Theory challenges of semiconducting spintronics spinHall effect and

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Theory challenges of semiconducting spintronics: spin-Hall effect and spin-dependent transport in spin-orbit coupled systems

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

The challenges ahead in semiconductor spintronics • Spin/charge transport in multi-band systems with interband

The challenges ahead in semiconductor spintronics • Spin/charge transport in multi-band systems with interband 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 spinaccumulation. • 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 Spin-orbit coupling “force” deflects like-spin

Anomalous Hall effect: where things started, the long debate Spin-orbit coupling “force” deflects like-spin particles majority __ FSO I minority Simple electrical measurement of magnetization V controversial theoretically: semiclassical theory identifies three contributions (intrinsic deflection, skew scattering, side jump scattering) Spin Hall effect _ FSO __ FSO non-magnetic I V=0 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 deflect to the right or to the left as they are

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) E 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. Side jump scattering 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. Skew scattering Asymmetric scattering due to the spinorbit 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 (EF ) Intrinsic `Berry Phase’

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

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. BTln 2 limit of dissipation

1. Intrinsic + Extrinsic: Connecting Microscopic and Semiclassical approaches Sinitsyn et al PRL 06,

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

2. From spin current to spin accumulation The new challenge: understanding spin accumulation Spin

2. From spin current to spin accumulation 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)

SPIN ACCUMULATION IN 2 DHG: EXACT DIAGONALIZATION STUDIES so>>ħ/ Width>>mean free path Nomura, Wundrelich

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

SHE experiment in Ga. As/Al. Ga. As 2 DHG n p 1. 5 m

SHE experiment in Ga. As/Al. Ga. As 2 DHG n p 1. 5 m channel LED 1 y z n LED 2 x Wunderlich, Kaestner, Sinova, Jungwirth, Phys. Rev. Lett. '05 - shows the basic SHE symmetries 10 m channel - edge polarizations can be separated over large distances with no significant effect on the magnitude - 1 -2% polarization over detection length of ~100 nm consistent with theory prediction (8% over 10 nm accumulation length) Nomura, Wunderlich, Sinova, Kaestner, Mac. Donald, Jungwirth, Phys. Rev. B '05

3. Charge based measurements of SHE Non-equilibrium Green’s function formalism (Keldysh-LB) Advantages: • No

3. Charge based measurements of SHE 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

PRL 05

PRL 05

H-bar for detection of Spin-Hall-Effect (electrical detection through inverse SHE) E. M. Hankiewicz et

H-bar for detection of Spin-Hall-Effect (electrical detection through inverse SHE) E. M. Hankiewicz et al. , PRB 70, R 241301 (2004)

New (smaller) sample layout 200 nm 1 m

New (smaller) sample layout 200 nm 1 m

SHE-Measurement insulating p-conducting strong increase of the signal in the p-conducting regime, with pronounced

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

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

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

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

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

WHERE WE ARE GOING (THEORY) Theoretical achievements: Intrinsic SHE back to the beginning on

WHERE WE ARE GOING (THEORY) Theoretical achievements: Intrinsic SHE back to the beginning on a higher level 2003 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+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 2006

EXTRAS

EXTRAS

WHERE WE ARE GOING (EXPERIMENTS) Experimental achievements Optical detection of current-induced polarization photoluminescence (bulk

WHERE WE ARE GOING (EXPERIMENTS) Experimental achievements Optical detection of current-induced polarization photoluminescence (bulk and edge 2 DHG) Kerr/Faraday rotation (3 D bulk and edge, 2 DEG) 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

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

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

Aharonov-Casher effect: corollary of Aharonov-Bohm effect with electric fields instead • M. Koenig, et

Aharonov-Casher effect: corollary of Aharonov-Bohm effect with electric fields instead • M. Koenig, et al, "Direct observation of the Aharonov-Casher phase", Phys. Rev. Lett. 96, 076804 (2006). • Alexey A. Kovalev, et al "Aharonov-Casher effect in a two dimensional hole ring with spin-orbit interaction", pre-print: cond-mat/0701534, submitted to Phys. Rev. B Control of conductance through a novel Berry’s phase effect induced by gate voltages instead of magnetic fields

Hg. Te Ring-Structures Three phase factors: Aharonov-Bohm Berry Aharonov-Casher

Hg. Te Ring-Structures Three phase factors: Aharonov-Bohm Berry Aharonov-Casher

THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH Skew scattering n, q n’,

THE THREE CONTRIBUTIONS TO THE AHE: MICROSCOPIC KUBO APPROACH Skew scattering n, q n’, k m, p n, q m, p 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 Intrinsic AHE Vertex Corrections σIntrinsic n, q n’ n, q Intrinsic σ0 /εF = -1 / 0 = 0

Success of intrinsic AHE approach in strongly SO coupled systems • • • DMS

Success of intrinsic AHE approach in strongly SO coupled systems • • • DMS systems (Jungwirth et al PRL 2002) Fe (Yao et al PRL 04) Layered 2 D ferromagnets such as Sr. Ru. O 3 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 Cu. Cr. Se. Br: 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 s. AH 1000 (W cm)-1 Theroy s. AH 750 (W cm)-1

First experimental observations at the end of 2004 Kato, Myars, Gossard, Awschalom, Science Nov

First experimental observations at the end of 2004 Kato, Myars, Gossard, Awschalom, Science Nov 04 Observation of the spin Hall effect bulk in semiconductors Local Kerr effect in n-type Ga. As and In. Ga. As: (weaker SO-coupling, stronger disorder) 1. 52 Wunderlich, Kästner, Sinova, Jungwirth, PRL 05 CP [%] Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system 1. 505 Light frequency (e. V)

OTHER RECENT EXPERIMENTS Transport observation of the SHE by spin injection!! Saitoh et al

OTHER RECENT EXPERIMENTS Transport observation of the SHE by spin injection!! Saitoh et al APL 06 Valenzuela and Tinkham condmat/0605423, Nature 06 Sih et al, Nature 05, PRL 05 “demonstrate that the observed spin accumulation is due to a transverse bulk electron spin current” SHE at room temperature in Hg. Te systems Stern et al PRL 06 !!!

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

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

Semiclassical approach II Golden Rule: Modified Boltzmann Equation: velocity: Sinitsyn et al PRL 06,

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

Single K-band with spin up Kubo-Streda formula: In metallic regime: Sinitsyn et al PRL

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

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

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

Success in graphene EF Armchair edge Zigzag edge

Success in graphene EF Armchair edge Zigzag edge

Comparing Boltzmann to Kubo in the chiral basis

Comparing Boltzmann to Kubo in the chiral basis

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

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

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. nonexchange field present (SHE-1) Difficulties: • Difficult to deal systematically with off-diagonal transport in multiband 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 Hg. Te-QW R = 5 -15 me. V 5 m

Actual gated H-bar sample Hg. Te-QW R = 5 -15 me. V 5 m Gate. Contact ohmic Contacts

First Data Hg. Te-QW R = 5 -15 me. V Signal due to depletion?

First Data Hg. Te-QW R = 5 -15 me. V Signal due to depletion?

Results. . . Symmetric Hg. Te-QW R = 0 -5 me. V Signal less

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