Spin + Electronics = Universitأ¤t Regensburg Dieter Weiss, Universitأ¤t Regensburg Spin +...
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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)
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:
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
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:
Universität Regensburg
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( )
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 = °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
↑↓ ↑↑ ↑↑ ↑↓
↑↑ ↑↓
− − = = =
−
Universität Regensburg
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
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