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⇐∇