JAIRO SINOVA Research fueled by: New Horizons in Condensed Matter Physics Aspen Center for Physics February 4 th 2008 Theory challenges of semiconducting spintronics: spin-Hall effect and spin-dependent transport in spin-orbit coupled systems NERC

The challenges ahead in semiconductor spintronics Spin/charge transport in multi-band systems with inter- band coherence (Berry’s phase dependent transport): SHE and AHE in strongly SO coupled systems, etc. What are the relevant length scales: spin-current connection to spin- accumulation. QSHE: transport in Z 2 systems. Technological issues: how dissipative is it? Interplay between quasiparticle and collective degrees of freedom in a multiband system: Carrier mediated ferromagnetism: diluted magnetic semiconductors Magnetization dynamics: obtaining phenomenological LLG coefficients through microscopic calculations

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

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. 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 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 Side jump scattering 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.

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 Quantum Spin Hall Effect (Kane et al and Zhang et al)

Future challenges in anomalous transport theory 1.Reaching agreement between different approaches (mostly AHE) 2.Connect spin current to spin accumulation for strongly SO system 3.Connect SHE to the inverse SHE in strongly SO coupled regime (charge based measurements of SHE) 4.Understanding weak localization corrections in SO coupled systems for Hall transport 5.Systematic treatment of microscopic calculations of AHE in strongly SO coupled ferromagnet (e.g. DMS) with complex band structure 6.Dissipation: answer the questions if a spin based device can really beat the k B Tln2 limit of dissipation

Need to match Kubo to Boltzmann to Keldysh Need to match Kubo to Boltzmann to Keldysh Kubo: systematic formalism Kubo: systematic formalism Boltzmann: easy physical interpretation of different contributions Boltzmann: easy physical interpretation of different contributions Keldysh: microscopic version of Boltzmann + more Keldysh: microscopic version of Boltzmann + more 1. Intrinsic + Extrinsic: Connecting Microscopic and Semiclassical approaches Sinitsyn et al PRL 06, PRB 07 AHE in Rashba systems with disorder: Dugaev et al PRB 05 Dugaev et al PRB 05 Sinitsyn et al PRB 05 Sinitsyn et al PRB 05 Inoue et al (PRL 06) Inoue et al (PRL 06) Onoda et al (PRL 06) Onoda et al (PRL 06) Borunda et al (PRL 07) All are done using same or equivalent linear response formulation–different or not obviously equivalent answers!!!

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 2. From spin current to spin accumulation

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

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 3. Charge based measurements of SHE

PRL 05

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

New (smaller) sample 1  m 200 nm sample layout

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

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

Mesoscopic hole SHE L calculated voltage signal (Hankiweicz, Sinova, & Molenkamp) L L/ 6 L/2

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)

EXTRAS

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)

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

Aharonov-Casher effect: corollary of Aharonov-Bohm effect with electric fields instead Control of conductance through a novel Berry’s phase effect induced by gate voltages instead of magnetic fields M. Koenig, et al, "Direct observation of the Aharonov-Casher phase", Phys. Rev. Lett. 96, (2006). Alexey A. Kovalev, et al "Aharonov-Casher effect in a two dimensional hole ring with spin-orbit interaction", pre-print: cond-mat/ , submitted to Phys. Rev. B

HgTe Ring-Structures Three phase factors: Aharonov-Bohm Berry Aharonov-Casher

THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH Skew scattering Side-jump scattering Intrinsic AHE 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 =  -1 / 0 Averaging procedures: = 0 

Success of intrinsic AHE approach in strongly SO coupled systems 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, (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. Experiment  AH  1000 (  cm) -1 Theroy  AH  750 (  cm) -1

First experimental observations at the end of 2004 Wunderlich, Kästner, Sinova, Jungwirth, PRL 05 Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system 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: (weaker SO-coupling, stronger disorder)

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 SHE at room temperature in HgTe systems Stern et al PRL 06 !!!

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

Golden Rule: Coordinate shift: Modified Boltzmann Equation: Berry curvature: velocity: current: Semiclassical approach II Sinitsyn et al PRL 06, PRB 06

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

For single occupied linear Rashba band; zero for both occupied !!

Armchair edge Zigzag edge EFEF Success in graphene

Comparing Boltzmann to Kubo in the chiral basis

The spintronics Hall effects: multi-band transport with inter-band coherence AHE SHE charge current gives spin current polarized charge current gives charge-spin current SHE -1 spin current gives charge current

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 Farraginous results of supposedly equivalent theories The Hall conductivities tend to be small

Actual gated H-bar sample HgTe-QW  R = 5-15 meV 5  m ohmic Contacts Gate- Contact

First Data HgTe-QW  R = 5-15 meV Signal due to depletion?

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