Spin-dependent Hall effects and other thoughts on recent progress and future challenges in spintronics Progress in Spintronics and Graphene Research June 7 th, 2010 KITPC, Beijing, China JAIRO SINOVA Texas A&M University Institute of Physics ASCR Research fueled by:

2 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Allan MacDonald U of Texas Tomas Jungwirth Texas A&M U. Inst. of Phys. ASCR U. of Nottingham Joerg Wunderlich Cambridge-Hitachi Laurens Molenkamp Würzburg Xiong-Jun Liu Texas A&M U. Mario Borunda Texas A&M Univ. Harvard Univ. Nikolai Sinitsyn Texas A&M U. U. of Texas LANL Alexey Kovalev Texas A&M U. UCLA Liviu Zarbo Texas A&M Univ. ASCR Xin Liu Texas A&M U. Ewelina Hankiewicz (Texas A&M Univ.) Würzburg University Principal Collaborators Gerrit Bauer TU Delft Bryan Gallagher U. of Nottingham Agent Smith UCLA

Nanoelectronics, spintronics, and materials control by spin-orbit coupling Valenzuela et al Nature 06 Inverse SHE Anomalous Hall effect: more than meets the eye Wunderlich, Kaestner, Sinova, Jungwirth PRL 04 Kato et al Science 03 Intrinsic Extrinsic V Mesoscopic Spin Hall Effect Intrinsic Brune,Roth, Hankiewicz, Sinova, Molenkamp, et al Nature Physics 10 Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Spin-injection Hall Effect Anomalous Hall Effect I _ FSOFSO FSOFSO _ _ majority minority V Spin Hall Effect I _ FSOFSO FSOFSO _ _ V

Why is important about understanding anomalous Hall transport Spin relaxation by spin-hot-spots Topological Insulators Band-structure engineered transport (intrinsic effects, topological dependent transport) Efficient thermoelectrics Interface transport in spin-injection Spin-charge transport theory remains incomplete

Nanoelectronics, spintronics, and materials control by spin-orbit coupling Simple electrical measurement of out of plane magnetization InMnAs Spin dependent “force” deflects like-spin particles ρ H =R 0 B ┴ +4π R s M ┴ Anomalous Hall Effect: the basics I _ F SO _ _ _ majority minority V

Anomalous Hall effect (scaling with ρ) Dyck et al PRB 2005 Kotzler and Gil PRB 2005 Co films Edmonds et al APL 2003 GaMnAs Material with dominant skew scattering mechanism Material with dominant scattering-independent mechanism

Phenomenological regimes of AHE Review of AHE (RMP 2010), Nagaosa, Sinova, Onoda, MacDonald, Ong 1.A high conductivity regime for σ xx >10 6 ( cm) -1 in which AHE is skew dominated 2.A good metal regime for σ xx ~ ( cm) -1 in which σ xy AH ~ const 3.A bad metal/hopping regime for σ xx 1 Skew dominated regime

Scattering independent regime

Hopping conduction regime: terra incognita Approximate scaling seen as a function of T Diagonal hopping conductivity for most systems showing approximate scaling phenomenology gives σ xy ~σ xx over a few decades

: Hall discovers the Hall and the anomalous Hall effect The tumultuous history of AHE 1970: Berger reintroduces (and renames) the side-jump: claims that it does not vanish and that it is the dominant contribution, ignores intrinsic contribution. (problem: his side-jump is gauge dependent) Berger Luttinger 1954: Karplus and Luttinger attempt first microscopic theory: they develop (and later Kohn and Luttinger) a microscopic theory of linear response transport based on the equation of motion of the density matrix for non- interacting electrons, ; run into problems interpreting results since some terms are gauge dependent. Lack of easy physical connection. Hall 1970’s: Berger, Smit, and others argue about the existence of side-jump: the field is left in a confused state. Who is right? How can we tell? Three contributions to AHE are floating in the literature of the AHE: anomalous velocity (intrinsic), side-jump, and skew contributions : Smit attempts to create a semi-classical theory using wave- packets formed from Bloch band states: identifies the skew scattering and notices a side-step of the wave-packet upon scattering and accelerating..Speculates, wrongly, that the side-step cancels to zero. The physical interpretation of the cancellation is based on a gauge dependent object!!

The tumultuous history of AHE: last three decades 2004’s: Spin-Hall effect is revived by the proposal of intrinsic SHE (from two works working on intrinsic AHE): AHE comes to the masses, many debates are inherited in the discussions of SHE. 1980’s: Ideas of geometric phases introduced by Berry; QHE discoveries 2000’s: Materials with strong spin-orbit coupling show agreement with the anomalous velocity contribution: intrinsic contribution linked to Berry’s curvature of Bloch states. Ignores disorder contributions ’s: Linear theories in simple models treating SO coupling and disorder finally merge: full semi-classical theory developed and microscopic approaches are in agreement among each other in simple models.

12 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Cartoon of the mechanisms contributing to AHE independent of impurity density 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 SO coupled quasiparticles Intrinsic deflection B 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. They however come out in a different band so this gives rise to an anomalous velocity through scattering rates times side jump. independent of impurity density Side jump scattering V imp (r) (Δso>ħ/τ)  ∝ λ* ∇ V imp (r) (Δso<ħ/τ) B Skew scattering Asymmetric scattering due to the spin-orbit coupling of the electron or the impurity. Known as Mott scattering. ~σ~1/n i V imp (r) (Δso>ħ/τ)  ∝ λ* ∇ V imp (r) (Δso<ħ/τ) A

Boltzmann semiclassical approach: easy physical interpretation of different contributions (used to define them) but very easy to miss terms and make mistakes. MUST BE CONFIRMED MICROSCOPICALLY! How one understands but not necessarily computes the effect. Kubo approach: systematic formalism but not very transparent. Keldysh approach: also a systematic kinetic equation approach (equivalent to Kubo in the linear regime). In the quasi-particle limit it must yield Boltzmann semiclassical treatment. Microscopic vs. Semiclassical

Kubo microscopic approach to transport: diagrammatic perturbation theory Averaging procedures: = 1/  0 =  0  = + Bloch Electron Real Eigenstates Need to perform disorder average (effects of scattering) n, q Drude Conductivity σ = ne 2  /m * ~1/n i Vertex Corrections  1-cos(θ) Perturbation Theory: conductivity n, q 11

10 “Skew scattering” “Side-jump scattering” Intrinsic AHE: accelerating between scatterings n, q m, p n’, k n, q n’  n, q Early identifications of the contributions Vertex Corrections  σ Intrinsic ~  0 or n 0 i Intrinsic  σ 0 /ε F  ~  0 or n 0 i Kubo microscopic approach to AHE n, q m, p n’, k matrix in band index m’, k’

Defining intrinsic anomalous Hall effect in materials where AHE is dominated by scattering-independent mechanisms 9 n, q n’  n, q

Scattering independent regime Q: is the scattering independent regime dominated by the intrinsic AHE? 8

intrinsic AHE approach in comparing to experiment: phenomenological “proof” n, q n’  n, q 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 et al (2001),Taguchi et al., Science 291, 2573 (2001), Fang et al Science 302, 92 (2003) colossal magnetoresistance of manganites, Ye et~al Phys. Rev. Lett. 83, 3737 (1999). CuCrSeBr compounts, Lee et al, Science 303, 1647 (2004) Experiment  AH  1000 (  cm) -1 Theroy  AH  750 (  cm) -1 AHE in Fe AHE in GaMnAs 7

19 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Contributions understood in simple metallic 2D models Semi-classical approach: Gauge invariant formulation Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07 Kubo microscopic approach: in agreement with semiclassical Borunda, Sinova, et al PRL 07, Nunner, JS, et al PRB 08 Non-Equilibrium Green’s Function (NEGF) microscopic approach Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08

Comparing Boltzmann to Kubo (chiral basis) for “Graphene” model 4 Kubo identifies, without a lot of effort, the order in n i of the diagrams BUT not so much their physical interpretation according to semiclassical theory Sinitsyn et al 2007

Generalization to 3D General band structure in the presence of delta-correlated Gaussian disorder N-band projected Hamiltonian expressed via envelope fields In the presence of Gaussian disorder To test our theory we will consider band structures of a 2D Rashba and 3D Luttinger models: 6-band Luttinger model will also be considered Kovalev, Sinova, Tserkovnyak PRL 2010

Idea behind this calculation 1. Use Kubo-Streda formalism or linearized version of Keldysh formalism to obtain where 2. Integrate out sharply peaked Green’s functions which leads to integrals over the Fermi sphere and no dependence on disorder 3. In order to identify the relevant terms in the strength of disorder it is convenient to use diagrams Kovalev, Sinova, Tserkovnyak PRL 2010

AHE conductivity expressed through band structure Well known intrinsic contribution Side jump contribution related to Berry curvature Remaining side jump contribution Kovalev, Sinova, Tserkovnyak PRL 2010

Results for Luttinger model: simplest model of GaMnAs Kovalev, Sinova, Tserkovnyak PRL 2010

Nagaosa, JS, Onoda, Ong, MacDonald et al RMP 10 2 Kovalev, Sinova, Tserkovnyak PRL 2010

Anomalous Hall effect in the hopping regime Three regimes of anomalous Hall effect 1. Intrinsic regime: 2. Skew scattering: 3. Hopping regime: This scaling relation has been seen in many experiments: B. A. Aronzon etal., phys. stat. sol. (b) 218, 169 (2000). W. Allen,etal., Phys. Rev. B 70, (2004). H. Toyosaki etal., Nature, 3, 221 (2004) K. Ueno etal., Appl. Phys. Lett. 90, (2007) T. Miyasato etal., Phys. Rev. Lett., 99, (2007) D. Venkateshvaran etal., Phys. Rev. B 78, (2008) A. Fernández-Pacheco etal., Phys. Rev. B 77, (R) (2008) Previous Theories: S. H. Chun etal., Phys. Rev. Lett. 84, 757 (2000), A. A. Burkov and L. Balents, Phys. Rev. Lett. 91, (2003), Cannot explain the scaling relation in the experiment.

Phonon-assisted hopping between localized states The Hamiltonian describing localized states and e-ph interaction (Holstein 1961, Burkov etal, 2003) with i j k phonon Localization: phonon-assisted hopping Electric current between two sites: RiRi RjRj RkRk : direct conductance due to two-site hopping. : off-diagonal conductance due to three-site hopping.

Percolation theory For each two site, a bond that can conduct electricity establishes when the direct conductance between them is no less than a critical value (Ambegaokar et al., 1971): This gives the condition: RiRi RjRj connected RiRi RjRj disconnected For a site with energy, the average number of sites connecting to it satisfying above condition is given by:

The macroscopic AH conductivity/resistivity should be averaged along the critical path: Anomalous Hall conductivity via percolation theory Critical paths appear when the average number : Instead of exactly calculating the above extremely complicated integral, we shall evaluate its two limits: the lower limit and upper limit, which will be more meaningful. This is because, in the insulating regime, the system is very complicated and the relation between normal and Hall conductivity cannot be uniquely determined by a few parameters. Therefore, in this regime it is more reasonable to consider the scaling relation between them has a range. Xiong-Jun Liu, Sinova, unpub. 2010

The lower and upper limits are given by (note the differences in the constrain) For the Mott hopping, we find Physically, the upper limit (γ=1.34) corresponds to the situation that most triads in the system are equilateral triangles (this is actually a regular distribution), while for the lower limit (γ=1.68) the geometry of triads is randomly distributed. Since the impurity sites are randomly distributed, we expect the realistic result is usually close to the lower limit. This is true for the experiment. Xiong-Jun Liu, Sinova, unpub. 2010

31 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

32 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

33 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

34 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Spin-dependent Hall effects and other thoughts on recent progress and future challenges in spintronics II Progress in Spintronics and Graphene Research June 14 th, 2010 KITPC, Beijing, China Research fueled by: JAIRO SINOVA Texas A&M University Institute of Physics ASCR Hitachi Cambridge Joerg W ü nderlich, A. Irvine, et al Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al

36 Spintronics Workshop KITPC: activity report

Nagaosa, Sinova, Onoda, MacDonald, Ong, RMP 2010 Kovalev, Sinova, Tserkovnyak PRL 2010 Xiong-Jun Liu, Sinova, 2010

Nanoelectronics, spintronics, and materials control by spin-orbit coupling Valenzuela et al Nature 06 Inverse SHE Anomalous Hall effect: more than meets the eye Wunderlich, Kaestner, Sinova, Jungwirth PRL 04 Kato et al Science 03 Intrinsic Extrinsic V Mesoscopic Spin Hall Effect Intrinsic Brune,Roth, Hankiewicz, Sinova, Molenkamp, et al Nature Physics 10 Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Spin-injection Hall Effect Anomalous Hall Effect I _ FSOFSO FSOFSO _ _ majority minority V Spin Hall Effect I _ FSOFSO FSOFSO _ _ V

39 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Towards a realistic spin-based non-magnetic FET device [001] [100] [010] Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system? Long standing paradigm: Datta-Das FET (1990) Exploiting the large Rashba spin-orbit coupling in InAs Electrons are confined in the z-direction in the first quantum state of the asymmetric trap and free to move in the x-y plane. gate k y [010] k x [100] Rashba effective magnetic field ⊗⊗⊗

40 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Can we achieve direct spin polarization injection, detection, and manipulation by electrical means in an all paramagnetic semiconductor system? Long standing paradigm: Datta-Das FET (1990) Exploiting the large Rashba spin-orbit coupling in InAs Towards a realistic spin-based non-magnetic FET device High resistance “0” Low resistance “1” BUT l MF << L S-D at room temperature

41 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Dephasing of the spin through the Dyakonov-Perel mechanism L SD ~ μm l MF ~ 10 nm

42 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism). New paradigm using SO coupling: SO not so bad for dephasing 1) Can we use SO coupling to manipulate spin AND increase spin-coherence? Can we detect the spin in a non-destructive way electrically?

43 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling a 2DEG is well described by the effective Hamiltonian:  > 0,  = 0 [110] _ k y [010] k x [100] Rashba: from the asymmetry of the confinement in the z-direction  = 0,  < 0 [110] _ k y [010] k x [100] Dresselhauss: from the broken inversion symmetry of the material, a bulk property 1) Can we use SO coupling to manipulate spin AND increase spin-coherence?

44 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D electron gas with Rashba and Dresselhauss spin-orbit coupling Something interesting occurs when spin along the [110] direction is conserved long lived precessing spin wave for spin perpendicular to [110] The nesting property of the Fermi surface: Bernevig et al PRL 06, Weber et al. PRL 07 Schliemann et al PRL 04

45 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Effects of Rashba and Dresselhaus SO coupling  = -  [110] _ k y [010] k x [100]  > 0,  = 0 [110] _ k y [010] k x [100]  = 0,  < 0 [110] _ k y [010] k x [100]

46 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-dynamics in 2D systems with Rashba and Dresselhauss SO coupling For the same distance traveled along [1-10], the spin precesses by exactly the same angle. [110] _ _

Nanoelectronics, spintronics, and materials control by spin-orbit coupling 33 Persistent state spin helix verified by pump-probe experiments Similar wafer parameters to ours

48 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-helix state when α ≠ β Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 For Rashba or Dresselhaus by themselves NO oscillations are present; only and over damped solution exists; i.e. the spin-orbit coupling destroys the phase coherence. There must be TWO competing spin-orbit interactions for the spin to survive!!!

49 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism). New paradigm using SO coupling: SO not so bad for dephasing 1) Can we use SO coupling to manipulate spin AND increase spin-coherence? Can we detect the spin in a non-destructive way electrically? Use the persistent spin-Helix state and control of SO coupling strength (Bernevig et al 06, Weber et al 07, Wünderlich et al 09) ✓

50 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Type (i) contribution much smaller in the weak SO coupled regime where the SO- coupled bands are not resolved, dominant contribution from type (ii) Crepieux et al PRB 01 Nozier et al J. Phys. 79 Two types of contributions: i)S.O. from band structure interacting with the field (external and internal) Bloch electrons interacting with S.O. part of the disorder Lower bound estimate of skew scatt. contribution AHE contribution to Spin-injection Hall effect in a 2D gas Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09

51 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Local spin-polarization → calculation of AHE signal Weak SO coupling regime → extrinsic skew-scattering term is dominant Lower bound estimate Spin-injection Hall effect: theoretical expectations

52 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Problem: Rashba SO coupling in the Datta-Das SFET is used for manipulation of spin (precession) BUT it dephases the spin too quickly (DP mechanism). New paradigm using SO coupling: SO not so bad for dephasing 1) Can we use SO coupling to manipulate spin AND increase spin-coherence? Can we detect the spin in a non-destructive way electrically? ✓ Use the persistent spin-Helix state and control of SO coupling strength (Bernevig et al 06, Weber et al 07, Wünderlich et al 09) Use AHE to measure injected current polarization at the nano-scale electrically (Wünderlich, et al 09, 04) ✓

53 Nanoelectronics, spintronics, and materials control by spin-orbit coupling 2DHG 2DEG e h e e ee e h h h h h VsVs VdVd VHVH Spin-injection Hall effect device schematics For our 2DEG system: Hence α ≈ -β

54 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-injection Hall device measurements trans. signal σoσoσoσo σ+σ+σ+σ+ σ-σ-σ-σ- σoσoσoσo VLVL

55 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Spin-injection Hall device measurements trans. signal σoσoσoσo σ+σ+σ+σ+ σ-σ-σ-σ- σoσoσoσo VLVL SIHE ↔ Anomalous Hall Local Hall voltage changes sign and magnitude along a channel of 6 μm

56 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Further experimental tests of the observed SIHE

57 Nanoelectronics, spintronics, and materials control by spin-orbit coupling T = 250K Further experimental tests of the observed SIHE (preliminary)

58 Nanoelectronics, spintronics, and materials control by spin-orbit coupling [110] - bar [1-10] - bar Further experimental tests of the observed SIHE (preliminary)

59 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Summary of spin-injection Hall effect  Basic studies of spin-charge dynamics and Hall effect in non-magnetic systems with SO coupling  Spin-photovoltaic cell: solid state polarimeter on a semiconductor chip requiring no magnetic elements, external magnetic field, or bias  SIHE can be tuned electrically by external gate and combined with electrical spin-injection from a ferromagnet (e.g. Fe/Ga(Mn)As structures)

60 Nanoelectronics, spintronics, and materials control by spin-orbit coupling First gating attempts of SIHE device

61 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Gating of SIHE device

62 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Gating of SIHE device (preliminary) Closing gate 1 and 2 gives no signal in H1 and H2, closing gate 2 only and keeping gate 1 open gives a signal only in H1, opening both gates gives a signal in both H1 and H2. The signal in H1 is about 6 times larger than the signal in H2 (4 um away from H1)

63 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

64 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

65 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

66 Nanoelectronics, spintronics, and materials control by spin-orbit coupling Control of materials and transport properties via spin-orbit couplingAs Ga Mn New magnetic materials Nano- transport Spintronic Hall effects Magneto- transport Caloritronics Topological transport effects Effects of spin-orbit coupling in multiband systems

Discussion points Spin-injection/ manipulation/detection Magnetization dynamics (current induced, spin-wave logic, anisotropy engineering..) Spin-caloritronics? Topological Insulators Anomalous and Spin Hall transport Majorana Fermions? Physics of strongly coupled multi-band systems (SO, etc.) Now we have a DD-room temperature transistor, so Semiconducting ferromagnets and anti- ferromagents Now we have a DD-room temperature transistor, so what? is it useful? What is next? Strong interacting regime, strong SO? Spin Seebeck effect? present explanation doubtful Will these “new” old materials give new many-body states? Better understanding but is there anything new and/or useful? microscopic/macroscopic room temperature DMS unlikely-- what about DAFS? If observed then what next?

69 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

70 Nanoelectronics, spintronics, and materials control by spin-orbit coupling