Universität Regensburg

Dieter Weiss, Universität Regensburg

Spin + Electronics = Spintronics

Electronic uses electrical charge of electrons….

−

−

= − ⋅

= ⋅ →

19

310

e 1.602 10 Cm 9.1 10 kg m *

−

= ±

μ = ⋅ 24B

1spin2

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

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Functionality provided by metal-oxide devices

Howabb

outsem

iconduc

torspin

tronics

?

Universität Regensburg

Ferromagnetic semiconductor: Ga1-xMnxAs

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

Bad Mn are interstitial:•Act as double donors thuscompensating holes

•Interstitial Mn is RKKY-inactive•Forms antiferromagnetic pairswith substitutional Mn

Curie-temperaturein mean field theory: MF 2 1/3

cT 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

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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

- vBeff

- vBeff

-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 ⇒ tunnelingbarriers*

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-localtransport 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 interactionin 2DEG

Separation of Rashba-and Dresselhaus

contributions

TAMRTunneling anisotropicmagnetoresistance

Universität Regensburg

Beff

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

Spin-orbitinteraction

- Bohr magneton(μB)

Beffdue to orbital motion= ・

Origin of spinOrigin of spin--orbit interactionorbit interaction

Dirac:

SO B 2E pˆ ˆH2mc

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

eff 2E pB2mc

×=

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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)

Universität Regensburg

2 2

SOkˆ ˆH H with

2m= +

x y y x x x y ySOˆ 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 k2m

= ± 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

kB

k⎛ ⎞

∝ ⎜ ⎟−⎝ ⎠

effB

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

Universität Regensburg

Presence of Rashba & Dresselhaus contributions to SO:

Rashba orDresselhaus

Rashba and Dresselhaus

= ± α − γ2 2kE ( ) k2m

= ± α + γ2 2kE ( ) k2m

]

Universität Regensburg

Spin-galvanic effect:

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

jx

SyM M

2DEG

α αβ ββ

= ∑j Q S

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

A spin-polarization in y-directionis 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 SDirection 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

ϕθ 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 QWnS = 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( )

Universität Regensburg

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

Universität Regensburg

Magnetic Tunnel JunctionsT. 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 DI D D D D

↑↑ ↑ ↑ ↓ ↓

↑↓ ↑ ↓ ↓ ↑

∝ +

∝ +

iD = Density of states in contact 1, 2

Spin polarization:

Tunneling magnetoresistance (TMR):

1 1 2 21 2

1 1 2 2

I I D D D DPP

I I D D D D↑↑ ↑↓ ↑ ↓ ↑ ↓

↑↑ ↑↓ ↑ ↓ ↑ ↓

− − −= ⋅ =

+ + +

1 2

1 2

R R I I 2PPTMRR 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)

dens

ityof

sta

tes

EF

1 2

1 2

R R 2PPTMRR 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 Regensburg

coherent transport

electron

scattering

electron

Incoherent vs. coherent tunneling

amorphousbarrier,e.g. Al-O

crystallinebarrier,e.g., MgO

fm electrode

fm electrode

Jullière model Landauer-Büttikerapproach

Universität Regensburg

Yuasa et al., Nature Materials 3, 868 (2004)

Huge TMR in epitaxial Fe/MgO/Fe systems

Universität Regensburg

Band structure of iron

symmetry of statesis relevant!

Universität Regensburg

Fe majority Δ1, ∆5, ∆2’Fe minority ∆2, ∆5, ∆2’

MgO lets through ∆1 mostly

Bands of MgOwith smallest κ

MgO acts as spin filter ….calculation: Heiliger et al. Phys. Rev. B 2006

Universität Regensburg

Fe FeGaAs

BΦ

EF5nm – 10nm

Spin-polarized tunneling through GaAs barriersSpin-injection: Spin-polarized tunneling through Schottky barrier →

upper limit for spin-injection4-point measurements

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-localtransport geometry:

How about tunneling in metal-semiconductor tunneling structures?

Universität Regensburg

Fe FeGaAs

BΦ

EF5nm – 10nm

Spin-polarized tunneling through GaAs barriersSpin-injection: Spin-polarized tunneling through Schottky barrier →

upper limit for spin-injection4-point measurements

Universität Regensburg

Fe

GaAs

AlGaAs

Fe

GaAs

TEM-micrograph:C.-H. Lai, Tsing Hua University, Taiwan

Universität Regensburg

TMR: crystalline tunneling barrier, polycrystalline iron

at 4.2 K……

B (T)

R (Ω

)TMR= 5.6%P = 16.5%

Co/Fe/GaAs(8nm)/Fe

4.2K5 mV bias

J. Moser et al. Appl. Phys. Lett. 89, 162106 (2006)

Universität Regensburg

…and at room temperature

TMR= 1.55%P = 8.8%

Co/Fe/GaAs(8nm)/Fe

4.2K5 mV bias

B (T)

R (Ω

)

J. Moser et al. Appl. Phys. Lett. 89, 162106 (2006)

Universität Regensburg

substrate

GaAs8 nm

Growth of GaAs barrier in molecular beam epitaxy system

Subsequently, the wafer is transferred to a magnetronsputtering system to deposit iron epitaxially

J. Moser et al. Appl. Phys. Lett. 89, 162106 (2006)

Device fabrication: one epitaxial Fe/GaAs interface

Universität Regensburg

UHV-Transport-System

HL-MBE Sputteranlage

Magnetron-Sputtering

SystemMBE

Growth of epitaxial Fe/GaAs interface

W. Wegscheider

Universität Regensburg

Substrate

GaAs8 nmFe

Substrate

FeGaAs

Substrate

Fe

Device fabrication

Universität Regensburg

AlGaAs

Fe

GaAs

TEM-micrograph:C.-H. Lai, Tsing Hua University, Taiwan

Universität Regensburg

Tunneling barrier sandwiched between two ferromagnetic layers

Experiments in TMR geometry

Fe

Fe

GaAs

Universität Regensburg

epitaxialinterface

V

Bias dependence of TMR

J. Moser et al. Appl. Phys. Lett. 89, 162106 (2006)

1 2

1 2

2PPTMR1 PP

=−

Jullière

Universität Regensburg

Outline

Tunneling magneto-resistance

Fe/GaAs/Fe

Spin-orbit interactionin 2DEG

Separation of Rashba-and Dresselhaus

contributions

TAMRTunneling anisotropicmagnetoresistance

Universität Regensburg

Are always two ferromagnetic layers necessary to see a magnetizationdependent resistance?

Our model system: Fe/GaAs/Au with epitaxial Fe/GaAs interface

R1

M

R2

M

1 2R R≠

FeGaAsAu

Spintronic with only one magnetic layer

Fe

GaAs

Au

Universität Regensburg

So far only observed for ferromagneticsemiconductors: (Ga,Mn)As/Al2O3/Au:

Gould et al. PRL 93, 117203 (2004)

TAMR: Tunneling Anisotropic Magnetoresistance

Non-epitaxial interface & amorphous barrier

Universität Regensburg

90°

[110]

[110]

-0,3 -0,2 -0,1 0,0 0,1 0,2 0,3918,0

918,5

919,0

919,5

920,0

920,5

R (Ω

)

B (T)

"TAMR" = -0,2 %

Tunneling magnetoresistance: B along [110] (at +89 mV)-

J. Moser et al., cond-mat/0611406

Universität Regensburg

-0,2 -0,1 0,0 0,1 0,2918,0

918,5

919,0

919,5

920,0

920,5

R (Ω

)

B (T)

"TAMR" = 0,08 %

0°

[110]

[110]

Tunneling magnetoresistance: B along [110] (at +89 mV)

J. Moser et al., cond-mat/0611406

Universität Regensburg

measured at T = 4.2 K and -90 mV

B = 0.5 Tesla

Co/Fe(epi)/GaAs(8nm)/Au

R

M

FeGaAsAu

J. Moser et al., cond-mat/0611406

Angular dependence of TAMR: negative bias

B

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measured at T = 4.2 K and +90 mV

B = 0.5 Tesla

Co/Fe(epi)/GaAs(8nm)/Au

J. Moser et al., cond-mat/0611406

Angular dependence of TAMR: positive bias

R

M

FeGaAsAu

T-dependence: see Lobenhofer et al.HL 19.4 Tue 11:30 H14

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Fe Au

zl zr

z

EF

φb

0 z BR DH H H H H= + + +

BR x y y x ii l r

i,

1H ( p p ) (z z )=

= σ − σ δ −α∑

z(z)H2

Δ= − ⋅n σ

x x y yD1H ( p (z

z)p )

z∂ ∂⎛ ⎞= σ − σ ⎜ ⎟∂ ∂⎝

γ⎠

2

01H V(z)

2 m(z)⎡ ⎤

= − ∇ ∇ +⎢ ⎥⎣ ⎦

2rl||

1|3 |

,1T (E,keI dEd k [f (E) f (E)])

(2 ) σσ=−

= −π

∑ ∫

particle transmissivity

lα rαγA. Matos-Abiague & J. Fabian cond-mat/0702387

Modelling

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lα γ

||w(k ) =y x

x y

k - k- k k 0

α γ⎛ ⎞⎜ ⎟

α + γ⎜ ⎟⎜ ⎟⎝ ⎠

2[110]||

Anisotropy determin ed by

[ ( )] R/R 1 ~ (cos2 1)⋅ → − αγ φ −n w k

Anisotropy vanishes for 0αγ → J. Moser et al., cond-mat/0611406

FeGaAs

Au

n

||w(k )

x

y

z

Origin of anisotropic resistance: SO-interaction duringtunneling (Rashba & Dresselhaus contribution)

Fe Au

zl zr

z

EF

φb

Universität Regensburg

γ = 0

α > γ > 0 α < 0γ > 0

|| ( )ϕkw

( , )x yk kw

α = 0

[100]kx

ky

[100]

kx

ky

ky

[100]

kx

[100]

kx

ky

Universität Regensburg

Anisotropy: Interference of Rashba & Dresselhaus

[100]kx

[110]

[100]

kx

ky[110]

Universität Regensburg

Funding by:

Spin-orbit interaction: Separation of Rashba- and Dresselhauscontributions

Spintronics is interesting both from a fundamental physics point of view as well as from an application perspective. Interplay of newmaterials, new phenomena and new concepts.

Summary

TAMR: Due to interference of Rashba- and Dresselhaus contributionsin epitaxial fm/semiconductor systems.

Many students and colleagues contributed to the work I presented. Many thanks!