirth, Phys. Rev. Lett. 94, 047204 (2005).K. Nomura, Jairo Sinova, T. Jungwirth, Q. Niu, A. H. MacDonald, Phys. Rev. B 71, 041304(R) (2005).E. M. Hankiewicz, L.W. Molenkamp, T. Jungwirth, and Jairo Sinova, Phys. Rev. B 70, 241301 (2004)N. A. Sinitsyn, E. H. Hankiewicz, Winfried Teizer, Jairo Sinova,Phys. Rev. B 70, 081212 (R), (2004).D. Culcer, Jairo Sinova, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Qian Niu, Phys. Rev. Lett 93, 046602 (2004).Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004).

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

  16. 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.

  17. 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

  18. 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

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

  20. n’, k n, q m, p m, p n, q n, q n’n, q THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH 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>] Skew scattering Side-jump scattering Vertex Corrections  σIntrinsic Intrinsic AHE: accelerating between scatterings Intrinsic σ0 /εF

  21. 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).

  22. Success of intrinsic AHE approach in comparing to experiment: phenomenological “proof” • DMS systems (Jungwirth et al PRL 2002, APL 03) • 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). • CuCrSeBr compounts, Lee et al, Science 303, 1647 (2004) Experiment sAH  1000 (W cm)-1 Theroy sAH  750 (W cm)-1 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 AND supposedly equivalent theories give different results when disorder is incorporated.

  23. _ _ _ 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

  24. 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

  25. 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)

  26. n, q n’n, q ‘Universal’ spin-Hall conductivity Color plot of spin-Hall conductivity: yellow=e/8π and red=0

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

  28. 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)

  29. For these models one can do the exact calculations numerically: testing the perturbation theory k1 Rashba: g=constant α = 1 k3 Rashba: g=constant α = 3 2DEG+Rahsba 2DHG+Rahsba Nomura et al. PRB 06

  30. Numerical results for SHE conductivities in 2D electrons and in 2D holes Nomura et al PRB 05 k^1 Rashba model k^3 Rashba model 2D electron+Rashba 2D holes+Rashba Prediction: one should observe strong intrinsic SHE in 2D hole systems

  31. OUTLINE • From electronics to spintronics: • Electron multipersonality: using the charge and using the spin • Success stories of metal based spintronics • Why semiconductor spintronics may be better • Spin-orbit coupling: the necessary evil • The usual example: Das-Datta transistor • Spin-Hall effect: • Normal and anomalous Hall effect and Spin Hall effect • Three contributions to the AHE • Turbulent history of the AHE • Recent focus on the intrinsic AHE • Application to the SHE • Short but turbulent history of the SHE • SHE experiments • Resolution of some of the controversy • Spin Hall spin accumulation • Theory challenges • Experimental challenges

  32. 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 CP [%] 1.505 1.52 Light frequency (eV) 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)

  33. How our experiment worked: creating a spin-meter at edges Conventionalvertical spin-LED Novel dual co-planar spin-LED Y. Ohno: Nature 402, 790 (1999) R. Fiederling: Nature 402, 787 (1999) ● SHE in 2DHG with strong and tunable SO ● SHE detected directly in the 2DHG ● Light emission near edge of the 2DHG ● No hetero-interface along the LED current 2DHG 2DEG Spin polarization detected through circular polarization of emitted light

  34. Experiment “A” LED 1 CP [%] -Ip a Experiment “B” +Ip LED 1 CP [%] LED 2 b a +Ip E [eV] Opposite perpendicular polarization for opposite Ip currents or opposite edges  SPIN HALL EFFECT

  35. 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”

  36. Next: solving some of the SHE controversy • Does the SHE conductivity vanish due to scattering? • Seems to be the case in 2DRG+Rashba, • does not for any other system studied • Dissipationless vs. dissipative transport • Is the SHE non-zero in the mesoscopic regime? • What is the best definition of spin-current to relate spin-conductivity to spin accumulation • ……

  37. A COMMUNITY WILLING TO WORK TOGETHER APCTP Workshop on Semiconductor Nano-Spintronics: Spin-Hall Effect and Related IssuesAugust 8-11, 2005 APCTP, Pohang, Korea http://faculty.physics.tamu.edu/sinova/SHE_workshop_APCTP_05.html

  38. Semantics agreement:The intrinsic contribution to the spin Hall conductivity is the spin Hall conductivity in the limit of strong spin orbit coupling and >>1. This is equivalent to the single bubble contribution to the Hall conductivity in the weakly scattering regime. • General agreement • The spin Hall conductivity in a 2DEG with Rashba coupling vanishes in the absence of a magnetic field and spin-dependent scattering. The intrinsic contribution to the spin Hall conductivity is identically cancelled by scattering (even weak scattering). This unique feature of this model can be traced back to the specific spin dynamics relating the rate of change of the spin and the spin current directly induced, forcing such a spin current to vanish in a steady non-equilibrium situation. • The cancellation observed in the 2DEG Rashba model is particular to this model and in general the intrinsic and extrinsic contributions are non-zero in all the other models studied so far. In particular, the vertex corrections to the spin-Hall conductivity vanish for p-doped models.

  39. 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)

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

  41. 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  !!

  42. 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 '05

  43. WHERE WE ARE GOING (THEORY) Theoretical achievements: Intrinsic SHE back to the beginning on a higher level 2003 2006 • Extrinsic SHE • approx microscopic modeling • Extrinsic + intrinsic AHE in graphene: • two approaches with the same answer Theoretical challenges: GUT the bulk (beyond simple graphene) intrinsic + extrinsic SHE+AHE+AMR Obtain the same results for different equivalent approaches (Keldysh and Kubo must agree) Others materials and defects coupling with the lattice effects of interactions (spin Coulomb drag) spin accumulation -> SHE conductivity

  44. 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

  45. Mario Borunda Texas A&M U. Sergio Rodriguez Texas A&M U. Xin Liu 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 NERC

  46. 2DEG VT 2DHG 2DEG 2DHG VD 2D spin-LED Spin-Hall effect measrement Measurement of 2DHG Rashba splitting Light emitted comes from Type II recombination processes: 3D electrons with 2D holes. 3D electrons have an asymmetric momentum space population (e.g. ky>0)

  47. 10 c B Wafer 1 a I 8 EL A PL 6 4 B A X 2 Int [a.u.] 0 10 I d b 8 p- AlGaAs C Wafer 2 E [eV] 6 GaAs A 4 B X 2 B C A 0 z [nm] 1.48 1.49 1.50 1.51 1.52 E [eV] Sub GaAs gap spectra analysis: EL vs PL X : bulk GaAs excitons I : recombination with impurity states B (A,C): 3D electron – 2D hole recombination

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