spintronics without magnets:...
TRANSCRIPT
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
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
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
a) magnetoelectronics
giant magnetoresistance (GMR), 1988
e e
Read Head IBM
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
Datta Das spin field effect transistor
FMFM
B
InxGa1-xAs
InxAl1-xAs
2D Electron Gas = 2DEGconduction band
e donors
InxAl1-xAsInxGa1-xAs
zy
x
InxAl1-xAsInxGa1-xAs
z
++
quantum well
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
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
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
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!
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= −∇
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= −∇
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.
significant variation of the Spin Orbit coupling constant
relatively small variation of density with the gate voltage∆n~0.1n
0.1α≈
0.05α≈
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
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.
Stern and Gerlach Experiment, 1922
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
spatially inhomogeneous spin-orbit interaction (lateral SO-interface)
cross-sectional view
lateral SO
lateral SO
Snell’s law for electrons
lateral SO
lateral SO
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
( ) 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:
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→ = −
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
region of inhomogeneous SO
further development :Shekhter, Khodas & A. F.Phys. Rev. B 71, 125114 (2005)
spin filter: analogy with opticsAngle of total internal reflection is also a “Brewster angle”
Spin Field Effect Transistoreffectiveness, fastness , size, temperature
Transparency of the stripe (in quasiclassics)
1
ϕ c/4π /2π
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)
Spin-splitting in p-type GaAs
S.J. Papadakis, E.P.De Poortere, M. Shayegan and R. Winkler.
2000
proven example of optics of particles
Neutrons OpticsD.J. Hughes
New York 1954
internal
cold neutrons are transported by supermirror neutron guides
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
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.
diffuse emission for the purposes of spin filtering
further development :Shekhter, Khodas & A. F.Phys. Rev. B 71, 125114 (2005)
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⇐∇