Physik
Ballistic Spin Resonance
Joshua Folk UBC Regensburg, 2008
Types of Spin Resonance Magnetic: Small oscillating transverse Bx sin(ωt)
+ Large static Bz
EDSR: Oscillating electric field E sin(ωt)
Hso ~ + α(k x σ)
Ballistic: periodic trajectory with period T=2π/ω
Hso ~ + α(k x σ)
=
Rapid depolarization when gμB=hω
Thanks to: Simulations My group Sergey Frolov (ex) Ananth Venkatesan (ex) Wing Wa Yu Yuan Ren Chung-Yu Lo George Kamps
S. Luescher, J.C. Egues, G. Usaj Heterostructures W. Wegscheider Funding CIFAR, CFI, NSERC
Outline
- Electrical measurement of pure spin currents - Quantum point contacts as injectors and detectors - Long-distance spin transport (> 50 microns) - Ballistic spin resonance
Detecting pure spin currents in a nonlocal geometry Injector circuit
Spin current
Detector circuit
V ferromagnets Jedema, van Wees et al, Nature 2002; dating back to Johnson and Silsbee, PRL 1985.
τs ∼ 1ns gµB B π!
=
vF channel width Vspin Iinj ∝ Pinj Pdet
Nanostructures in GaAs/AlGaAs electron gas Rspin =
Vspin (x) ∼
−x
R Pinj Pdet λs e λs Iinj 2L
Vspin (x) ∝ λs e
Gate Voltage(s)
−x λs
Gates
−x L−x ) sinh( λ
R R Vspin (x) ∼ Iinj 2L Pdet λsse λs injP detλ 2L Pinj −x λs
Vspin spin (x) V (x) ∝ ∝λ λssesinh( L−x λs )
L e λs
s
sinh( L−x ) λ
s λ ∼ (x) 0 ∼ Iinj R Pinj PdetBias Vsspin λ s L 2L e λs λs ∼ 30µm Voltage sinh( L−x ) λs V (x) ∝ λ spin s L λs = ∞
This material:
e λs 11 cm−2 −2 11 1.1 × 10 1.4
nee = µ = 4 × 1066 cm22 /V s → mf p ∼ 50µm 17µm V ∝ P ∝ I2
= (Idc + I0 sin(ωt))22 2 sin(ωt) + + sin sin22(ωt) (ωt) = Idc + 2Idc I0 sin(ωt) λs = 50µm
An alternative spin contact for 2DEGs Injector circuit
Spin current
Detector circuit
V
An alternative spin contact for 2DEGs Injector circuit
Spin current
Detector circuit
V - Quantum point contacts allow injection and detection with nearly 100% polarization - Require external magnetic field and low temperature.
Device geometry
Quantum point contact injector or detector A
V
Charge current flows to left, spin current to right
1μm channel width
Quantum point contacts:
Quantized Conductance
In-plane B=10T A
g (e2/h)
---------- B = 0T ---------- B =10T
Vgate 1µm Gate voltage (mV)
Spin-resolved plateau, transmits only spin up
Detecting spin currents Detector spacing 10μm to tec e D
2
3e
/h
ond C r
Inj
nce a t uc
In-plane B=10T
ec tor Co nd uc ta
nc e
2/h e 2
1 e2
/h 1e 2
2 e2
/h
3 e2
/h
/h
Spin voltage (µV)
A
1.0 0.5 0.0 -90
Inje
-100
-80
ctor
-80
-70
Gat
-60
eV olta ge
-60 -50
(mV
)
-40 -40
-20 0
Vo e t a rG
to
c Dete
V)
(m ltage
V
Detecting spin currents Detector spacing 10μm
Inj ec
ce tan
tor
c
u ond
rC
to tec e D
Spin voltage (µV)
2/h 3e
2/h 2e
Co n
du
1e
2
1 e2
/h
2 e2
/h
cta
/h
nc
e
3 e2
/h
1.0 0.5 0.0 -90
Inje
-100
-80
ctor
Gat
Vspin (x) ∼
-80
-70
e V -60 olta ge -50 (mV )
-60 -40
-40
-20 0
ate G r o ct Dete
V)
e (m g a t l Vo
R Iinj 2L Pinj Pdet λs e
λs = 50µm
−x λs
Anisotropy in field dependence due to anisotropy in relaxation
110
Bin-plane
110
T=250mK Spin voltage (nV)
1200
A
800 400 0 0
2
4
6
Bin-plane (T)
8
10
V
Anisotropy in field dependence
110
Bin-plane
110
Spin voltage (nV)
1200 800
T=250mK
400 A
0 0
2
4
6
8
10
Bin-plane (T)
•Crystal axis anisotropy in SOI •Geometric anisotropy: long intrinsic mean free path
leads to rapid bouncing across channel, with slow diffusive motion along channel
V
p
y
p
x
y
px
110
110 E!
n u t h y 0 D i s n g e u . t r r l e w r r v y e s e m , p h s n r s 7 n es s p i i t e i e n l 2 i n e d d l . i h 2 n s u 5 p c st o . g th au a R s c g on he f b e eo e s s m . p p s fin m ch i a p e n a e t r e in m i rg n H i e ffi c e a c or n fo l t f ie bi t e e r a ti s ntl t i fo y nr b ac i t a p l
c a onn c e o bulk asymmetry
110
Bin-plane
V
A
F I G el . d s 1: i a n d (c r r uc ol t ow ed or i v s o b ) e n O ly Ω y R lin R e I . a ( ) I s O (α ns p) hb a e I t = a ) l = : (
structural asymmetry
110
Ballistic Spin Resonance for 110 spins Duckheim PRB 07
Anisotropy in field dependence
110
Bin-plane
110
Spin voltage (nV)
1200 800
T=250mK
400 A
V
0 0
2
4
6
8
10
Bin-plane (T)
•Crystal axis anisotropy in SOI •comes from cancellation between linear structural (Rashba) and bulk (Dresselhaus) asymmetry terms in SOI hamiltonian
•anisotropy is weak in GaAs heterostructures due to strong large structural asymetry
Anisotropy in field dependence
110
Bin-plane
110
Spin voltage (nV)
1200 800
T=250mK
400 A
0 0
2
4
6
8
10
Bin-plane (T)
•Crystal axis anisotropy in SOI •Geometric anisotropy: long intrinsic mean free path
leads to rapid bouncing across channel, with slow diffusive motion along channel
V
i r t m ik pl
f
ce
s
si
t
spins relax due to transverse field 110 spins relax due to Bso(110)
typical trajectory in channel
comes from k(110)
Bso(110)
0
i
FI h da G r fi py o in e li s ga ad d (r eld . 1 . t r ed s i : e e d s a n d (c h o f p r u o pu t t ect row ce lor d y h p x s p e ive s) b o c re n p a l i es S ly Ω y i O R p 19 n o R l n a ne f I . o s a p t S ( In (p sh ) . ω fu of lit O α se ) b a) t I t n = : = aM fi L τ ct the ing le ( α b β E gur = ion re in ads ) Th (p lac om s 2 a t t is e s y , k en i ( of o c c
px
110
a
E!
θ!
nd cs M he e. in oit th in pin a t W g s er d p a e n t r i s e o PA a n e d th p j e h he so so la g r e i a A C r n a i i d i c v i n n b n a t S z e s as o t r n r e a ce te nt re at D in ility c o r i u m n e f n u m e s d io s o ( i b n en r pi tw n e D t m c a e n sem to h t o r n a y kh e t n n t e p c s t r : e , ei p rp of e o -di d o ic c l o d 7 o 3 : Un m l re th be ar m its s ni on h e . t a i c t e e 2 e d O i a n z a r w v a 3 a t i c . z s s 1. uc ren -b t er n a io sp ee ti sio sso o s t , i ) ys B to t b i n in n o n c n a t o 7 e 3 o te a r ly n of s R c l ia r y m . n n ff c 2 6 d t us as an el ted 1 h , e a er s d- an on .F s e ce hb b ec s 2 r c g r ing le str os tr r sp pt a e tro pi , a o i 10 ie u b i 7 d n ibi an st n nc tr l 6 e u r , l d s 1 r s th . t o s t i c 3 y H 1 t u 0 i ,1 pi e o r ctu he n u ty D ng s all . 2 p r v ,1 n s rre w re ly tem o a e e s , p v 3 7 e i nt hi ss re s i ss s a n s p i e n l 2 ffi a i n e d l . h d . 2 s c . t th ibil tro c s t o 5 p in h a uc . n h o a i R le ien e t n c ge e us ed g e f y b e t c . om sp sp o t s fin m ch 20 in e n s t in- in t o pi em a ar i c r r d i h o effi nc H -o e n ge u a l c em c or n fo l all o t f ie bi t e t w ed e e c h n t o f r i a t t m l i s o i er y n s o a nt e sp f w r a i t c b n s e er n e i p t a ag con al lect re in p l y fi n e fi e ri so c n rb tic gur lds c a on ti r fi ati co ra nce o ar eld on up dio u s y d of lin , t sp efi t g h o in n he i s a n b ed s t tan rota g
110
110
Bin-plane
Ballistic Spin Resonance for 110 spins
Bso(110)
Duckheim PRB 07
Ballistic Spin Resonance for 110 spins
Bin-plane
110
typical trajectory in channel
Bso(110)
Fast relaxation when guB matches characteristic frequency of Bso(110)
τs ∼ 1ns gµB B h gµB B π!
=
R
=
=
vF 2×channel width −1 τcross Vspin
∝P
P
comes from k(110)
t
Monte Carlo Simulations
Bso(110)
10μm mean free path trajectory of 8000τcross, showing only 1st 40um 1um
zoom in to 50τcross 1um 0
10
20 -6 microns x10
30
40
k110 k110 0
20
40
τcross
60
80
100
all simulations due to S. Luescher
Monte Carlo Simulations
Bso(110)
k110 k110 0
20
40
Power Spectra
80
k110
-9
Power (a.u.)
τcross
60
10
k110
-11
10
-13
10
-15
10
0.0
0.1
0.2
0.3
0.4
0.5 0.0
0.1
frequency (a.u.)
0.2
0.3
0.4
0.5
100
Ballistic Spin Resonance for 110 spins Bin-plane
110
Spin voltage (nV)
1200
k110 B110
-9
10
-11
10
-13
10
-15
10
800
0.0
0.1
0.2
0.3
0.4
0.5
400 0 0
2
4
τs ∼ 1ns gµB B h gµB B π!
=
=
6
8
10
110
k110 B110
Bin-plane (T)
vF 2×channel width −1 τcross
0.0
0.1
0.2
0.3
0.4
frequency (a.u.)
0.5
Ballistic Spin Resonance for 110 spins Spin voltage (nV)
1200
Bin-plane
110
800 400
typical trajectory in channel
0 0
2
4
6
8
10
Bin-plane (T)
Bso(110)
τs ∼ 1ns gµB B h gµB B π!
=
=
Rspin =
vF 2×channel width −1 τcross Vspin ∝ P P inj det Iinj R
comes from k(110)
t
−x
Fermi velocity controls crossing time
Bin-plane
Spin voltage (nV)
1200 800 400
τs ∼ 1ns
0 0
2
4
6
8
10
Bin-plane (T)
gµB B h gµB B π!
vF = 2×channel width −1 = τcross Vspin Rspin ∝ P P Monte carlo= simulation inj det I inj -13
decreasing vF 0.6
a.u.
110
based on α=3x10 eVm, β=0 for SOI, mfp=10μm, R spin by thermal QPC inj 2L multiplied polarization (S. Luescher) −x
0.4
V
0.2 0.0
0
2
4
6
8
10
Bin-plane (T)
12
14
(x) ∼ I
Pinj Pde
λs V (x) ∝ λ e spin s Experiment
R Pinj Pde Vspin (x) ∼ Iinj 2L L−x
Effect of out-of-plane field B Power (a.u.)
-9
10
B =0
Power Spectra B =0
k110
k110
-11
10
-13
10
-15
10
(mT)
100
B
150
50
0.0
0.1
0.2
0.3
0.4
0.5
0.0
150
Simulation: Log-scale power spectrum of -16 -18 k110
100
0.1
0.2
0.3
0.4
0.5
Simulation: Log-scale power spectrum of k110
-16 -18 -20
-20
50
-22
-22
-24
-24
0
0 0
20
40
60
80
100
0
frequency (a.u.)
20
40
60
80
100
crossing time depends on B
Bin-plane
Spin voltage (nV)
1200
110
800 400
τs ∼ 1ns
0 0
2
4
6
8
10
Bin-plane (T) Experiment: Spin signal
150
nV 800
80
100
600 400
B
(mT)
100
gµB B π!
60
50
200
4
5
6
7
Bext(-110) (T)
8
0
vF = channel width Vspin Simulation: Log-scale Rspin = Iofinj ∝ Pinj Pde power spectrum k110
Vspin (x) ∼
-16
R -18 Iinj 2L Pinj P -20
Vspin (x) ∝ λs e
−x λs
-22 -24
R 0Vspin 20 (x) 40 ∼ I 60inj 2L 80 Pinj 100 P frequency (a.u.) L−x Vspin (x) ∝ λs sinh( λ
B adds periodic term to k110
Bin-plane
Spin voltage (nV)
1200
110
800 400
τs ∼ 1ns
0 0
2
4
6
8
10
Bin-plane (T)
150
Experiment 1.5 1.0
60
B
0.5
100
microvolts
(mT)
80
gµB B π!
50
0.0
40
0
0
2
4
6
Bext(110) (T)
8
10
vF = channel width Vspin R ∝ P P spin = ILog-scale inj de Simulation: inj
power spectrum of -16 R -18 Vk110 spin (x) ∼ Iinj 2L Pinj P
Vspin (x) ∝ λs e
−x λs
-20 -22 -24
R Iinj 2L 0 Vspin 20 (x) 40 ∼ 60 80 P100 inj P frequency (a.u.) L−x Vspin (x) ∝ λs sinh( λ
Conclusions
Inj
ce
r cto ete
ec to
n cta ndu
rC
Co
on du c
tan ce
D
•Electrical generation and detection of
2
3e
Spin voltage (µV)
pure spin currents in a 2D electron gas
•Dramatically different relaxation for
rotation for well-defined trajectories
•Negative polarization from unpolarized contacts?
/h
1e
2
1 e2
/h
2 e2
/h
3 e2
/h
/h
0.0
Inje
-100
-80
ctor
-80
Gat
-70
e V -60 olta ge -50 (mV )
-60
-40 -40
-20 0
ctor
Dete
V)
e (m
g Volta Gate
1200 Spin voltage (nV)
•Next steps: coherent resonant
2
0.5
-90
•Resonant enhancement of relaxation
2e
1.0
spin along 2 crystal axes
for spins in bouncing trajectory
/h
800 400 0 0
2
4
6
Bin-plane (T)
8
10
Joshua Folk UBC Regensburg, 2008
Types of Spin Resonance Magnetic: Small oscillating transverse Bx sin(ωt)
+ Large static Bz
EDSR: Oscillating electric field E sin(ωt)
Hso ~ + α(k x σ)
Ballistic: periodic trajectory with period T=2π/ω
Hso ~ + α(k x σ)
=
Rapid depolarization when gμB=hω
Thanks to: Simulations My group Sergey Frolov (ex) Ananth Venkatesan (ex) Wing Wa Yu Yuan Ren Chung-Yu Lo George Kamps
S. Luescher, J.C. Egues, G. Usaj Heterostructures W. Wegscheider Funding CIFAR, CFI, NSERC
Outline
- Electrical measurement of pure spin currents - Quantum point contacts as injectors and detectors - Long-distance spin transport (> 50 microns) - Ballistic spin resonance
Detecting pure spin currents in a nonlocal geometry Injector circuit
Spin current
Detector circuit
V ferromagnets Jedema, van Wees et al, Nature 2002; dating back to Johnson and Silsbee, PRL 1985.
τs ∼ 1ns gµB B π!
=
vF channel width Vspin Iinj ∝ Pinj Pdet
Nanostructures in GaAs/AlGaAs electron gas Rspin =
Vspin (x) ∼
−x
R Pinj Pdet λs e λs Iinj 2L
Vspin (x) ∝ λs e
Gate Voltage(s)
−x λs
Gates
−x L−x ) sinh( λ
R R Vspin (x) ∼ Iinj 2L Pdet λsse λs injP detλ 2L Pinj −x λs
Vspin spin (x) V (x) ∝ ∝λ λssesinh( L−x λs )
L e λs
s
sinh( L−x ) λ
s λ ∼ (x) 0 ∼ Iinj R Pinj PdetBias Vsspin λ s L 2L e λs λs ∼ 30µm Voltage sinh( L−x ) λs V (x) ∝ λ spin s L λs = ∞
This material:
e λs 11 cm−2 −2 11 1.1 × 10 1.4
nee = µ = 4 × 1066 cm22 /V s → mf p ∼ 50µm 17µm V ∝ P ∝ I2
= (Idc + I0 sin(ωt))22 2 sin(ωt) + + sin sin22(ωt) (ωt) = Idc + 2Idc I0 sin(ωt) λs = 50µm
An alternative spin contact for 2DEGs Injector circuit
Spin current
Detector circuit
V
An alternative spin contact for 2DEGs Injector circuit
Spin current
Detector circuit
V - Quantum point contacts allow injection and detection with nearly 100% polarization - Require external magnetic field and low temperature.
Device geometry
Quantum point contact injector or detector A
V
Charge current flows to left, spin current to right
1μm channel width
Quantum point contacts:
Quantized Conductance
In-plane B=10T A
g (e2/h)
---------- B = 0T ---------- B =10T
Vgate 1µm Gate voltage (mV)
Spin-resolved plateau, transmits only spin up
Detecting spin currents Detector spacing 10μm to tec e D
2
3e
/h
ond C r
Inj
nce a t uc
In-plane B=10T
ec tor Co nd uc ta
nc e
2/h e 2
1 e2
/h 1e 2
2 e2
/h
3 e2
/h
/h
Spin voltage (µV)
A
1.0 0.5 0.0 -90
Inje
-100
-80
ctor
-80
-70
Gat
-60
eV olta ge
-60 -50
(mV
)
-40 -40
-20 0
Vo e t a rG
to
c Dete
V)
(m ltage
V
Detecting spin currents Detector spacing 10μm
Inj ec
ce tan
tor
c
u ond
rC
to tec e D
Spin voltage (µV)
2/h 3e
2/h 2e
Co n
du
1e
2
1 e2
/h
2 e2
/h
cta
/h
nc
e
3 e2
/h
1.0 0.5 0.0 -90
Inje
-100
-80
ctor
Gat
Vspin (x) ∼
-80
-70
e V -60 olta ge -50 (mV )
-60 -40
-40
-20 0
ate G r o ct Dete
V)
e (m g a t l Vo
R Iinj 2L Pinj Pdet λs e
λs = 50µm
−x λs
Anisotropy in field dependence due to anisotropy in relaxation
110
Bin-plane
110
T=250mK Spin voltage (nV)
1200
A
800 400 0 0
2
4
6
Bin-plane (T)
8
10
V
Anisotropy in field dependence
110
Bin-plane
110
Spin voltage (nV)
1200 800
T=250mK
400 A
0 0
2
4
6
8
10
Bin-plane (T)
•Crystal axis anisotropy in SOI •Geometric anisotropy: long intrinsic mean free path
leads to rapid bouncing across channel, with slow diffusive motion along channel
V
p
y
p
x
y
px
110
110 E!
n u t h y 0 D i s n g e u . t r r l e w r r v y e s e m , p h s n r s 7 n es s p i i t e i e n l 2 i n e d d l . i h 2 n s u 5 p c st o . g th au a R s c g on he f b e eo e s s m . p p s fin m ch i a p e n a e t r e in m i rg n H i e ffi c e a c or n fo l t f ie bi t e e r a ti s ntl t i fo y nr b ac i t a p l
c a onn c e o bulk asymmetry
110
Bin-plane
V
A
F I G el . d s 1: i a n d (c r r uc ol t ow ed or i v s o b ) e n O ly Ω y R lin R e I . a ( ) I s O (α ns p) hb a e I t = a ) l = : (
structural asymmetry
110
Ballistic Spin Resonance for 110 spins Duckheim PRB 07
Anisotropy in field dependence
110
Bin-plane
110
Spin voltage (nV)
1200 800
T=250mK
400 A
V
0 0
2
4
6
8
10
Bin-plane (T)
•Crystal axis anisotropy in SOI •comes from cancellation between linear structural (Rashba) and bulk (Dresselhaus) asymmetry terms in SOI hamiltonian
•anisotropy is weak in GaAs heterostructures due to strong large structural asymetry
Anisotropy in field dependence
110
Bin-plane
110
Spin voltage (nV)
1200 800
T=250mK
400 A
0 0
2
4
6
8
10
Bin-plane (T)
•Crystal axis anisotropy in SOI •Geometric anisotropy: long intrinsic mean free path
leads to rapid bouncing across channel, with slow diffusive motion along channel
V
i r t m ik pl
f
ce
s
si
t
spins relax due to transverse field 110 spins relax due to Bso(110)
typical trajectory in channel
comes from k(110)
Bso(110)
0
i
FI h da G r fi py o in e li s ga ad d (r eld . 1 . t r ed s i : e e d s a n d (c h o f p r u o pu t t ect row ce lor d y h p x s p e ive s) b o c re n p a l i es S ly Ω y i O R p 19 n o R l n a ne f I . o s a p t S ( In (p sh ) . ω fu of lit O α se ) b a) t I t n = : = aM fi L τ ct the ing le ( α b β E gur = ion re in ads ) Th (p lac om s 2 a t t is e s y , k en i ( of o c c
px
110
a
E!
θ!
nd cs M he e. in oit th in pin a t W g s er d p a e n t r i s e o PA a n e d th p j e h he so so la g r e i a A C r n a i i d i c v i n n b n a t S z e s as o t r n r e a ce te nt re at D in ility c o r i u m n e f n u m e s d io s o ( i b n en r pi tw n e D t m c a e n sem to h t o r n a y kh e t n n t e p c s t r : e , ei p rp of e o -di d o ic c l o d 7 o 3 : Un m l re th be ar m its s ni on h e . t a i c t e e 2 e d O i a n z a r w v a 3 a t i c . z s s 1. uc ren -b t er n a io sp ee ti sio sso o s t , i ) ys B to t b i n in n o n c n a t o 7 e 3 o te a r ly n of s R c l ia r y m . n n ff c 2 6 d t us as an el ted 1 h , e a er s d- an on .F s e ce hb b ec s 2 r c g r ing le str os tr r sp pt a e tro pi , a o i 10 ie u b i 7 d n ibi an st n nc tr l 6 e u r , l d s 1 r s th . t o s t i c 3 y H 1 t u 0 i ,1 pi e o r ctu he n u ty D ng s all . 2 p r v ,1 n s rre w re ly tem o a e e s , p v 3 7 e i nt hi ss re s i ss s a n s p i e n l 2 ffi a i n e d l . h d . 2 s c . t th ibil tro c s t o 5 p in h a uc . n h o a i R le ien e t n c ge e us ed g e f y b e t c . om sp sp o t s fin m ch 20 in e n s t in- in t o pi em a ar i c r r d i h o effi nc H -o e n ge u a l c em c or n fo l all o t f ie bi t e t w ed e e c h n t o f r i a t t m l i s o i er y n s o a nt e sp f w r a i t c b n s e er n e i p t a ag con al lect re in p l y fi n e fi e ri so c n rb tic gur lds c a on ti r fi ati co ra nce o ar eld on up dio u s y d of lin , t sp efi t g h o in n he i s a n b ed s t tan rota g
110
110
Bin-plane
Ballistic Spin Resonance for 110 spins
Bso(110)
Duckheim PRB 07
Ballistic Spin Resonance for 110 spins
Bin-plane
110
typical trajectory in channel
Bso(110)
Fast relaxation when guB matches characteristic frequency of Bso(110)
τs ∼ 1ns gµB B h gµB B π!
=
R
=
=
vF 2×channel width −1 τcross Vspin
∝P
P
comes from k(110)
t
Monte Carlo Simulations
Bso(110)
10μm mean free path trajectory of 8000τcross, showing only 1st 40um 1um
zoom in to 50τcross 1um 0
10
20 -6 microns x10
30
40
k110 k110 0
20
40
τcross
60
80
100
all simulations due to S. Luescher
Monte Carlo Simulations
Bso(110)
k110 k110 0
20
40
Power Spectra
80
k110
-9
Power (a.u.)
τcross
60
10
k110
-11
10
-13
10
-15
10
0.0
0.1
0.2
0.3
0.4
0.5 0.0
0.1
frequency (a.u.)
0.2
0.3
0.4
0.5
100
Ballistic Spin Resonance for 110 spins Bin-plane
110
Spin voltage (nV)
1200
k110 B110
-9
10
-11
10
-13
10
-15
10
800
0.0
0.1
0.2
0.3
0.4
0.5
400 0 0
2
4
τs ∼ 1ns gµB B h gµB B π!
=
=
6
8
10
110
k110 B110
Bin-plane (T)
vF 2×channel width −1 τcross
0.0
0.1
0.2
0.3
0.4
frequency (a.u.)
0.5
Ballistic Spin Resonance for 110 spins Spin voltage (nV)
1200
Bin-plane
110
800 400
typical trajectory in channel
0 0
2
4
6
8
10
Bin-plane (T)
Bso(110)
τs ∼ 1ns gµB B h gµB B π!
=
=
Rspin =
vF 2×channel width −1 τcross Vspin ∝ P P inj det Iinj R
comes from k(110)
t
−x
Fermi velocity controls crossing time
Bin-plane
Spin voltage (nV)
1200 800 400
τs ∼ 1ns
0 0
2
4
6
8
10
Bin-plane (T)
gµB B h gµB B π!
vF = 2×channel width −1 = τcross Vspin Rspin ∝ P P Monte carlo= simulation inj det I inj -13
decreasing vF 0.6
a.u.
110
based on α=3x10 eVm, β=0 for SOI, mfp=10μm, R spin by thermal QPC inj 2L multiplied polarization (S. Luescher) −x
0.4
V
0.2 0.0
0
2
4
6
8
10
Bin-plane (T)
12
14
(x) ∼ I
Pinj Pde
λs V (x) ∝ λ e spin s Experiment
R Pinj Pde Vspin (x) ∼ Iinj 2L L−x
Effect of out-of-plane field B Power (a.u.)
-9
10
B =0
Power Spectra B =0
k110
k110
-11
10
-13
10
-15
10
(mT)
100
B
150
50
0.0
0.1
0.2
0.3
0.4
0.5
0.0
150
Simulation: Log-scale power spectrum of -16 -18 k110
100
0.1
0.2
0.3
0.4
0.5
Simulation: Log-scale power spectrum of k110
-16 -18 -20
-20
50
-22
-22
-24
-24
0
0 0
20
40
60
80
100
0
frequency (a.u.)
20
40
60
80
100
crossing time depends on B
Bin-plane
Spin voltage (nV)
1200
110
800 400
τs ∼ 1ns
0 0
2
4
6
8
10
Bin-plane (T) Experiment: Spin signal
150
nV 800
80
100
600 400
B
(mT)
100
gµB B π!
60
50
200
4
5
6
7
Bext(-110) (T)
8
0
vF = channel width Vspin Simulation: Log-scale Rspin = Iofinj ∝ Pinj Pde power spectrum k110
Vspin (x) ∼
-16
R -18 Iinj 2L Pinj P -20
Vspin (x) ∝ λs e
−x λs
-22 -24
R 0Vspin 20 (x) 40 ∼ I 60inj 2L 80 Pinj 100 P frequency (a.u.) L−x Vspin (x) ∝ λs sinh( λ
B adds periodic term to k110
Bin-plane
Spin voltage (nV)
1200
110
800 400
τs ∼ 1ns
0 0
2
4
6
8
10
Bin-plane (T)
150
Experiment 1.5 1.0
60
B
0.5
100
microvolts
(mT)
80
gµB B π!
50
0.0
40
0
0
2
4
6
Bext(110) (T)
8
10
vF = channel width Vspin R ∝ P P spin = ILog-scale inj de Simulation: inj
power spectrum of -16 R -18 Vk110 spin (x) ∼ Iinj 2L Pinj P
Vspin (x) ∝ λs e
−x λs
-20 -22 -24
R Iinj 2L 0 Vspin 20 (x) 40 ∼ 60 80 P100 inj P frequency (a.u.) L−x Vspin (x) ∝ λs sinh( λ
Conclusions
Inj
ce
r cto ete
ec to
n cta ndu
rC
Co
on du c
tan ce
D
•Electrical generation and detection of
2
3e
Spin voltage (µV)
pure spin currents in a 2D electron gas
•Dramatically different relaxation for
rotation for well-defined trajectories
•Negative polarization from unpolarized contacts?
/h
1e
2
1 e2
/h
2 e2
/h
3 e2
/h
/h
0.0
Inje
-100
-80
ctor
-80
Gat
-70
e V -60 olta ge -50 (mV )
-60
-40 -40
-20 0
ctor
Dete
V)
e (m
g Volta Gate
1200 Spin voltage (nV)
•Next steps: coherent resonant
2
0.5
-90
•Resonant enhancement of relaxation
2e
1.0
spin along 2 crystal axes
for spins in bouncing trajectory
/h
800 400 0 0
2
4
6
Bin-plane (T)
8
10
