spintronics without magnets:...
TRANSCRIPT
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Spintronics without Magnets:“spin-optics”
Maxim Khodas and Arcadi ShekhterA.M. Finkel’stein
Dept of Condensed Matter PhysicsWeizmann Institute of Science, Rehovot, Israel
Phys. Rev. Lett. 92, (2004)Phys. Rev. B 71, (2005)
German-Israeli Foundationfor Scientific Research and Development
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Spintronics:
“…spin-based electronics, where it is not the electron charge but the electron spin that carriers information, and this offers opportunities for a new generations of devices combining standard microelectronics with spin-dependent effects…”
S.A. Wolf et. al. Science 294, 1488 (2001)
“Microelectroncs devices that function by using the spin of the electrons are nascent multibillion-dollar industry—and may lead to quantum microchips”
Scientific American 2002
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a) Magnetoelectronics (hard drives, MRAM)
b) Spin field effect transistor
c) Quantum computer 1998-99:“Quantum computing and singe-qubit measurements using the spin-filter effect”
d) Time-resolved optical experiments, Spins in quantum dots, Spin-dependent tunneling,Spin-Hall effect
“Chiral spin resonance and spin-Hall conductivity…” PRB 2005
“Spin Relaxation in the Presence of Electron-Electron Interactions” PRL 2006
1Γ
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a) magnetoelectronics
giant magnetoresistance (GMR), 1988
e e
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Read Head IBM
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b) spin field effect transistor
“Electronic analogue of the electro-optic modulator”S. Datta and B. Das , Appl. Phys. Lett., 1990
Kerr cell electro-optic material
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Datta Das spin field effect transistor
FMFM
B
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InxGa1-xAs
InxAl1-xAs
2D Electron Gas = 2DEGconduction band
e donors
InxAl1-xAsInxGa1-xAs
zy
x
InxAl1-xAsInxGa1-xAs
z
++
quantum well
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spin-orbit interaction in semiconductors
2 2 ([ ] )4
: soe
eHm c
spin orbit σ− = − ×p E
is a direction ofasymmetry to the plane of 2D gas
l̂
: ˆ([ ] )Rashba term α σ×p l
structure inversion asymmetry (SIA)
l̂1ˆ([
" " :
] )2 B
individual magnetic field
gα σ µ σ× = ⋅pp l B
2D heterostructures:electrons are confined in anasymmetrical potential well
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2 21 1 ˆ([ ] )2 2R x yH p pm m
α σ= + + ×p l
0.04 0.05InAs em m≈ ÷
two chiralities
( )pε
Xp
Yp
Fε
2( 2 ( ) )bp m E E m α α± = − / + ∓
2( 1 )Fm v α α= + +ˆ[ ]
current operator
em
α σ⎛ ⎞= + ×⎜ ⎟⎝ ⎠
pJ l
/ Fvα α= - dimensionless
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Das et al. Phys. Rev. B 39, 1411 (1989)
beating pattern in Shubnikov-de Haasoscillations due to the Spin Orbit splitting
x 1-xIn Ga As/InAlAs
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1ˆ([ ] )2 Bgα σ µ σ× = ⋅pp l Bspin precession
pB
FM FM
“The spin-orbit-coupling constant is proportional to the expectation value of the electric field at the heterostructure interface and, in principle, can be controlled by the application of a gate voltage. However, this has not yet been demonstrated experimentally”.
S. Datta and B. Das , Appl. Phys. Lett., 1990
suspicious prediction, becausethe expectation value of the electric field (of the confining potential)at the heterostructure interface is actually ZERO,
but it is correct!
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why the expectation value of the electric field
(at the heterostructure interface)is NOT zero:
0 0 0 0
20 0
( ) ( ) [ (
??
)]
( 0 ?) [ 2 ]
z z
z z
V z i p V z
i p E p m
Ψ ∇ Ψ = / Ψ , Ψ =
= / Ψ , − / Ψ =
( )z zeE V z= −∇
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why the expectation valueof the electric field
(at the heterostructure interface)is NOT zero:
0 0 0 0
20 0
20 0
( ) ( ) [ ( )]
( ) [ 2 ]
( )
??
( 2)
?
0[ !1 ( )] ! !
z z
z z
z z
V z i p V z
i p E p m
i p p m z
Ψ ∇ Ψ = / Ψ , Ψ =
= / Ψ , − / Ψ =
= / / Ψ / Ψ ≠,
( )z zeE V z= −∇
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Gate voltage control of the spin-splitting
Ψ(z)
InGaAs
gateV
InAlAs
The electron wave function shifts back and forth in response to the gate voltage.The spin-splitting is sensitive to the closeness of the wave function to the interface.
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significant variation of the Spin Orbit coupling constant
relatively small variation of density with the gate voltage∆n~0.1n
0.1α≈
0.05α≈
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Problems with the injection of spin carriers from magnets (metals with high values of the Fermi-momentum) to semiconductors.
“Electronic analogue of the electro-optic modulator”
Magnetic semiconductors—tremendous efforts:“How to make semiconductor ferromagnetic-A first course on spintronics”“Why ferromagnetic semiconductors?”“Spintronics: Fundamentals and Applications” Rev.Mod.Phys. 2004
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Problems with the injection of spin carriers from magnets (metals with high values of the Fermi-momentum) to semiconductors.
“17 years after”
Spintronics without magnets: “spin-optics”Maxim Khodas, Arcadi Shekhter & A.F.
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Stern and Gerlach Experiment, 1922
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Basic idea: spin-split trajectories
Stern Gerlach, 1922
- spin-orbit coupling constants 2α α≠1
2α
α1
α∇
ˆ( )[ ]xm
α σ= + ×pJ l
acts as a spin-dependent Lorentz force ( )xα∇
( )ˆ ( )xα σ
= ∇×
∝ ∇ ⋅eff effB A
l
/e mc− effA
y
Spatial inhomogeneous spin-orbit interaction leads to splitting of the trajectories;spin-orbit analogy of the Stern-Gerlach experiment
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spatially inhomogeneous spin-orbit interaction (lateral SO-interface)
cross-sectional view
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lateral SO
lateral SO
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Snell’s law for electrons
lateral SO
lateral SO
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later
al S
O
( 2 )( 2 )
2
θ
α
π
π ϕ
/ − ≈
/ − ≈
≈
c
c
angle of the total internal reflection and the aperture angle
ϕC
θC
ϕC
θC
electrons propagating at small tangent angles are most sensitive to the SO interaction
shadow interval
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( ) 0 0( )
SO SOxz N N
p xm x
α σ⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦
− Ψ = ; Ψ =
sharp and smooth interfaces
1η <<smooth interface--WKB:
( ) ( )( ) ( )x xi p dx i p dx
x x
x xx e x ev v
χ χφ φ+ −
+ −+
++ −++ −
∫ ∫Ψ = +
( ) 1 ; ( ) 0x xφ φ++ −+= −∞ = = −∞ = .
d -- width of the lateral interface;
-- wave length.λ( / ) / /Fd dx p dη α α λ= ∼
0
0
x x xN N Nz
x xSO SO
ip x ip x ip xip z
ip x ip x
e e r e r xe
e t e t x
χ χ χ
χ χ+ −
− −+ + −++ −++
+ −++ −+
⎧ + + , <⎪Ψ = ⎨+ , >⎪⎩
from N to SO
sharp interface--continuity conditions:1η ≥
Solution of the “Fresnel’s” problem:
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Solution of the “Fresnel’s” problem:
spin carriers pass through (and reflect from)the region of inhomogeneous spin-orbit interaction practically without changing their chirality:
for any spin-split spectrum (Rashba, Dresselhaus):
( )4 F
E EEα
+ −−=
" "SO Nα δα α α→ = −
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α⇐∇
the intensities per unit outgoing angle of the transmitted electrons.Full line: sharp N-SO interface. Dashed line: smooth N-SO interface
0.1α =
( / ) / / 1Fd dx p dη α α λ= ∼ smooth interface:curves become almost rectangular
important forpotential applications
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region of inhomogeneous SO
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further development :Shekhter, Khodas & A. F.Phys. Rev. B 71, 125114 (2005)
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spin filter: analogy with opticsAngle of total internal reflection is also a “Brewster angle”
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Spin Field Effect Transistoreffectiveness, fastness , size, temperature
Transparency of the stripe (in quasiclassics)
1
ϕ c/4π /2π
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feasibility of the proposal
the connection between geometrical optics and ballistic electron transport was established by TMF (transverse magnetic focusing):
“control of ballistic electrons in macroscopic 2D electron systems” 1990“hot electron spectrometry with quantum point contacts” 1990
Appl. Phys. Lett.vol. 74, 1281 (1999)
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Spin-splitting in p-type GaAs
S.J. Papadakis, E.P.De Poortere, M. Shayegan and R. Winkler.
2000
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proven example of optics of particles
Neutrons OpticsD.J. Hughes
New York 1954
internal
cold neutrons are transported by supermirror neutron guides
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conclusion:the tasks of spintronics can be solved by ballistic electrons;spintronics can work with electron spin the way optics does it routinely with light polarization;this approach exploiting the analogy with the optics of polarized light can be called “spin-optics”.
Thanks to Maxim Khodas and Arcadi Shekhterfor the fruitful collaboration
German-Israeli Foundationfor Scientific Research and Development
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2000
All over the world, "spin doctors" are working to understand thecharacteristics of spin-dependent phenomena in order to developa new generation of electronic-spintronic devices.
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diffuse emission for the purposes of spin filtering
further development :Shekhter, Khodas & A. F.Phys. Rev. B 71, 125114 (2005)
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sharp N-SO interface: the intensities per unit outgoing angle of the transmitted electrons
0.1α =
( / ) / / 1Fd dx p dη α α λ= ∼
smooth SO-interface:curves become almost rectangular
important forpotential applications
α⇐∇