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

2. Tomas Jungwirth 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 Nikolai SinitsynAlexey Kovalev Karel Vyborny

3. 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. B 75, 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. B 75, 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 ONR FUNDED TAMU SPIN PROGRAM ACTIVITY 2006-2007

4. OUTLINE Motivation: Motivation: What is the problem What is the problem Challenges and outlook: ITRS 2005 Challenges and outlook: ITRS 2005 ONR Spintronics TAMU program ONR Spintronics TAMU program Towards a comprehensive theory of anomalous transport: Towards a comprehensive theory of anomalous transport: The three spintronics Hall effects The three spintronics Hall effects Similarities and differences: why is it so difficult Similarities and differences: why is it so difficult Anomalous Hall effect and Spin Hall effect Anomalous Hall effect and Spin Hall effect AHE phenomenology and its long history AHE phenomenology and its long history Three contributions to the AHE Three contributions to the AHE Microscopic approach: focus on the intrinsic AHE Microscopic approach: focus on the intrinsic AHE Application to the SHE: theory, experiment, current status Application to the SHE: theory, experiment, current status Equivalence of Kubo and Boltzmann: a success history of the Graphene model Equivalence of Kubo and Boltzmann: a success history of the Graphene model New results in 2D-Rashba systems: absence of skew scattering New results in 2D-Rashba systems: absence of skew scattering Diluted Magnetic Semiconductors: towards a higher Tc Diluted Magnetic Semiconductors: towards a higher Tc Experimental and theory trends of Tc Experimental and theory trends of Tc Strategies to achieve higher Tc Strategies to achieve higher Tc Using mathematical theorems to increase Tc Using mathematical theorems to increase Tc A-C effect in mesoscopic rings with SO coupling 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. ITRS 2005 WHY IS CMOS SO HARD TO BEAT

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

9. 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. B 75, 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. Spin and Anomalous Hall Effect:

10. The spintronics Hall effects AHE SHE charge current gives spin current polarized charge current gives charge-spin current SHE -1 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. 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 InMnAs controversial theoretically: semiclassical theory identifies three contributions (intrinsic deflection, skew scattering, side jump scattering)

13. 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.

14. 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 

15. 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, 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. Experiment  AH  1000 (  cm) -1 Theroy  AH  750 (  cm) -1

16. 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.

17. 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

18. 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) 1.505 1.52 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)

19. 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/0605423, 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 !!!

20. Need to match the Kubo to the Boltzmann Need to match the Kubo to the Boltzmann Kubo: systematic formalism Kubo: systematic formalism Botzmann: easy physical interpretation of different contributions Botzmann: easy physical interpretation of different contributions Intrinsic + Extrinsic: Connecting Microscopic and Semiclassical approach 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 (cond-mat 07) All are done using same or equivalent linear response formulation–different or not obviously equivalent answers!!!

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

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

23. Armchair edge Zigzag edge EFEF Success in graphene

24. In metallic regime: Kubo-Streda formula: Single K-band with spin up 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. 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 SHE in the mesoscopic regime

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. B 75, 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 Jungwirth, Sinova, Mašek, Kučera, MacDonald, Rev. Mod. Phys. (2006), http://unix12.fzu.cz/ms - 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!!!

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

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

33. Can a dilute moment ferromagnet have a high Curie temperature ? The questions that we need to answer are: 1.Is there an intrinsic limit in the theory models (from the physics of the phase diagram) ? 2.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 (Ga,Mn)As coupling strength / Fermi energy band-electron density / local-moment density

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 Phenomenological k.p  Local Moment 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 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. As Ga Mn T c linear in Mn Ga local moment concentration; falls rapidly with decreasing hole density in more than 50% compensated samples; nearly independent of hole density for compensation < 50%. Jungwirth, Wang, et al. Phys. Rev. B 72, 165204 (2005) Intrinsic properties of (Ga,Mn)As

37. 8% Mn Open symbols as grown. Closed symbols annealed High compensation Linear increase of Tc with Mn eff = Mn sub -Mn Int Tc as grown and annealed samples Concentration of uncompensated Mn Ga 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. - Effective concentration of uncompensated Mn Ga moments has to increase beyond 6% of the current record T c =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 Getting to higher Tc: Strategy A

39. 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) Getting to higher Tc: Strategy B

40. conc. of wide gap component 0 1 lattice constant (A) 5.4 5.7 (Al,Ga)As Ga(As,P) (Al,Ga)As & Ga(As,P) hosts d5d5 d5d5 local moment - hole spin-spin coupling J pd S. s Mn d - As(P) p overlapMn d level - valence band splitting GaAs & (Al,Ga)As (Al,Ga)As & Ga(As,P)GaAs Ga(As,P) Mn As Ga

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

42. Using DEEP mathematics to find a new material 3=1+2 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)?

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 Masek, et al. PRB (2006) LDA+U says that Mn-doped are also twin DMSs

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

45. Electron mediated Mn-Mn coupling n-type Li(Zn,Mn)As - similar to hole mediated coupling in p-type (Ga,Mn)As L As p-orb. Ga s-orb. As p-orb. EFEF Comparable T c '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: 1 st benefit of this meeting (UCSD+TAMU)

48. 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, 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

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

50. High Electron Mobility  > 3 x 10 5 cm 2 /Vsec

51. Rashba Effect in HgTe Rashba splitting energy 8 x 8 k  p band structure model A. Novik et al., PRB 72, 035321 (2005). Y.S. Gui et al., PRB 70, 115328 (2004).

52. HgTe Ring-Structures Modeling E. Hankiewicz, J. Sinova, Concentric Tight Binding Model + B-field EXPERIMENT THEORY

53. Semiconductor nano-spintronics (TAMU): ONR AWARD N00014-06-1-0122 Scientific objectives Rationale and motivation Task 1- Develop quantitative theories of spin transport and accumulation in spin-orbit coupled systems: spin-Hall and anomalous Hall effect and spin-transport phenomena Task 2- Develop quantitative theories for novel spintronics materials that couple semiconducting properties and ferromagnetic properties Task 3- Develop a theory of spin Coulomb drag in systems with spin-orbit coupling Task 1- Possibility of manipulating spin and spin currents by solely electrical means in a controlled fashion. New switching devices. Task 2- Allows control of new transport phenomena such as anisotropic tunneling magneto-resistance by gates. New memory devices. Task 3- Allows for longer spin coherence times in spin transport and makes larger spin based devices more likely to impact the IT field. Task 1- Possibility to create new logical switching devices with lower dissipative heat consumption, increasing reliability and speed. Task 2- Novel MRAM devices for larger memory density capabilities and reliability (no mechanical parts) Task 3- Allows for larger size devices in the mesoscopic range. Navy/DoD relevanceAccomplishments 2006/2007 Theory of anomalous Hall effect in graphene. Discovery of Aharonov-Casher phase in transport measurements. Extensive review of diluted magnetic semiconductors and analysis of ferromagnetic temperature trends Prediction of new DMS materials with room temperature ferromagnetism possibilities. Extended theory of spin accumulation in coherent mesoscopic devices.

54. EXTRAS

55. Keeping Score The effective Hamiltonian (MF) and weak scattering theory (no free parameters) describe (III,Mn)V shallow acceptor metallic DMSs very well in the regime that is valid: Ferromagnetic transition temperatures   Magneto-crystalline anisotropy and coercively   Domain structure   Anisotropic magneto-resistance   Anomalous Hall effect   MO in the visible range   Non-Drude peak in longitudinal ac-conductivity  Ferromagnetic resonance  Domain wall resistance  TAMR  BUT it is only a peace of the theoretical mosaic with many remaining challenges!! TB+CPA and LDA+U/SIC-LSDA calculations describe well chemical trends, impurity formation energies, lattice constant variations upon doping

56. ● Energy dependence of Jpd ● Localization effects ● Contributions due to impurity states: Flatte’s approach of starting from isolated impurities ● Systematic p and x eff study (need more than 2 m eff data points) Possible issues regarding IR absorption