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

Branislav Nikolic U. of Delaware Allan MacDonald U of Texas Tomas Jungwirth Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Laurens Molenkamp Wuerzburg Kentaro Nomura U. Of Texas Ewelina Hankiewicz U. of Missouri Texas A&M U. Mario Borunda Texas A&M U. Nikolai Sinitsyn Texas A&M U. 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 Sergio Rodriguez Texas A&M U. Xin Liu Texas A&M U. Alexey Kovalev Texas A&M U.

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

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

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

Using the spin ferromagnetism: work horse of information storing

1 st generation spintronic devices based on ferromagnetic metals: GMR– already in every computer GMR  allowed read-out heads in hard drives to be MUCH smaller 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!!!

A brighter future with semiconductor spintronics MORE KNOBS = MORE PHYSICS 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 - 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 spin-orbit coupling - tunable spin-orbit coupling

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)

Spin-orbit coupling interaction (one of the few echoes of relativistic physics in the solid state) Ingredients: -“Impurity” potential V(r) - Motion of an electron Produces an electric field 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 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!!

Using SO: Datta-Das spin FET V - v B eff - v - v V/2

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

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

SPIN HALL EFFECT A 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, (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, (2006). B. Kaestner, J. Wunderlich, Jairo Sinova, T. Jungwirth, Appl. Phys. Lett. 88, (2006). K. Nomura, Jairo Sinova, N.A. Sinitsyn, and A. H. MacDonald, Phys. Rev. B. 72, (2005). E. M. Hankiewicz, Tomas Jungwirth, Qian Niu, Shun-Qing Shen, and Jairo Sinova, Phys. Rev. B.72, (2005). N.A. Sinitsyn, Qian Niu, Jairo Sinova, K. Nomura, Phys. Rev. B 72, (2005). Branislav K. Nikolic, Satofumi Souma, Liviu P. Zarbo, Jairo Sinova, Phys. Rev. Lett. 95, (2005). Joerg Wunderlich, Bernd Kaestner, Jairo Sinova, Tomas Jungwirth, Phys. Rev. Lett. 94, (2005). K. Nomura, Jairo Sinova, T. Jungwirth, Q. Niu, A. H. MacDonald, Phys. Rev. B 71, (R) (2005). E. M. Hankiewicz, L.W. Molenkamp, T. Jungwirth, and Jairo Sinova, Phys. Rev. B 70, (2004) N. A. Sinitsyn, E. H. Hankiewicz, Winfried Teizer, Jairo Sinova, Phys. Rev. B 70, (R), (2004). D. Culcer, Jairo Sinova, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Qian Niu, Phys. Rev. Lett 93, (2004). Jairo Sinova, Dimitrie Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, A.H. MacDonald, Phys. Rev. Lett. 92, (2004).Phys. Rev. Lett. 97, (2006)Solid State Comm. 138, 214 (2006).Phys. Rev. B 96, (2006).Appl. Phys. Lett. 88, (2006).Phys. Rev. B. 72, (2005).Phys. Rev. B.72, (2005).Phys. Rev. B 72, (2005).Phys. Rev. Lett. 95, (2005)Phys. Rev. Lett. 94, (2005)Phys. Rev. B 71, (R) (2005)Phys. Rev. B 70, (2004)Phys. Rev. B 70, (R), (2004)Phys. Rev. Lett 93, (2004).Phys. Rev. Lett. 92, (2004).

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

Intrinsic deflection 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. Movie created by Mario Borunda 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)

Skew scattering Movie created by Mario Borunda 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.

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

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

THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH Skew scattering Side-jump scattering Intrinsic AHE: accelerating between scatterings Skew σ H Skew  (  skew ) -1  2~ σ 0 S where S = Q(k,p)/Q(p,k) – 1~ V 0 Im[ ] Vertex Corrections  σ Intrinsic Intrinsic  σ 0 /ε F  n, q m, p n’, k n, q n’  n, q

FOCUS ON INTRINSIC AHE: semiclassical and Kubo 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). Semiclassical approach in the “clean limit” Kubo: n, q n’  n, q STRATEGY: compute this contribution in strongly SO coupled ferromagnets and compare to experimental results, does it work?

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, (2001)] colossal magnetoresistance of manganites, Ye et~al Phys. Rev. Lett. 83, 3737 (1999). CuCrSeBr compounts, Lee et al, Science 303, 1647 (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 AND supposedly equivalent theories give different results when disorder is incorporated. Experiment  AH  1000 (  cm) -1 Theroy  AH  750 (  cm) -1

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

Spin Hall Effect (Dyaknov and Perel) Interband Coherent Response  (E F  ) 0 Occupation # Response `Skew Scattering‘  (e 2 /h) k F (E F  ) 1 X `Skewness’ [Hirsch, S.F. Zhang] Intrinsic `Berry Phase’  (e 2 /h) k F  [Murakami et al, Sinova et al] Influence of Disorder `Side Jump’’ [Inoue et al, Misckenko et al, Chalaev et al…] Paramagnets

INTRINSIC SPIN-HALL EFFECT: INTRINSIC SPIN-HALL EFFECT: Murakami et al Science 2003 (cond-mat/ ) Sinova et al PRL 2004 (cont-mat/ ) as there is an intrinsic AHE (e.g. Diluted magnetic semiconductors), there should be an intrinsic spin-Hall effect!!! Inversion symmetry  no R-SO Broken inversion symmetry  R-SO Bychkov and Rashba (1984) (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) n, q n’  n, q

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

SHE conductivity: all contributions– Kubo formalism perturbation theory Skew  σ 0 S Vertex Corrections  σ Intrinsic Intrinsic  σ 0 /ε F  n, q n’  n, q = j = -e v = j z = {v,s z }

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? Ladder partial sum vertex correction: Inoue et al PRB 04 Raimondi et al PRB 04 Mishchenko et al PRL 04 Loss et al, PRB 05 the vertex corrections are zero for 3D hole systems (Murakami 04) and 2DHG (Bernevig and Zhang 05) n, q n’  n, q + +…=0 For the Rashba example the side jump contribution cancels the intrinsic contribution!!

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

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

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

First experimental observations at the end of 2004 Wunderlich, Kästner, Sinova, Jungwirth, cond-mat/ 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 [%] 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)

Spin polarization detected through circular polarization of emitted light Conventional vertical 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 How our experiment worked: creating a spin-meter at edges

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

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

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 ……

APCTP Workshop on Semiconductor Nano-Spintronics: Spin-Hall Effect and Related Issues August 8-11, 2005 APCTP, Pohang, Korea A COMMUNITY WILLING TO WORK TOGETHER

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.

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

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

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  !!

1.5  m channel n n p y x z LED  m channel SHE experiment in GaAs/AlGaAs 2DHG - 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) Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05 Nomura, Wunderlich, Sinova, Kaestner, MacDonald, Jungwirth, Phys. Rev. B '05

Theoretical achievements: 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 Intrinsic SHE back to the beginning on a higher level Extrinsic SHE approx microscopic modeling Extrinsic + intrinsic AHE in graphene: two approaches with the same answer WHERE WE ARE GOING (THEORY)

Experimental achievements Experimental (and experiment modeling) challenges: 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 Optical detection of current-induced polarization photoluminescence (bulk and edge 2DHG) Kerr/Faraday rotation (3D bulk and edge, 2DEG) Transport detection of the SHE General edge electric field (Edelstein) vs. SHE induced spin accumulation SHE detection at finite frequencies detection of the effect in the “clean” limit WHERE WE ARE GOING (EXPERIMENTS)

Branislav Nikolic U. of Delaware Allan MacDonald U of Texas Tomas Jungwirth Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Laurens Molenkamp Wuerzburg Kentaro Nomura U. Of Texas Ewelina Hankiewicz U. of Missouri Texas A&M U. Mario Borunda Texas A&M U. Nikolai Sinitsyn Texas A&M U. 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 Sergio Rodriguez Texas A&M U. Xin Liu Texas A&M U. Alexey Kovalev Texas A&M U. NERC

2D spin-LED 2DHG2DEG 2DHG 2DEG VTVT VDVD Light emitted comes from Type II recombination processes: 3D electrons with 2D holes. 3D electrons have an asymmetric momentum space population (e.g. k y >0) Measurement of 2DHG Rashba splitting Spin-Hall effect measrement

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

OUTLINE Metal and semiconductor based spintronics Metal and semiconductor based spintronics Spin-orbit coupling in semiconducting systems Spin-orbit coupling in semiconducting systems Hall effect, Anomalous Hall effect, and Spin Hall effect Hall effect, Anomalous Hall effect, and Spin Hall effect Ordinary and quantum Hall effect Ordinary and quantum Hall effect Anomalous Hall effect and spin Hall effect (SHE) Anomalous Hall effect and spin Hall effect (SHE) Intrinsic SHE in Rashba SO couple systems Intrinsic SHE in Rashba SO couple systems Optical detection of the polarization Optical detection of the polarization Our measuring technique: LED probe of polarization Our measuring technique: LED probe of polarization Lateral 2DEG-2DHG junction Lateral 2DEG-2DHG junction Comparison of electro-luminescence and photo- luminescence Comparison of electro-luminescence and photo- luminescence Measurement of the SO splitting: in-plane polarization through asymmetric recombination Measurement of the SO splitting: in-plane polarization through asymmetric recombination SHE measurement SHE measurement Conclusions and outlook Conclusions and outlook

Light polarization due to recombination with SO-split hole-subband in a p-n LED under forward bias spin operators of holes: j=3s HH + HH - - HH - HH + HH + k y [nm -1 ] spin-polarization of HH+ and HH- subbands in-plane  in-plane polarization s=1/2 electrons to j=3/2 holes plus selection rules  circular polarization of emitted light Microscopic band-structure calculations of the 2DHG: E [meV] a HH+ HH- LH -- ++ k y [nm -1 ] 3D electron-2D hole Recombination ,2   0 20

 NO perp.-to-plane component of polarization at B=0  B≠0 behavior consistent with SO-split HH subband In-plane detection angle/polarization Perp.-to plane detection angle/polarization 20  m n p Junction y x z 20  m n p Junction y x z