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Transcript of Spin + Electronics = Universitأ¤t Regensburg Dieter Weiss, Universitأ¤t Regensburg Spin +...

  • Universität Regensburg

    Dieter Weiss, Universität Regensburg

    Spin + Electronics = Spintronics

    Electronic uses electrical charge of electrons….

    = − ⋅

    = ⋅ →

    19

    31 0

    e 1.602 10 C m 9.1 10 kg m *

    = ±

    μ = ⋅ 24B

    1spin 2

    9.27 10 J/T

    ….but electron possesses also spin and hence a magnetic moment, responsible, e.g., for ferromagnetism

  • Universität Regensburg

    GMR: Giant magnetoresistance

    GMR read-out heads in hard drives

    Grünberg group: PRB 39, 4828 (1989) Fert group: PRL,61, 2472 (1988)

    ΔR /R

    (% )

  • Universität Regensburg

    TMR: tunnelling magnetoresistance

    Julliere, Meservey, Tedrow, Moodera, Miyazaki…

    Nonvolatile MRAM memory

  • Universität Regensburg

    Freescale's MRAM – a new kind of memory chip

    4Mbit memory array (2006)

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    Memory cell of MRAM

  • Universität Regensburg

    Functionality provided by metal-oxide devices

    How abb

    out sem

    icon duc

    tor spin

    tro nics

    ?

  • Universität Regensburg

    Ferromagnetic semiconductor: Ga1-xMnxAs

    Good Mn are substitutinal: •Act as acceptors providing holes •Holes mediate ferromagnetic order between 5/2-Mn moments

    Bad Mn are interstitial: •Act as double donors thus compensating holes

    •Interstitial Mn is RKKY-inactive •Forms antiferromagnetic pairs with substitutional Mn

    Curie-temperature in mean field theory: MF 2 1/3cT J p x∝

    hole concentration Mn-concentrationT. Dietl (2000)

    H. Ohno et al. (1992)

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    Tuning of magnetization by electric fields

    H. Ohno et al., Nature (2000)

    Tunability of ferromagnetism

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    Combination of ferromagnets with semiconductors?

    Transistor: Most important device in electronics

    Can electronics (logic) be combined with magnetism (memory)?

    Review: Wolf et al., Science 294, 1488 (2001) Awschalom & Flattè, Nature Physics 3, 153 (2007)

    10nm

  • Universität Regensburg

    V

    - v Beff

    - v Beff

    -v Beff

    V/2

    Paradigmatic device: Datta-Das spin transistor

    S. Datta & B. Das, Appl. Phys. Lett. 56, 665 (1990)

  • Universität Regensburg

    V

    Spin-injection

    Spin-detectionTo avoid conductanceMismatch ⇒ tunneling barriers*

    Spin-manipulation * 2

    G(2 L/V )mΔθ = α

    G. Schmidt et al., PRB 62, R4790 (2000) E. Rashba, Phys. Rev. B 62 R16267 (2000) A. Fert et al. , Phys. Rev. B 64 184420 (2001)

    *

    Paradigmatic device: Datta-Das spin transistor

    L

  • Universität Regensburg

    X. Lou et al, Nature Physics 3, 197 (2007)

    Detection of spin transport in lateral Fe/GaAs devices

    Detection of clear spin signal and Hanle effect only in non-local transport geometry:

  • Universität Regensburg

    X. Lou et al, Nature Physics 3, 197 (2007)

    Detector signal: Hanle effect:

  • Universität Regensburg

    Outline

    Tunneling magneto- resistance

    Fe/GaAs/Fe

    Spin-orbit interaction in 2DEG

    Separation of Rashba- and Dresselhaus

    contributions

    TAMR Tunneling anisotropic magnetoresistance

  • Universität Regensburg

    Beff

    -(Z-1)e -(Z-1)e-(Z-1)e

    Spin-orbit interaction

    - Bohr magneton (μB)

    Beff due to orbital motion= ・

    Origin of spinOrigin of spin--orbit interactionorbit interaction

    Dirac:

    SO B 2 E pˆ ˆH 2mc

    ×⎡ ⎤= −μ σ ⋅ ⎢ ⎥⎣ ⎦ Zeeman B ˆ ˆH B= −μ σ ⋅

    eff 2 E pB 2mc

    × =

  • Universität Regensburg

    Origin of electric field E in solidsOrigin of electric field E in solids

    Bulk inversion asymmetry (BIA) Lack of inversion symmetry in III-V semiconductors "Dresselhaus contribution γ"

    Structure inversion asymmetry (SIA) due to macroscopic confining potential: "Rashba contribution α". Tunable by external electric field!

    Interface asymmetry

    2(z)Ψ

    V(z)

  • Universität Regensburg

    2 2

    SO kˆ ˆH H with

    2m = +

    x y y x x x y ySO ˆ H ( k k ) ( k k )= α σ − σ + γ σ − σ

    Pauli spin matrix

    Spin-orbit interaction in 2DEG: Rashba & Dresselhaus terms

    Rashba Dresselhaus

    tunable by gate voltage

    2 2kE k 2m

    = ± α

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    Description of zero-field spin splitting by Beff

    = α σ − σ + γ σ − σ σ ⋅SO x y y x x x ey fy fˆ H ( k k ) ( ~ ˆ Bk k )

    Rashba Dresselhaus

    x x y y z zeff B B Bˆ Bσ ⋅ = σ + σ + σ

    Comparison of coefficients. E.g. only Rashba contribution: yeff x

    k B

    k ⎛ ⎞

    ∝ ⎜ ⎟−⎝ ⎠

    effB

    E.A. de Andrada e Silva PRB 46, 1921 (1992)

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    Presence of Rashba & Dresselhaus contributions to SO:

    Rashba or Dresselhaus

    Rashba and Dresselhaus

    = ± α − γ 2 2kE ( ) k 2m

    = ± α + γ 2 2kE ( ) k 2m

    ]

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    Spin-galvanic effect:

    Ganichev et al., Nature , 153 (2002)417

    jx

    SyM M

    2DEG

    α αβ β β

    = ∑j Q S

    In plane spin polarization is prepared by an in-plane magnetic field (like Hanle effect)

    A spin-polarization in y-direction is expected to drive a current in x-direction (C2v symmetry)

    Spin polarization drives an electrical current:S

    [110] [110]

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    Spin-galvanic-effect ….

    Ganichev et al., Nature , 153 (2002)417

    4.2 K

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    Rashba (γ=0) Dresselhaus (α = 0) α γ ≠both ( and 0)

    γ −α⎛ ⎞ ∝ ⎜ ⎟α −γ⎝ ⎠

    j S Direction of photocurrent:

  • Universität Regensburg

    Direction of photocurrent: γ −α⎛ ⎞ ∝ ⎜ ⎟α −γ⎝ ⎠

    j S

    Rashba (γ=0) Dresselhaus (α = 0) α γ ≠both ( and 0)

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    D Rj cos( ) j sin(j( )) ϕ+ +θ= θ − ϕθ

    ϕ θ S

    j

    Direction of photocurrent:

    S. D. Ganichev et al., PRL 92, 256601 (2004)

    γ −α⎛ ⎞ ∝ ⎜ ⎟α −γ⎝ ⎠

    j S

    Rashba (γ=0) Dresselhaus (α = 0) α γ ≠both ( and 0)

  • Universität Regensburg

    S

    B

    θ = θ + ϕ + θ − ϕD Rj( ) j cos( ) j sin( )

    ϕ: direction of spin polarization S, adjusted by direction of B

    θ: direction of photocurrent

    Experiment: angular dependence of photo current

    Sample*: InAs/Al0.3Ga 0.7Sb QW nS = 1.3 x 1012 cm-2 μ = 20.000 cm2/Vs at RT

    * from J. de Boeck and S. Borghs, IMEC

    FIR-Laser: λ = 148 μm, 10 kW

    θj( )

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    Experimental result: angular dependence of photocurrent

    = − RDj j j

    += RDj j j

    α= γ ≈R D/ /j j 2.1

    S. D. Ganichev et al., PRL 92, 256601 (2004)

    ϕ = °45

    ϕ = − °45

    Room temperature

  • Universität Regensburg

    Experiment: continued

    = γα ±≈DR / / 2j .1 ( 0j .25)also here:

    theoretical value from k.p calculations: α/γ = 1.85 Pfeffer, Zawadzki, PRB59, R5312 (1999)

    ϕ = °0 S. D. Ganichev et al., PRL 92, 256601 (2004)

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    Magnetic Tunnel Junctions T. Miyazaki and N.J. Tezuka JMMM 139, L231 (1995); J.S. Moodera, et al. PRL 74, 3273 (1995).

    Small TMR and amorphous barrier (Al2O3)⇒ Julliere model

  • Universität Regensburg

    Tunneling between ferromagnets

    Jullière model:

    1 2 1 2

    1 2 1 2

    I D D D D I D D D D

    ↑↑ ↑ ↑ ↓ ↓

    ↑↓ ↑ ↓ ↓ ↑

    ∝ +

    ∝ +

    iD = Density of states in contact 1, 2

    Spin polarization:

    Tunneling magnetoresistance (TMR):

    1 1 2 2 1 2

    1 1 2 2

    I I D D D D PP

    I I D D D D ↑↑ ↑↓ ↑ ↓ ↑ ↓

    ↑↑ ↑↓ ↑ ↓ ↑ ↓

    − − − = ⋅ =

    + + +

    1 2

    1 2

    R R I I 2PPTMR R I 1 PP

    ↑↓ ↑↑ ↑↑ ↑↓

    ↑↑ ↑↓

    − − = = =

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    P TMR

    Fe

    Co

    Ni

    44% 48%

    34% 26%

    11% 1%

    DOS and P: bcc iron

    Energy (eV)

    de ns

    ity of

    s ta

    te s

    EF

    1 2

    1 2

    R R 2PPTMR R 1 PP

    ↑↓ ↑↑

    ↑↑

    − = =

  • Universität Regensburg

    [1] Yuasa et al., Jpn. J. Appl. Phys. 43, L558 (2004); [2] Yuasa et al., Nature Mater. 3, 868 (2004); [3] Parkin et al., Nature Mater. 3, 862 (2004); [4] Djayaprawira et al., Appl. Phys.Lett. 86, 092502 (2005)

    Huge TMR in epitaxial Fe/MgO/Fe systems

  • Universität R