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JAIRO SINOVA

Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systems Diluted Magnetic Semiconductors and Magnetization Dynamics ONR N00014-06-1-0122. JAIRO SINOVA. Denver March 9 th 2007. Research fueled by:. Alexey Kovalev. Nikolai Sinitsyn.

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JAIRO SINOVA

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  1. Spin currents, spin-Hall spin accumulation, and anomalous Hall transport in strongly spin-orbit coupled systemsDiluted Magnetic Semiconductors and Magnetization DynamicsONR N00014-06-1-0122 JAIRO SINOVA Denver March 9th 2007 Research fueled by:

  2. Alexey Kovalev Nikolai Sinitsyn Tomas Jungwirth Karel Vyborny Allan MacDonald, Qian Niu, Ken Nomura from U. of Texas Marco Polini from Scuola Normale Superiore, Pisa Rembert Duine from Utretch Univeristy, The Netherlands Joerg Wunderlich from Cambridge-Hitachi Laurens Molenkamp et al from Wuerzburg Brian Gallager, Richard Campton, and Tom Fox from U. of Nottingham Mario Borunda and Xin Liu from TAMU Ewelina Hankiewicz from U. Missouri and TAMU Branislav Nikolic, S. Souma, and L. Zarbo from U. of Delaware

  3. ONR FUNDED TAMU SPIN PROGRAM ACTIVITY 2006-2007 • Spin and Anomalous Hall Effect: • N. A. Sinitsyn, et al, "Charge and spin Hall conductivity in metallic graphene", Phys. Rev. Lett. 97, 106804 (2006). • N. A. Sinitsyn, et al, "Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach", Phys. Rev. B75, 045315 (2007). • Mario F. Borunda, et al, "Absence of skew scattering in two-dimensional systems: Testing the origins of the anomalous Hall Effect", pre-print: cond-mat/0702289, submitted to Phys. Rev. Lett. • Diluted Magnetic Semiconductors/ Magnetization Dynamics: • T. Jungwirth, et al, "Theory of ferromagnetic (III,Mn)V Semiconductors", Rev. Mod. Phys. 78, 809 (2006) • J. Masek, et al, "Mn-doped Ga(As,P) and (Al,Ga)As ferromagnetic semiconductors", Phys. Rev. B75, 045202 (2007). • J. Wunderlich, et al, “Local control of magnetocrystalline anisotropy in (Ga,Mn)As microdevices”, submitted to Phys. Rev. B • R. Duine, et al “Functional Keldysh Theory of spin-torques”, submitted to PRB • Aharonov-Casher effect • 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

  4. OUTLINE • Motivation: • What is the problem • Challenges and outlook: ITRS 2005 • ONR Spintronics TAMU program • Towards a comprehensive theory of anomalous transport: • The three spintronics Hall effects • Similarities and differences: why is it so difficult • 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: theory, experiment, current status • Equivalence of Kubo and Boltzmann: a success history of the Graphene model • New results in 2D-Rashba systems: absence of skew scattering • Diluted Magnetic Semiconductors: towards a higher Tc • Experimental and theory trends of Tc • Strategies to achieve higher Tc • Using mathematical theorems to increase Tc • A-C effect in mesoscopic rings with SO coupling

  5. GETTING SMALLER IS NOT THE PROBLEM, GETTING HOTTER IS Circuit heat generation is the main limiting factor for scaling device speed

  6. Did we have this problem before: Yes Did we solve it: Yes (but temporarily)

  7. WHY IS CMOS SO HARD TO BEAT ITRS 2005

  8. International Technology Roadmap for Semiconductors 2005: EMERGING RESEARCH DEVICES

  9. Spin and Anomalous Hall Effect: • N. A. Sinitsyn, et al, "Charge and spin Hall conductivity in metallic graphene", Phys. Rev. Lett. 97, 106804 (2006). • N. A. Sinitsyn, et al, "Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach", Phys. Rev. B75, 045315 (2007). • Mario F. Borunda, et al, "Absence of skew scattering in two-dimensional systems: Testing the origins of the anomalous Hall Effect", pre-print: cond-mat/0702289, submitted to Phys. Rev. Lett.

  10. 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

  11. 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

  12. 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)

  13. Intrinsic deflection E 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) 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 spin-orbit coupling of the electron or the impurity. This is also known as Mott scattering used to polarize beams of particles in accelerators.

  14. 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

  15. Success of intrinsic AHE approach in strongly SO coupled systems 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.

  16. _ _ _ 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

  17. 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

  18. First experimentalobservations 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 GaAs and InGaAs: (weaker SO-coupling, stronger disorder) 1.52 Wunderlich, Kästner, Sinova, Jungwirth, PRL 05 Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system CP [%] 1.505 Light frequency (eV)

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

  20. Intrinsic + Extrinsic:Connecting Microscopic and Semiclassical approach Sinitsyn et al PRL 06, PRB 07 • Need to match the Kubo to the Boltzmann • Kubo: systematic formalism • Botzmann: easy physical interpretation of different contributions 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!!!

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

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

  23. Success in graphene EF Armchair edge Zigzag edge

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

  25. Comparing Boltzmann to Kubo in the chiral basis

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

  27. 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

  28. Landauer-Keldish approach B.K. Nicolić, et al PRL.95.046601, Mario Borunda and J. Sinova unpublished

  29. Diluted Magnetic Semiconductors/ Magnetization Dynamics • T. Jungwirth, et al, "Theory of ferromagnetic (III,Mn)V Semiconductors", Rev. Mod. Phys. 78, 809 (2006) • J. Masek, et al, "Mn-doped Ga(As,P) and (Al,Ga)As ferromagnetic semiconductors", Phys. Rev. B75, 045202 (2007). • J. Wunderlich, et al, “Local control of magnetocrystalline anisotropy in (Ga,Mn)As microdevices”, submitted to Phys. Rev. B • R. Duine, et al “Functional Keldysh Theory of spin-torques”, submitted to PRB

  30. Dilute Magnetic Semiconductors: the simple picture 5 d-electrons with L=0 S=5/2 local moment moderately shallow acceptor (110 meV)  hole -Mn local moments too dilute (near-neghbors cople AF) - Holes do not polarize in pure GaAs - Hole mediated Mn-Mn FM coupling FERROMAGNETISM MEDIATED BY THE CARRIERS!!! Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), http://unix12.fzu.cz/ms

  31. Ga1-xMnxAs As anti-site deffect: Q=+2e Substitutioanl Mn: acceptor +Local 5/2 moment Interstitial Mn: double donor BUT THINGS ARE NOT THAT SIMPLE Anti- site Mn As Inter- stitial Ga Low Temperature - MBE Ferromagnetic: x=1-8% courtesy of D. Basov

  32. Mn Mn Mn As Ga Problems for GaMnAs (late 2002) • Curie temperature limited to ~110K. • Only metallic for ~3% to 6% Mn • High degree of compensation • Unusual magnetization (temperature dep.) • Significant magnetization deficit “110K could be a fundamental limit on TC” But are these intrinsic properties of GaMnAs ??

  33. Can a dilute moment ferromagnet have a high Curie temperature ? • The questions that we need to answer are: • Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ? • Is there an extrinsic limit from the ability to create the material and its growth (prevents one to reach the optimal spot in the phase diagram)?

  34. Magnetism in systems with coupled dilute moments and delocalized band electrons coupling strength / Fermi energy band-electron density / local-moment density (Ga,Mn)As

  35. Theoretical Approaches to DMSs • First Principles Local Spin Density Approximation (LSDA) PROS: No initial assumptions, effective Heisenberg model can be extracted, good for determining chemical trends CONS: Size limitation, difficulty dealing with long range interactions, lack of quantitative predictability, neglects SO coupling (usually) • Microscopic Tight Binding models PROS: “Unbiased” microscopic approach, correct capture of band structure and hybridization, treats disorder microscopically (combined with CPA), good agreement with LDA+U calculations CONS: difficult to capture non-tabulated chemical trends, hard to reach large system sizes • Phenomenological k.p  Local Moment PROS: simplicity of description, lots of computational ability, SO coupling can be incorporated, CONS: applicable only for metallic weakly hybridized systems (e.g. optimally doped GaMnAs), over simplicity (e.g. constant Jpd), no good for deep impurity levels (e.g. GaMnN)

  36. Mn Mn Mn As Ga Intrinsic properties of (Ga,Mn)As Jungwirth, Wang, et al. Phys. Rev. B 72, 165204 (2005) Tc linear in MnGa local moment concentration; falls rapidly with decreasing hole density in more than 50% compensated samples; nearly independent of hole density for compensation < 50%.

  37. Linear increase of Tc with Mneff = Mnsub-MnInt High compensation 8% Mn Tc as grown and annealed samples Open symbols as grown. Closed symbols annealed • Concentration of uncompensated MnGa moments has to reach ~10%. Only 6.2% in the current record Tc=173K sample • Charge compensation not so important unless > 40% • No indication from theory or experiment that the problem is other than technological - better control of growth-T, stoichiometry

  38. Getting to higher Tc: Strategy A - Effective concentration of uncompensated MnGa moments has to increase beyond 6% of the current record Tc=173K sample. A factor of 2 needed  12% Mn would still be a DMS - Low solubility of group-II Mn in III-V-host GaAs makes growth difficult Low-temperature MBE Strategy A: stick to (Ga,Mn)As - alternative growth modes (i.e. with proper substrate/interface material) allowing for larger and still uniform incorporation of Mn in zincblende GaAs More Mn - problem with solubility

  39. Getting to higher Tc: Strategy B • Find DMS system as closely related to (Ga,Mn)As as possible with • larger hole-Mn spin-spin interaction • lower tendency to self-compensation by interstitial Mn • larger Mn solubility • independent control of local-moment and carrier doping (p- & n-type)

  40. d5 d5 Mn As Ga (Al,Ga)As & Ga(As,P) hosts 5.7 (Al,Ga)As lattice constant (A) Ga(As,P) 5.4 0 1 conc. of wide gap component local moment - hole spin-spin coupling Jpd S . s Mn d - As(P) poverlap Mn d level - valence band splitting GaAs & (Al,Ga)As Ga(As,P) GaAs (Al,Ga)As & Ga(As,P)

  41. (Al,Ga)As p-d coupling and Tc in mixed (Al,Ga)As and Ga(As,P) theory 10% Mn Ga(As,P) Smaller lattice const. more important for enhancing p-d coupling than larger gap  Mixing P in GaAs more favorable for increasing mean-field Tc than Al Factor of ~1.5 Tc enhancement 10% Mn Ga(As,P) 5% Mn theory Mašek, et al. PRB (2006) Microscopic TBA/CPA or LDA+U/CPA

  42. Steps so far in strategy B: • larger hole-Mn spin-spin interaction : DONE BUT DANGER IN PHASE DIAGRAM • lower tendency to self-compensation by interstitial Mn: DONE • larger Mn solubility ? • independent control of local-moment and carrier doping (p- & n-type)? Using DEEP mathematics to find a new material 3=1+2

  43. III = I + II  Ga = Li + Zn GaAs and LiZnAs are twin SC Wei, Zunger '86; Bacewicz, Ciszek '88; Kuriyama, et al. '87,'94; Wood, Strohmayer '05 LDA+U says that Mn-doped are also twin DMSs Masek, et al. PRB (2006)

  44. No solubility limit for group-II Mn substituting for group-II Zn theory Additional interstitial Li in Ga tetrahedral position - donors n-type Li(Zn,Mn)As

  45. EF L As p-orb. Ga s-orb. As p-orb. Electronmediated Mn-Mn coupling n-type Li(Zn,Mn)As - similar to hole mediated coupling in p-type (Ga,Mn)As Comparable Tc's at comparable Mn and carrier doping and Li(Mn,Zn)As lifts all the limitations of Mn solubility, correlated local-moment and carrier densities, and p-type only in (Ga,Mn)As Li(Mn,Zn)As just one candidate of the whole I(Mn,II)V family

  46. Wunderlich et al, submitted to PRB 07

  47. COLLABORATION BETWEEN INDIVIDUAL ONR PROJECTS: 1st benefit of this meeting (UCSD+TAMU)

  48. 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

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

  50. High Electron Mobility m> 3 x 105 cm2/Vsec

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