Spin + Electronics = Spintronics · Universität Regensburg Dieter Weiss, Universität Regensburg...
Transcript of Spin + Electronics = Spintronics · Universität Regensburg Dieter Weiss, Universität Regensburg...
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
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GMR: Giant magnetoresistance
GMR read-out heads in hard drives
Grünberg group: PRB 39, 4828 (1989)Fert group: PRL,61, 2472 (1988)
ΔR/R
(%)
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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)
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Memory cell of MRAM
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Functionality provided by metal-oxide devices
Howabb
outsem
iconduc
torspin
tronics
?
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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)
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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
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V
- vBeff
- vBeff
-v
Beff
V/2
Paradigmatic device: Datta-Das spin transistor
S. Datta & B. Das, Appl. Phys. Lett. 56, 665 (1990)
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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:
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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 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)
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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
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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
kB
k⎛ ⎞
∝ ⎜ ⎟−⎝ ⎠
effB
E.A. de Andrada e Silva PRB 46, 1921 (1992)
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Presence of Rashba & Dresselhaus contributions to SO:
Rashba orDresselhaus
Rashba and Dresselhaus
= ± α − γ2 2kE ( ) k2m
= ± α + γ2 2kE ( ) k2m
]
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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)
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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)
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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( )
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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
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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)
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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
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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
↑↓ ↑↑
↑↑
−= =
−
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[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
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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
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Yuasa et al., Nature Materials 3, 868 (2004)
Huge TMR in epitaxial Fe/MgO/Fe systems
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Band structure of iron
symmetry of statesis relevant!
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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
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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
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Fe
GaAs
AlGaAs
Fe
GaAs
TEM-micrograph:C.-H. Lai, Tsing Hua University, Taiwan
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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)
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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
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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
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AlGaAs
Fe
GaAs
TEM-micrograph:C.-H. Lai, Tsing Hua University, Taiwan
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Tunneling barrier sandwiched between two ferromagnetic layers
Experiments in TMR geometry
Fe
Fe
GaAs
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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
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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
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-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
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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
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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
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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!