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