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Albert FERT Graphene Spintronics Albert Fert graduated in 1962 from the École Normale Supérieure in Paris. He

received his master's degree in 1963 at the University of Paris, and earned his

PhD in 1970 at the Université Paris-Sud.

Currently Professor at Université Paris-Sud in Orsay and scientific director of a

joint laboratory between the Centre National de la Recherche Scientifique

(National Scientific Research Centre) and Thales Group.

He was awarded the 2007 Nobel Prize in Physics jointly with Peter Grünberg,

"for the discovery of Giant Magnetoresistance".

Graphene and spintronics

Graphene 2020-opportunities for Europe

Brussels, March 21, 2011Albert Fert

UMP CNRS/Thales and University Paris-Sud

1) Graphene (or CNT) much better than classical metals andsemiconductors for spin transport to macroscopic distances and implementation of large scale spintronic logic circuits

2) Review of more sophisticated quantum effects for graphene-based spintronics

Graphene and spintronics

Graphene 2020-opportunities for Europe

Brussels, March 21, 2011Albert Fert

UMP CNRS/Thales and University Paris-Sud

F

Spin transport through a nonmagnetic lateral cchannel betwen ferromagnetic contacts

(for logic gate, logic circuit or transistor-like applications)

≈1 μm

F1 F2Semiconductor

channel

V

Normal metal

VI IF1 F2

Normal metal

universal logic gate

Graphene and spintronics

F2F1

F1, F2 = ferromagnetic

contact

I

VI I

F1 F2

Metal/metal

ΔR ≈ mΩ(≈ ρlsf /S =spin

resistance)

ΔR/R ≈ a few%, ΔV ≈ μV

Experimental review: 1) Metallic lateral channellocal

nonlocal« spin signal »ΔR = (VAP-VP)/I

local

V

P

AP

P

ΔRL≈ 20mΩnonlocal

ΔRNL=ΔRL/2 ≈ 10mΩΔRL

ΔRNL

Fe/Ag (Kimura et al, PRL07)

I

VI I

F1 F2

Fe/Ag (Kimura et al, PRL07)

Co/Al2O3/Ag (Jedema et al, Nat02)

Tunnel contacts

ΔR ≈ mΩ (Valenzuela et al, APL08:

ΔR= 2.5Ω)

(≈ ρlsf /S = spin resistance)

ΔR/R < 10-4, ΔV ≈ μV

Experimental review: 1) Metallic lateral channellocal

nonlocal« spin signal »ΔR = (VAP-VP)/I

local nonlocal

nonlocal

ΔR

V

P

AP

PΔRL

ΔRNL

ΔRNL=ΔRL/2 ≈ 10mΩ

ΔRL≈ 20mΩ Metal/metal

ΔR ≈ mΩ(≈ ρlsf /S =spin

resistance)

ΔR/R ≈ a few%, ΔV ≈ μV

2) Semiconductor lateral channel

(Fe/Al2O3/Si) :ΔV = 8 µV for I

= 100 µA,ΔR=80 mΩ,

ΔR/Rbias ≈ 5x10-4

O. Van’t Erve et al., Appl. Phys.

Lett. 2007

I

V

Fe/GaAs, ΔV = 17 µV (I = 0.8 mA),ΔR=21mΩ

X. Lou et al, Phys. Rev. Lett. 2006X. Lou et al, Nat. Phys. 2007

Hanle

F1 F2Semiconductor channel

PAP

M

Semiconductor channel:

« Measured effects of the order of 0.1-1% have

been reported for the voltage or resistance change

(between P and AP)…. », from the review article

« Electrical Spin Injection and Transport in Semiconductors » by BT Jonker

and ME Flatté in Nanomagnetism (ed.: DL Mills and JAC Bland, Elsevier 2006)

F1 F2Semiconductor channel

PAP

L.Hueso, N.D. Mathur,A.F. et al, Nature 445, 410, 2007

M

LSMO LSMO

LSMO = La2/3Sr1/3O3

MW-CNT 1.5 μm

Carbon nanotubes (metallic):

ΔR/R ≈ 60-70%, VAP-VP ≈ 20-60 mV

Tunnel RTTunnel RT

Semiconductor channel:

« Measured effects of the order of 0.1-1% have

been reported for the voltage or resistance change

(between P and AP)…. », from the review article

« Electrical Spin Injection and Transport in Semiconductors » by BT Jonker

and ME Flatté in Nanomagnetism (ed.: DL Mills and JAC Bland, Elsevier 2006)

L.Hueso, N.D. Mathur,A.F. et al, Nature 445, 410, 2007

F1 F2Semiconductor channel

PAP

M

LSMO LSMO

LSMO = La2/3Sr1/3O3

MW-CNT 1.5 μm

Carbon nanotubes: (metallic)

ΔR/R ≈ 60-70%, VAP-VP ≈ 20-60 mV

Tunnel RTTunnel RT

MR ≈ 72%

Semiconductor channel:

« Measured effects of the order of 0.1-1% have

been reported for the voltage or resistance change

(between P and AP)…. », from the review article

« Electrical Spin Injection and Transport in Semiconductors » by BT Jonker

and ME Flatté in Nanomagnetism (ed.: DL Mills and JAC Bland, Elsevier 2006)

L.Hueso, N.D. Mathur,A.F. et al, Nature 445, 410, 2007

F1 F2Semiconductor channel

PAP

M

LSMO LSMO

LSMO = La2/3Sr1/3O3

MW-CNT 1.5 μm

Carbon nanotubes: (metallic)

ΔR/R ≈ 60-70%, VAP-VP ≈ 20-60 mV

Tunnel RTTunnel RT

60%

ΔR = 90MΩ≈ RT >>RCNT

R (M

Ω)

B (mT)

MR

(%)

Semiconductor channel:

« Measured effects of the order of 0.1-1% have

been reported for the voltage or resistance change

(between P and AP)…. », from the review article

« Electrical Spin Injection and Transport in Semiconductors » by BT Jonker

and ME Flatté in Nanomagnetism (ed.: DL Mills and JAC Bland, Elsevier 2006)

Wang et al, PR B77,020402,2008 (local, without MTJ)

Results on graphene in Kawakami’s group (Riverside)

Wei Han et al, preprint(nonlocal with MgO MTJ)

ΔR ≈130 Ω, ΔR/R ≈ 3x10-3

ΔR =10 Ω, ΔR/R ≈ 7%

M

1.8µm 250nm600nm

Al2O3

CoAl2O3

Co

Graphene

-0 .3 -0 .2 -0 .1 0 .0 0 .1 0 .2

43M

44M

45M

46M

R (O

hm)

H (T)

≈ 2 MΩ

RTunnelRTunnel

B. Dlubak et al, CNRS/Thales 2010

1000 1500 2000 2500 3000 3500

0

9000

18000

27000

Inte

nsity

(cou

nts)

Ram an shift (cm -1)

2 layer flake 2 layer flake + Al 6A oxided

1010µµmm

exfoliated graphene

strip

Al2O3(1nm)/Co bars

T=10K

Graphene (bilayer, exfoliated): ΔR/R ≈ (5-10%), ΔR ≈ 2 MΩVAP-VP ≈ 0.5 mV

Tunnel resistances ≈ a few MΩLarge signal: MR ≈ 10% ΔR ≈ 1MΩ, ΔV ≈ a few mV for V = 20 mV)

B. Dlubak et al, CNRS/Thales 2010, col. De Heer, C. Berger, Georgia Tech

10µm

Graphene (multilayer grown on C-face 4H-SiC)

Al2O3

CoAl2O3

Co

GrapheneRTunnel

RTunnel

ΔR/R≈10%

ΔR ~ 1MΩ

T=10K

-1000 -500 0 500 1000

5,8M

5,9M

6,0M

6,1M

6,2M

6,3M

6,4M

6,5M

ΔR/R

=MR

(%)R

esis

tanc

e (Ω

)

Magnetic field (Oe)-2

0

2

4

6

8

10

12L= 0.8 μm, R = 6MΩ

B. Dlubak et al, CNRS/Thales 2010, col. De Heer, C. Berger, Georgia TechGraphene (multilayer grown on C-face 4H-SiC)

Al2O3

CoAl2O3

Co

GrapheneRTunnel

RTunnel

ΔR/R≈10%

ΔR ~ 1MΩ

T=10K

-1000 -500 0 500 1000

5,8M

5,9M

6,0M

6,1M

6,2M

6,3M

6,4M

6,5M

ΔR/R

=MR

(%)R

esis

tanc

e (Ω

)

Magnetic field (Oe)-2

0

2

4

6

8

10

12

-1000 -500 0 500 1000136,0M

136,5M

137,0M

137,5M

138,0M

ΔR/R

=MR

(%)

Res

ista

nce

(Ω)

Magnetic field (Oe)

-0,2

0,0

0,2

0,4

0,6

0,8

1,0

1,2

L= 0.8 μm, R = 6MΩ L= 2 μm, R = 136MΩ

Tunnel resistances ≈ a few MΩLarge signal: MR ≈ 10% ΔR ≈ 1MΩ, ΔV ≈ a few mV for V = 20 mV)

B. Dlubak et al, CNRS/Thales 2010, col. De Heer, C. Berger, Georgia Tech

Al2O3

CoAl2O3

Co

GrapheneRTunnel

RTunnel

ΔR/R≈10%

ΔR ~ 1MΩ

T=10K

-1000 -500 0 500 1000

5,8M

5,9M

6,0M

6,1M

6,2M

6,3M

6,4M

6,5M

ΔR/R

=MR

(%)R

esis

tanc

e (Ω

)

Magnetic field (Oe)-2

0

2

4

6

8

10

12

-1000 -500 0 500 1000950.00k

1.00M

1.05M

1.10M

1.15M

1.20M

1.25M

1.30M

R(Ω

)

Champ Mag. (Oe)

RoomTemp.ΔR/R≈10%

Graphene (multilayer grown on C-face 4H-SiC)

L= 0.8 μm, R = 6MΩ

Tunnel resistances ≈ a few MΩLarge signal: MR ≈ 10% ΔR ≈ 1MΩ, ΔV ≈ a few mV for V = 20 mV)

B. Dlubak et al, CNRS/Thales 2010, col. De Heer, C. Berger, Georgia Tech

Al2O3

CoAl2O3

Co

GrapheneRTunnel

RTunnel

ΔR/R≈10%

ΔR ~ 1MΩ

T=10K

-1000 -500 0 500 1000

5,8M

5,9M

6,0M

6,1M

6,2M

6,3M

6,4M

6,5M

ΔR/R

=MR

(%)R

esis

tanc

e (Ω

)

Magnetic field (Oe)-2

0

2

4

6

8

10

12

-1000 -500 0 500 1000-30k

-20k

-10k

0

10k

RN

L(Ω

)

Champ Mag (Oe)

T = 10 K nonlocal detection

Nonlocal detectionLocal detection

Graphene (multilayer grown on C-face 4H-SiC)

Tunnel resistances ≈ a few MΩLarge signal: MR ≈ 10% ΔR ≈ 1MΩ, ΔV ≈ a few mV for V = 20 mV)

drainsourcenanotube

VSD

Quasi-continuous DOS, same conditions as for semiconducting or metallic channel

(also diffusive transport regime)

Uc=e2/2CδE+Uc

eΔV ≈ meV

Usual conditions: experiments at small bias

voltage

LSMO/CNT/LSMO:experiments at higher

voltage, thanks to relatively large interface

resistances and smallV2/R heating at large V

Oscillatory variation of the conductance, different signs of the MR depending on the

bias voltage and from sample to sample

Uc≈ 0.2-0.3 meV, δE ≈ 1 meV

drainsourcenanotube

eΔV = 25-500 meV >> Coulomb energy

and level spacing, 4 K< T <120 K

drainsourcenanotube

VSD

Quasi-continuous DOS, same conditions as for semiconducting or metallic channel

(also diffusive transport regime)

Uc=e2/2CδE+Uc

eΔV ≈ meV

Usual conditions: experiments at small bias

voltage

LSMO/CNT/LSMO:experiments at higher

voltage, thanks to relatively large interface

resistances and smallV2/R heating at large V

Uc≈ 0.2-0.3 meV, δE ≈ 1 meV

drainsourcenanotube

eΔV = 25-500 meV >> Coulomb energy

and level spacing, 4 K< T <120 K

Sahoo et al, Nat.Phys.2005

) small and(largelong..

,2 if largeis/1

)1/( *22

Mvifei

vLMR

tvL

RR

sf

T

rnsf

sfnP

+

∝=>+

−=Δ

τ

ττττγγ

Nanotubes and graphene)CNTin M small (largeandlong +vsfτ

Small spin-orbit coupling

of carbon

→ long spin lifetime

Dispersion in CNT and graphene

→ large velocity (even for smallcarrier density)

C-based vs metals

or semiconductors

Fert et al, IEEE Transactions on Electronic Devices,54,5,921,2007 H.Jaffres, A. Fert et al, PR B 82,

140408(R), 2010

)50

,45,50(

grapheneinm

CNTinmns

sf

sfsf

μλμλτ

≈

≈≈

VI I

F1 F2RT>>RN

L

Semiconductors→ΔR≈10-100 mΩ << RT, ΔR/R≈ 10-4-10-3, ΔV ≈ 10-100 μVvsf smallbut long τ

Metals→ΔR ≈ mΩ (≈ RN), metal contact: ΔR/R<10%, ΔV ≈ μV, ,

tunnel: RN<<RT, ΔR/R≈ 10-4-10-3, ΔV ≈ 10-100 μV,

sfshort butlarge τv

C-based vs metals

or semiconductors

Nanotubes and graphene

) small and(largelong..

,2 if largeis/1

)1/( *22

Mvifei

vLMR

tvL

RR

sf

T

rnsf

sfnP

+

∝=>+

−=Δ

τ

ττττγγ

)CNTin M small (largeandlong +vsfτ

VI I

F1 F2RT>>RN

Fert et al, IEEE Transactions on Electronic Devices,54,5,921,2007 H.Jaffres, A. Fert et al, PR B 82,

140408(R), 2010

L

L I

VI I

F1 F2 L

12

xjjEeN

jjjx

j

sf

F

e

∂−∂

=−

=+∂

∂=

↓↑↓↑

↓↑±

↓↑↓↑

)())((2

,1

)()(

τμμ

μρ

Spin signal (VAP – VP) ≈ Δμ/eand Δ μ derived from the

drift/diffusion equations

+ boundary conditions for spin-dependent interface resistances

*)(

)()(0)(

0)(

)1( TT

Txx

RR

IR

γ

μμ

m=

=−

↓↑

↓↑↓↑>↓↑

<↓↑

N

V

Spin accumulationΔ μ = EF↑- EF↓

L

VI I

F1 F2

3

+ interplay between spin accumulations at different interfaces

VP = -VAPVAP > VP

VAP – VP ≈ Δμ/e≈λN

T. Valet and A.F., PR B 1993

EF↑

EF↓

L I

VI I

F1 F2 L

12

xjjEeN

jjjx

j

sf

F

e

∂−∂

=−

=+∂

∂=

↓↑↓↑

↓↑±

↓↑↓↑

)())((2

,1

)()(

τμμ

μρ

Spin signal (VAP – VP) ≈ Δμ/eand Δ μ derived from the

drift/diffusion equations

+ boundary conditions for spin-dependent interface resistances

*)(

)()(0)(

0)(

)1( TT

Txx

RR

IR

γ

μμ

m=

=−

↓↑

↓↑↓↑>↓↑

<↓↑

N

V

L

VI I

F1 F2

3

+ interplay between spin accumulations at different interfaces

VP = -VAPVAP > VP

VAP – VP ≈ Δμ/e ≈λN

T. Valet and A.F., PR B 1993

μ ↑(↓) =eV + EF[↑(↓)]

Δμ = μ↑- μ↓

≈

10-4 10-2 100 102 104 1060.0

0.5

1.0

ΔV/V

PB

IAS

R*T / RN

1

2

3

3

VI I

F1 F2L

3

≈2γ2TR*

sfn ττ >>

sfn

TRRττ

γ/1

2 *2

+≈Δ

RT*>>RNλN/LΔR/R

2ch

2N

2 )(R4R4LLNN λγλγ =≈

« spin signal » ΔR = (VAP-VP)/I calculated from

drift/diffusion equations (RT* =tunnel resistance,

RN= channel spin resistance = ρN λN/AN)RT*RT*

rn tV

Ltimedwell2=τ

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105

0

20

40

60

R*

T=R

N

ΔR (

a.

u.)

R*

T/R

N

λN=5L

γ=0.8

≈

10-4 10-2 100 102 104 1060.0

0.5

1.0

ΔV/V

PB

IAS

R*T / RN

1

2

3

3

VI I

F1 F2L

3

≈2γ2TR*

sfn ττ >>

sfn

TRRττ

γ/1

2 *2

+≈Δ

RT*>>RNλN/L

X

XX,X,X,X: CNT serieswith ΔR increasing as γ2RT*∝ γ2R and

ΔR/R ≈ constant (72%, 60%, 54%, 53%) for R varying between 33

and 150 MΩ

XXX

XXX

X

X

X

X

XX

X,X,X,X:graphene with ΔR ≈ constant and ΔR/R ∝ 1/R as RT* and R ≈ 2 RT*

increases ΔR/R

2ch

2N

2 )(R4R4LLNN λγλγ =≈

X

« spin signal » ΔR = (VAP-VP)/I calculated from

drift/diffusion equations (RT* =tunnel resistance,

RN= channel spin resistance = ρN λN/AN)RT*RT*

10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105

0

20

40

60

R*

T=R

N

ΔR (

a.

u.)

R*

T/R

N

λN=5L

γ=0.8

rn tV

Ltimedwell2=τ

Sample #4RP = 150 MΩ

MR= 60 %

Sample #1

Sample #3

RP = 110 MΩMR = 54 %

RP = 33 MΩMR=53 %

Sample #2

RP = 90 MΩMR=72 %

R(ΩM) exp.MR calc. MR1 90 72% 74% 2 150 60% 58% 3 110 54% 68% 4 33 53% 99%

Best fits of MR in a series of 4 samples with

..

2

/1)1/( 22

resisttunneloftcoefontransmissithefromderivedis

tVLwhere

RR

r

rGrn

sfnP

=

+−≈Δ

τ

ττγγ

for γ = 0.75 and τsf = 50 ns(λN ≈ 45 μm)

Analysis for Carbon Nanotubes

0 50 100 150

0

2

4

6

8

10

12

ΔR/R

=MR

(%)

Rb*L (Ω.m)

∗ sf = 100 µm

Measured MR

A

B

CD

E

∗ sf = 200 µm

Model (4):∗ sf = 3.9 µm

∗ sf = 50 µm

MR (%)

ΔR (MΩ)

R (MΩ)

λN(μm)

L (μm)

ED

C

BA 0.8

22

2

2

6834

14

1.92.9 0.55

0.15

0.35

0.41.5

9.53.9

1.2

0.71.1

10870

99

116205

Interpretation of the MR of the SiC graphene with the

expression for RT*>>RN:

LRw

LRRR

lyequivalentorRR

T

N

N

T

sfn

T

*

2

2

*2

2

*2

)/2

1(

1)1(

,,/1

2

λ

ρλγ

γ

ττγ

∝+−

=Δ

+=Δ

T

λN

λN

λN

λN

MRexp γ = 0.4

ΔR/R vs RT*L

Spin diffusion length λN calculated from ΔR/R, L, w and RT* with

γ=0.4

grapheneN RL

R 22

2max )(

12 λ

γγ

−=Δ

0 50 100 150

0

2

4

6

8

10

12

ΔR/R

=MR

(%)

Rb*L (Ω.m)

∗ sf = 100 µm

Measured MR

A

B

CD

E

∗ sf = 200 µm

Model (4):∗ sf = 3.9 µm

∗ sf = 50 µm

MR (%)

ΔR (MΩ)

R (MΩ)

λN(μm)

L (μm)

ED

C

BA 0.8

22

2

2

6834

14

1.92.9 0.55

0.15

0.35

0.41.5

9.53.9

1.2

0.71.1

10870

99

116205

Interpretation of the MR of the SiC graphene with the

expression for RT*>>RN:

LRw

LRRR

lyequivalentorRR

T

N

N

T

sfn

T

*

2

2

*2

2

*2

)/2

1(

1)1(

,,/1

2

λ

ρλγ

γ

ττγ

∝+−

=Δ

+=Δ

T

λN

λN

λN

λN

MRexp γ = 0.4

ΔR/R vs RT*L

10-4 10-2 100 102 104 1060.0

0.5

1.0

ΔV/V

PB

IAS

R*T / RN

1

2

3 XXXX

XX

X

ΔR/R

CNT

graphene

Pure spin currents

Pure spin current, J↑ = - J↑ , in N at the right of F1

(no charge current and no capacitance effects)

Spin injection

Spin ↑current

Spin ↓ current

Spin accumulation (spin pressure)

Pure spin currents for spin « only » processing ?

Beyond CMOS with treatment of information (logic gates, etc) using

pure spin currents ?Pure spin current, J↑ = - J↑ ,

in N at the right of F1 (no charge current and no

capacitance effects)

Spin injection Spin accumulation

(spin pressure)Spin ↑ current

Spin ↓ current

Spin “only”processing unit

array of spin injectors

array of spin detectors

INPUT

OUTPUTCourtesy

C.Chappert

Theory of spin-orbit effects and spin relaxation in CNT(Huertas-Hernando et al, PR B 06, Huertas-H. et al, Eur. Phys.J.Sp.Top. 07 Bulaev et al,PR B08): main effect from curvature

Exper. (F. Kuemmeth et al, Nature 2008): level spectroscopy in Coulomb blockade regime

Carbon Nanotubes

nmmeVd

nmmevd

calccurv

/9.1

/6.1

.exp

..

=Δ

=Δ Spin-orbit Δ + scattering

spin relaxation (depending on d)

Graphene: Role of corrugation (curvature), role of scattering ?

Longer spin propagation than 100 μm ?

Next steps

Theory of spin-orbit effects and spin relaxation in CNT(Huertas-Hernando et al, PR B 06, Huertas-H. et al, Eur. Phys.J.Sp.Top. 07 Bulaev et al,PR B08): main effect from curvature

Exper. (F. Kuemmeth et al, Nature 2008): level spectroscopy in Coulomb blockade regime

Carbon Nanotubes

nmmeVd

nmmevd

calccurv

/9.1

/6.1

.exp

..

=Δ

=Δ Spin-orbit Δ + scattering

spin relaxation (depending on d)

Graphene: Role of corrugation (curvature), role of scattering ?

Longer spin propagation than 100 μm ?

Next steps

Spin manipulation by gate ?I I

F1 F2

spin gate?By ?

Proximity with a ferromagnetic material

Amplification of spin-orbit by proximity with large S-O material + Electric field or ferroelectric gate

Edges effects

Graphene and spintronics

Meeting on Graphene

Brussels, Feb. 15, 2011Albert Fert

UMP CNRS/Thales and University Paris-Sud

1) Graphene (or CNT) much better than classical metals andsemiconductors for spin transport to macroscopic distances and implementation of large scale spintronic logic circuits

2) Review of more sophisticated quantum effects for graphene-based spintronics

Conclusions

Major advantage of graphene (and CNT) over classical metals and semiconductors

(for spin transport in general)

Long spin lifetime (small spin-orbit, etc)

Large electron velocity+

Spin propagation length ≈100 μm (longer can be expected)

allowing, for example, the implementation of large scale

spintronic logic circuits

1

2 Next stage: paradigmatic concepts based on the exploitation of edge effects, proximity interactions,

gate potentials, pseudo-spin effects