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

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Freescale's MRAM – a new kind of memory chip

4Mbit memory array (2006)

Universität Regensburg

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)

Universität Regensburg

Tuning of magnetization by electric fields

H. Ohno et al., Nature (2000)

Tunability of ferromagnetism

Universität Regensburg

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:

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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

× =

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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)

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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

Universität Regensburg

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)

Universität Regensburg

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

]

Universität Regensburg

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]

Universität Regensburg

Spin-galvanic-effect ….

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

4.2 K

Universität Regensburg

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

γ −α⎛ ⎞ ∝ ⎜ ⎟α −γ⎝ ⎠

j S Direction of photocurrent:

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

j S

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

Universität Regensburg

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)

Universität Regensburg

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