Spin-injection Hall Effect: a new member of the spintronics Hall family Nanoelectronics, spintronics, and materials control in multiband complex systems JAIRO SINOVA Texas A&M University Institute of Physics ASCR Institute of Physics ASCR Tomas Jungwirth, Vít Novák, et al Hitachi Cambridge Joerg Wünderlich, A. Irvine, et al University of Texas Allan MacDonald, et al University of Würzburg Laurens Molenkamp, E. Hankiewiecz, et al University of Nottingham Bryan Gallagher, Richard Campion, et al. University of Texas December 3rd, 2009 Research fueled by:

Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling Technology motivation Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors Tunneling anisotropic magnetoresistance Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

The need for basic research in technology development Industry has been successful in doubling of transistor numbers on a chip approximately every 18 months (Moore’s law). Although expected to continue for several decades several major challenges will need to be faced. Circuit heat generation is one key limiting factor for scaling device speed The IT industry, as most of you know, has been very successful for close to over five decades in maintaining More’s law of exponential growth of computational power which is expected to continue for several more decades within the present technological bases. Although the demise within 10 year of this exponential progress has been announced over the past three decades there are certain fundamental obstacles which the IT community face which could stop this progression. One of this very important roadblocks is the power density generation in circuits. One can see the problem by looking at its evolution over the last decade as shown in this figure. Today’s circuits are using about 100 W/cm^2, about the limiting capabilities of air cooling, and unfortunately things are getting hotter. This power density increase already brought the bipolar transistor based technology of the eighties to its collapse which was then solved by going to the new CMOS architecture to build transistors. Nanoelectronics, spintronics, and materials control by spin-orbit coupling

The need for basic research in technology development International Technology Roadmap for Semiconductors 1D systems Single electron systems (FETs) Spin dependent physics Ferromagnetic transport Molecular systems New materials Strongly correlated systems Basic Research Inc. Nanoelectronics The industry has enjoyed a nice ride in this technology road but they are also very aware of the possible obstacles for progress. They have laid them out in detail in the International Technology Roadmap for Semiconductors (which is updated yearly) where they identify important roadblocks ahead. This is where Basic Research begins to play its important role through the study of topics connected loosely with possible IT which can create roads that could overcome such roadblocks. One important topic is Nanoelectornics and its many subfields such as (list here) as well as new materials and strongly correlated systems. All these “alternative roads” to the present one are of course closely interlinked and one should not think of them as separate fields at all and are indeed many of the topics which are tackled here at Julich and within the JARA-FIT program. Within the US a consortium of several technology companies, among them IBM and Intel, have implemented the Nanoelectronics Research Initiative in which several virtual institutes have been formed, each made up of a cluster of University Principal Investigators connected by general themes of study of basic science research of interest to the industry. Nanoelectronics Research Initiative SWAN MIND INDEX WIN Advanced Micro Devices, Inc. IBM Corporation Intel Corporation MICRON Technology, Inc. Texas Instruments Incorporated Nanoelectronics, spintronics, and materials control by spin-orbit coupling

International Technology Roadmap for Semiconductors 2005: EMERGING RESEARCH DEVICES Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling Technology motivation Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors Tunneling anisotropic magnetoresistance Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Spin-orbit coupling interaction (one of the few echoes of relativistic physics in the solid state) Classical explanation (in reality it is quantum mechanics + relativity ) “Impurity” potential V(r) Produces an electric field ∇V Beff p s In the rest frame of an electron the electric field generates and effective magnetic field Motion of an electron This gives an effective interaction with the electron’s magnetic moment Consequences Effective quantization axis of the spin depends on the momentum of the electron. Band structure (group velocities, scattering rates, etc.) mixed strongly in multi-band systems If treated as scattering the electron gets asymmetrically scattered to the left or to the right depending on its “spin” Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

Control of materials and transport properties via spin-orbit coupling Ferromagnetic Semiconductors Need true FSs not FM inclusions in SCs Mn Ga As GaAs - standard III-V semiconductor + Group-II Mn - dilute magnetic moments & holes (Ga,Mn)As - ferromagnetic semiconductor Nano-transport Magneto-transport Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Transition to a ferromagnet when Mn concentration > 1.5-2 % DOS spin ↓ spin ↑ valence band As-p-like holes Nano-transport Mn Ga As >2% Mn EF ferromagnetism onset near MIT when localization length is longer than Mn-Mn spacing. Zener type model Magneto-transport As Ga Mn New magnetic materials Jungwirth, Sinova, et al RMP 06 Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Mn Ga As Ferromagnetic Ga1-xMnxAs x>1.5% Ferromagnetism mediated by delocalized band states: polarized carriers with large spin-orbit coupling px py ∇V Hso p s Many useful properties FM dependence on doping Low saturation magnetization Transition to a ferromagnet when Mn concentration increases DOS spin ↓ spin ↑ valence band As-p-like holes Mn Ga As >2% Mn EF ferromagnetism onset near MIT when localization length is longer than Mn-Mn spacing. Zener type model Nano-transport Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects What are the consequences of the strong spin-orbit coupling of the carriers “gluing” the localized Mn moments ? Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Control of magnetic anisotropy Strain & SO ↓ Strain induces changes in the band structure and, in turn, change the ferromagnetic easy axis. Piezoelectric devices: fast magnetization switching Wunderlich, Sinova, et al PRB 06 Tensile strain Compressive strain M → Mn Ga As Ferromagnetic Ga1-xMnxAs x>1.5% Ferromagnetism mediated by delocalized band states: polarized carriers with large spin-orbit coupling px py ∇V Hso p s What are the consequences of the strong spin-orbit coupling of the carriers “gluing” the localized Mn moments ? Many useful properties FM dependence on doping Low saturation magnetization Nano-transport Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Magneto-transport in GaMnAs G(T)MR ~ 100% MR effect Nano-transport Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Fert, Grunberg et al. 1988 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Magneto-transport in GaMnAs G(T)MR ~ 100% MR effect Nano-transport Exchange split bands: σ~ TDOS(↑↓) < TDOS(↑↑) Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Fert, Grunberg et al. 1988 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Magneto-transport in GaMnAs TAMR Tunneling Anisotropic Magnetoresistance discovered in (Ga,Mn)As Gold et al. PRL’04 Au σ ~ TDOS (M) → TAMR can be enormous depending on doping Now discovered in FM metals !! TMR ~ 100% MR effect Nano-transport Exchange split bands: σ~ TDOS(↑↓) < TDOS(↑↑) Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Ruster, JS, et al PRL05 Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Control of materials and transport properties via spin-orbit coupling Magneto-transport in GaMnAs TAMR Tunneling Anisotropic Magnetoresistance discovered in (Ga,Mn)As Gold et al. PRL’04 Au σ ~ TDOS (M) → TAMR can be enormous depending on doping Ruster, JS, et al PRL05 Now discovered in FM metals !! Nano-transport Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

Control of materials and transport properties via spin-orbit coupling Nano-transport Anomalous Hall effects I FSO majority minority V Nagaosa, Sinova, Onoda, MacDonald, Ong, RMP 10 Magneto-transport As Ga Mn New magnetic materials Effects of spin-orbit coupling in multiband systems Caloritronics Spintronic Hall effects Topological transport effects Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Anomalous Hall Effect: the basics Spin dependent “force” deflects like-spin particles I _ FSO majority minority V ρH=R0B ┴ +4π RsM┴ InMnAs Simple electrical measurement of out of plane magnetization 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 Vimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(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/ni Vimp(r) (Δso>ħ/τ) or ∝ λ*∇Vimp(r) (Δso<ħ/τ) A Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Contributions understood in simple metallic 2D models 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 Semi-classical approach: Gauge invariant formulation Kovalev, Sinova et al PRB 08, Onoda PRL 06, PRB 08 Sinitsyn, Sinvoa, et al PRB 05, PRL 06, PRB 07 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Phenomenological scaling regimes of AHE Review of AHE (to appear in RMP 2010), Nagaosa, Sinova, Onoda, MacDonald, Ong A high conductivity regime for σxx>106 (Ωcm)-1 in which AHE is skew dominated A good metal regime for σxx ~104-106 (Ωcm) -1 in which σxyAH~ const A bad metal/hopping regime for σxx<104 (Ωcm) -1 for which σxyAH~ σxyα with α>1 Scattering independent regime Q: is the scattering independent regime dominated by the intrinsic AHE? Skew dominated regime Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Experiment: σAH ∼ 1000 (Ω cm)-1 Intrinsic AHE approach in comparing to experiment: phenomenological “proof” n, q n’≠n, q DMS systems (Jungwirth et al PRL 2002, Jungwirth, Sinova, et al APL 03) layered 2D ferromagnets e.g. SrRuO3 ferromagnets (Taguchi et al, Science 01, Fang et al, Science 03) CuCrSeBr compounds ( Lee et al, Science 04) Fe (Yao et al PRL 04) Experiment: σAH ∼ 1000 (Ω cm)-1 Theory: σAH ∼ 750 (Ω cm)-1 AHE in Fe AHE in GaMnAs Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling Technology motivation Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors Tunneling anisotropic magnetoresistance Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Towards a realistic spin-based non-magnetic FET device 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 Unfortunately it has not worked : no reliable detection of spin-polarization in a diagonal transport configuration No long spin-coherence in a Rashba spin-orbit coupled system (Dyakonov-Perel mechanism) Nanoelectronics, spintronics, and materials control by spin-orbit coupling

New paradigm using SO coupling: SO not so bad for dephasing 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). 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) Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Device schematic - material p 2DHG i n

Device schematic - trench p 2DHG i n

Device schematic – n-etch p n 2DHG 2DEG

Device schematic – Hall measurement Vd Vs VH 2DHG 2DEG 22

Spin-injection Hall effect device schematics 2DHG 2DEG e h Vs Vd VH Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

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

Spin-dynamics in 2D electron gas with Rashba and Dresselhauss SO coupling a 2DEG is well described by the effective Hamiltonian: 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 Nanoelectronics, spintronics, and materials control by spin-orbit coupling For our 2DEG system: Hence α ≈ -β

The long lived spin-excitation: “spin-helix” Finite wave-vector spin components Shifting property essential An exact SU(2) symmetry Only Sz, zero wavevector U(1) symmetry previously known: J. Schliemann, J. C. Egues, and D. Loss, Phys. Rev. Lett. 90, 146801 (2003). K. C. Hall et. al., Appl. Phys. Lett 83, 2937 (2003). 30 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Effects of Rashba and Dresselhaus SO coupling α > 0, β = 0 [110] _ ky [010] kx [100] α = -β [110] _ ky [010] kx [100] α = 0, β < 0 [110] _ ky [010] kx [100] 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] [110] _ [110] _ Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

The Spin-Charge Drift-Diffusion Transport Equations For arbitrary α,β spin-charge transport equation is obtained for diffusive regime For propagation on [1-10], the equations decouple in two blocks. Focus on the one coupling Sx+ and Sz: For Dresselhauss = 0, the equations reduce to Burkov, Nunez and MacDonald, PRB 70, 155308 (2004); Mishchenko, Shytov, Halperin, PRL 93, 226602 (2004) Nanoelectronics, spintronics, and materials control by spin-orbit coupling 34

Spin-helix state when α ≠ β Spatial variation scale consistent with the one observed in SIHE Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

AHE contribution to Spin-injection Hall effect Two types of contributions: S.O. from band structure interacting with the field (external and internal) Bloch electrons interacting with S.O. part of the disorder 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 Lower bound estimate of skew scatt. contribution Wunderlich, Irvine, Sinova, Jungwirth, et al, Nature Physics 09 Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

Nanoelectronics, spintronics, and materials control in multiband complex systems through spin-orbit coupling Role of basic research in technology development Control of material and transport properties through spin-orbit coupling: Ferromagnetic semiconductors Tunneling anisotropic magnetoresistance Anomalous Hall effect and spin-dependent Hall effects Spin injection Hall effectMaking the deviceBasic observation; analogy to AHEThe effective HamiltonianSpin-charge DynamicsStrong and weak spin-orbit couple contributions of AHE SIHE new experimental results, further checks Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

Non public slides deleted. Please contact Sinova if interested Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Non public slides deleted. Please contact Sinova if interested Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Semiclassical Monte Carlo of SIHE Numerical solution of Boltzmann equation Spin-independent scattering: Spin-dependent scattering: phonons, remote impurities, interface roughness, etc. side-jump, skew scattering. AHE Realistic system sizes (μm). Less computationally intensive than other methods (e.g. NEGF). Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Single Particle Monte Carlo Spin-Dependent Semiclassical Monte Carlo Temperature effects, disorder, nonlinear effects, transient regimes. Transparent inclusion of relevant microscopic mechanisms affecting spin transport (impurities, phonons, AHE contributions, etc.). Less computationally intensive than other methods(NEGF). Realistic size devices. Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Effects of B field: current set-up Out-of plane magnetic field In-Plane magnetic field Nanoelectronics, spintronics, and materials control by spin-orbit coupling

Comment 1: Datta-Das type of device S. Datta, B. Das, Appl. Phys. Lett. 56 665 (1990). … works only - if channel is 1dimensional - or under Spin Helix conditions for 2D channel Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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

The family of spintronic Hall effects SHE B=0 charge current gives spin current Optical detection SHE-1 B=0 spin current gives charge current Electrical detection j s – + + + + + + + + + + iSHE AHE B=0 polarized charge current gives charge-spin current Electrical detection I _ FSO majority minority V Nanoelectronics, spintronics, and materials control by spin-orbit coupling

The family of spintronics Hall effects SIHE B=0 Optical injected polarized current gives charge current Electrical detection SHE B=0 charge current gives spin current Optical detection SHE-1 B=0 spin current gives charge current Electrical detection AHE B=0 polarized charge current gives charge-spin current Electrical detection 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) Nanoelectronics, spintronics, and materials control by spin-orbit coupling

A question from Natasha Dear Professor Sinova,           My name is Natasha, and I am a middle school student. Thank you for taking the time to read this email. I read the article, "New Technology May Cool The Laptop" on www.sciencedaily.com, and it mentioned your name. I was wondering if you could answer a few questions:   1. When it says you use the electrons to process information, what type of information are you referring to?(i.e. emails, documents, etc.) 2. Does it matter what type of laptop your device is used on? Thank you again, Natasha Nanoelectronics, spintronics, and materials control by spin-orbit coupling

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