Zagreb, May 2008, A. Fert, CNRS/Thales, Palaiseau, and Université Paris-Sud
In classical spintronics:
new types of MTJ
Spin transfer: switching,
oscillators, synchronization
Tulapurkar et al
Mz
and future of
0.0
A
P
P
-0.1
1.0
0.5
0.0
-0.5
-1.0
-0.5
M
x
Spintronics
m
0.0
0.5
1.0
-1.0
M
y
The present
0.1
Hruska et al
Spintronics with
semiconductors
Spintronics with
molecules
single-electron
devices
Introduction :
Spin dependent conduction in
ferromagnetic conductors,
Giant Magnetoresistance (GMR),
Tunnel Magnetoresistance (TMR)
Spin dependent conduction in ferromagnetic metals
(two current model)
n (E)
Mott, Proc.Roy.Soc A153, 1936
EF
Fert et al, PRL 21, 1190, 1968
Loegel-Gautier, JPCS 32, 1971
E
I
n (E)
I
Fert et al,J.Phys.F6, 849, 1976

Dorlejin et al, ibid F7, 23, 1977
=  /  or
 = ( -  )/ ( +  )
= ( - 1)/( + 1)

  0.3
=  / 

n (E)
Ni d band EF
Cr d level
  20

Ti V Cr Mn Fe Co Ni
Virtual
bound
state
E
Ni d band
n (E)
Cr d level
Mixing impurities A and B with opposite or similar spin asymmetries:
the pre-concept of GMR
Example: Ni + impurities A and B (Fert-Campbell, 1968, 1971)
1st case
2d case
 = /
A > 1, B < 1
A and B > 1
High mobility channel low 
spin
spin
spin
spin
AB >> A+ B
J. de Physique 32, 1971
AB  A+ B
• Magnetic multilayers
Fe
Cr
Fe
Cr
Fe
• Magnetic multilayers
Magnetizations of
Fe layers at zero field
in Fe/Cr multilayers
Fe
Cr
Fe
Cr
Fe
P. Grünberg, 1986  antiferromagnetic interlayer coupling
• Magnetic multilayers
Magnetizations of
Fe layers in an
applied field
in Fe/Cr multilayers
H
Fe
Cr
Fe
Cr
Fe
P. Grünberg, 1986  antiferromagnetic interlayer coupling
• Giant Magnetoresistance (GMR)
(Orsay, 1988, Fe/Cr multilayers, Jülich, 1989, Fe/Cr/Fe trilayers)
Orsay
Jülich
Resistance ratio
~ + 80%
V=RI
Magnetic field (kGauss)
Current
AP (AntiParallel) P (Parallel)
• Giant Magnetoresistance (GMR)
(Orsay, 1988, Fe/Cr multilayers, Jülich, 1989, Fe/Cr/Fe trilayers)
Anti-parallel magnetizations
(zero field, high resistance)
Resistance ratio
Fe
Cr
Fe
~ + 80%
Parallel magnetizations
(appl. field, low resist.)
Magnetic field (kGauss)
Fe
Cr
Fe
net
current
Current
AP (AntiParallel) P (Parallel)
Condition for GMR:
layer thickness  nm
Read head of
hard disc drive
voltage
current
Recent review :
« The emergence
of spintronics in
data storage »
Chappert, AF et al
Nat. Mat.(Nov.07)
Magnetic fields
generated by the media
track
0 5 nm
GMR sensor
1997 (before GMR) : 1 Gbit/in2 , 2007 : GMR heads ~ 600 Gbit/in2
• Magnetic Tunnel Junctions,Tunneling Magnetoresistance (TMR)
 0.1 m
ferromagnetic
electrodes
Jullière, 1975,
low T, hardly
reproducible
P
~ 100 nm
tunneling
barrier
(insulator)
Low resistance state
AP
High resistance state
Moodera et al, 1995, Miyasaki et al,1995, CoFe/Al2O3/Co, MR 30-40%
Applications: - read heads of Hard Disc Drive
- M-RAM (Magnetic Random Access Memory)
MRAM : density/speed of
DRAM/SRAM +
nonvolatilty + low
energy consumption
Epitaxial magnetic tunnel junctions (MgO, etc)
First examples on Fe/MgO/Fe(001):
CNRS/Thales (Bowen, AF et al, APL2001)
Nancy (Faure-Vincent et al, APL 2003)
Tsukuba (Yuasa et al, Nature Mat. 2005)
IBM (Parkin et al, Nature Mat. 2005)
….etc
2006-2007
Yuasa et al, Fe/MgO/Fe
Nature Mat. 2005
ΔR/R = (RAP-RP)/ RP  200% at RT
CoFeB/MgO/CoFeB,
ΔR/R  500% at RT in several
laboratories in 2006-2007
+
Clearer picture of the
physics of TMR:
what is inside the word
« spin polarization »?
1
P
2’
AP
5
1
2’
5
Mathon and Umerski, PR B 1999
Mavropoulos et al, PRL 2000 Butler et
al , PR B 2001
Zhang and Butler, PR B 2004 [bcc
Co/MgO/bcc Co(001)]
Zhang and Butler, PR B 2004
Beyond MgO
MgO, ZnSe (Mavropoulos et al, PRL 2000), etc
1
 1 symmetry (sp) slowly decaying
P
 tunneling of Co majority spin electrons
2’
5
SrTiO3 and other d-bonded insulators
(Velev et al , PRL 95, 2005; Bowen et al, PR B 2006)
5 symmetry (d) slowly decaying
 tunneling of Co minority spin electrons
AP
1
2’
in agreement with the negative polarization
of Co found in TMR with SrTiO3 ,TiO2 and
Ce1-xLaxO2 barriers
(de Teresa,
5
A.F. et al, Science 1999)
Zhang and Butler, PR B 2004
Beyond MgO
MgO, ZnSe (Mavropoulos et al, PRL 2000), etc
1
 1 symmetry (sp) slowly decaying
P
 tunneling of Co majority spin electrons
2’
5
SrTiO3 and other d-bonded insulators
(Velev et al , PRL 95, 2005; Bowen et al, PR B 2006)
5 symmetry (d) slowly decaying
 tunneling of Co minority spin electrons
AP
1
2’
in agreement with the negative polarization
of Co found in TMR with SrTiO3 ,TiO2 and
Ce1-xLaxO2 barriers
(de Teresa,
5
A.F. et al, Science 1999)
Physical basis of « spin polarization »(SP)
¤Tunneling: SP of the DOS for the
symmetry selected by the barrier
¤Electrical conduction: SP depends on
scatterers, impurities,..
Spin Transfer
(magnetic switching, microwave generation)
Spintronics with semiconductors
Spintronics with molecules
Spin Transfer
(magnetic switching, microwave generation)
Spintronics with semiconductors
Spintronics with molecules
Common physics:
spin accumulation
spins injected to long distances
by diffusion
Co/Cu: Current  to Plane (CPP) -GMR of multilayered nanowires
(L.Piraux, AF et al, APL 1994,JMMM 1999)
10
MR ratio (%)
8
CPP-GMR
subsists at
almost 1m
100 nm
6
4
400 nm
2
0
0
100
200
300
400
500
Co thickness (nm)
CPP-GMR
CIP-GMR
scaling length = mean free path
scaling length = spin diffusion length
>> mean free path
spin accumulation theory
(Valet-Fert, PR B 1993)
Other results: MSU group, PRL 1991, JMMM 1999
Spin injection/extraction at a NM/FM interface
NM
FM
(illustration in the simplest
case = flat band, low current,
no interface resistance,
single polarity)
FM
lsf = spin diffusion length in FM
zone of spin
accumulation
lNM
sf = spin diffusion length in NM
l
FM
sf
l
NM
sf
E
EF = spin chemical potential
Spin accumulation
= EF-EF
(beyond ballistic range)
(example: 0.5 m in Cu,
>10m in carbon
nanotube)
EF-EF ~ exp(z/ lFM
) in FM
sf
z
EF-EF ~ exp(-z/ lNM ) in NM
EF
sf
EF= spin chemical potential
Spin current
= J-J
z
lNM
sf
lFM
sf
J-J
J+J
= current spin polarization
Spin injection/extraction at a NM/FM interface
NM
FM
zone of spin
accumulation
l
FM
sf
l
NM
sf
E
E F
Spin accumulation
= EF-EF
lNM
sf = spin diffusion length in NM
(example: 0.5 m in Cu,
>10m in carbon
nanotube)
-CPP-GMR: typical multi-interface
problem (spin accumulation overlaps)
EF
EF
z
(illustration in the simplest
case = flat band, low current,
no interface resistance,
single polarity)
FM
lsf = spin diffusion length in FM
Extension to more complex situations
z
Spin current
= J-J
(beyond ballistic range)
lNM
sf
J-J
J+J
-Spin transfer: multi-interface
problem with non-colinear magnetic
configurations
-Spintronics with semiconductors:
spin inject. from metals complicated
by « density of states mismatch »,
band bending, etc
Spin injection/extraction at a Semiconductor/FM interface
NM = metal or
semiconductor
FM
zone of spin
accumulation
1) situation without
interface resistance
(« conductivity mismatch »)
lFM
sf
(Schmidt et al, PR B 2000)
l
NM
sf
Semiconductor/ F metal
E
E F
Spin accumulation
= EF-EF
If similar spin spliting on both sides but
much larger density of states in F metal
z
EF
EF
Spin current
= J-J
z
much larger spin accumulation density
and much more spin flips
on magnetic metal side
NM= metal
lNM
sf
lFM
sf
NM =
semiconductor
almost complete depolarization of
the current before it enters the SC
Spin injection/extraction at a Semiconductor/FM interface
NM =
semiconductor
FM
spin dependent. interf.
resist. (ex:tunnel barrier)
e-
Spin dependent drop of the
electro-chemical potential
lNM
sf
z
Spin accumulation
= EF-EF
lFM
sf
E F
EF
EF
EF
Current Spin
Polarization
(J-J)/(J+J)
rb*  rN   N l sfN
Discontinuity increases the
spin accumulation in NM
re-balanced spin relaxations
in F and NM
extension of the spinpolarized current into the
semiconductor
Rasbah, PR B 2000
A.F-Jaffrès, PR B 2001
Spin transfer
(J. Slonczewski, JMMM 1996, L. Berger, PR B 1996)
Ex:Cobalt/Copper/ Cobalt
S
Spin transfer
(J. Slonczewski, JMMM 1996, L. Berger, PR B 1996)
Ex:Cobalt/Copper/ Cobalt
The transverse component of the spin
current is absorbed and transferred
to the total spin of the layer
S
 j M x (M x M0)
 Torque on S
 Mx(MxM0)
S
Experiments on pillars
Au
Free ferro
Cu
Fixed
ferro
4 nm
10 nm
I-
Cu
V-
Metallic pillar  50x150 nm²
b) Second regime (high H):
steady precession
(microwave generation)
Au
Free ferro
4 nm
10 nm
barrier
Fixed
ferro
I-
Cu
a) First regime (low H):
irreversible switching
(CIMS)
V-
Tunnel junction
E-beam lithography + etching
Regime of irreversible magnetic switching
AP state
of m
First experiments on pillars:
M
Cornell (Katine et al, PRL 2000)
Mz
IBM (Sun et al, APL 2002)
0.0
P
1.0
0.5
0.0
-0.5
-1.0
-0.5
M
x
0.0
Py/Cu/Py 50nmX150nm (Boulle, AF et al)
0.5
-1.0
1.0
14,6
AP
P
-2
Py = permalloy
0
I (mA)
550000
Resistance()
dV/dI ()
14,5
GaMnAs/InGaAs/GaMnAs
tunnel junction (MR=150%)
(Elsen, AF et al, PR B 2006)
H=7 Oe
RT
14,4
P state
of m
-0.1
M
y
CNRS/Thales (Grollier et al, APL 2001)
m
AP
0.1
30 K
500000
450000
400000
-1.0x10
typical switching current  107A/cm2
switching time can be as short as 0.1 ns (Chappert et al)
5
-5.0x10
4
0.0
5.0x10
4
Current density (A.cm-2 )
1.0x10
5
1 x 105 A/cm2
Regime of steady precession (microwave frequency range)
15,0
5600G
9G
14,4
-4
0
3
2
1
0
3,5
4,0
Frequency (GHz)
I (mA)
M
Hd
Hd m
1.0
0.5
-1.0
0.0
-0.5
0.0
-0.5
0.5
1.0
H
0.0
-0.5
M
x
0.5
-1.0
-0.5
b
1.0
0.5
-1.0
0.0
-0.5
0.0
M
x
-0.5
0.5
1.0
-1.0
Increasing current
H
0.0
m
-0.5
1.0
0.5
-1.0
0.0
-0.5
0.0
M
x
-0.5
0.5
1.0
-1.0
M
y
m
Mz
P
0.0
Hd
0.5
M
y
m
H
Mz
0.5
Mz
AP
H
M
y
dV/dI ()
15,6
Power (pW/GHz)
CNRS/Thales, Py/Cu/PY (Grollier et al)
(Py = permalloy)
Regime of steady precession or vortex motion(microwave frequency range)
PSD (nW/GHz)
90
60
H = -303G
CoFeB/MgO/CoFeB junction (J.Grollier, AF et al 2008,
1.40mA
Lorentzian fit
collaboration S. Yuasa et al, AIST)
PSDmax =
90 nW/GHz
width=62MHZ
30
AP
H
M
m
0
4.5
5.0
Frequency (GHz)
5.5
MgO
P
PSD (nW/mA2GHz)
 ~ 20 – 30 nm
PSDmax =
50 nW/GHz
width=8MHZ
Low frequency vortex excitation
in Py/Au/Co nanocontacts
(M.Darques, AF et al, 2008)
Frequency (MHz)
Regime of steady precession or vortex motion(microwave frequency range)
PSD (nW/GHz)
90
60
H = -303G
CoFeB/MgO/CoFeB junction (J.Grollier, AF et al 2008,
1.40mA
Lorentzian fit
collaboration S. Yuasa et al, AIST)
PSDmax =
90 nW/GHz
width=62MHZ
30
PSD (nW/mA2GHz)
0
4.5
5.0
Frequency (GHz)
5.5
Spin Transfer mixes very different
(and interacting) problems:
transport (in metallic pillars,
tunnel junctions, point contacts)
problems of non-linear dynamics
micromagnetism (non-uniform
excitations, vortex motion..)
PSDmax =
50 nW/GHz
width=8MHZ
Low frequency vortex excitation
in Py/Au/Co nanocontacts
(M.Darques, AF et al, 2008)
Frequency (MHz)
100x170nm²
Py/Cu/Py (standard)
15,6
dV/dI ()
Co/Cu/Py (« wavy » angular variation
calculated by Barnas, AF et al, PR B 2005)
Au Py (8nm, free)
Cu ( 8nm)
Co (8nm, fixed)
IrMn (15nm)
or CoO or Cu
15,0
5600G
9G
14,4
free Py:fast spin
relaxation
fixed Co: slower spin
relaxation
-4
0
I (mA)
Negative I (mA)
Power (pW/GHz)
30
H0
H H0= 2(2OeOe)
20
9,5 mA
9 mA
8,5 mA
8 mA
7,5mA
7 mA
6,5 mA
6 mA
10
0
1.5
2.0
2.5
Frequency (GHz)
3.0
3.5
Boulle, AF et al,
Nature Phys. 2007
oscillations at H=0
Positive I
Switching of reprogrammable devices (example: MRAM)
1) By external magnetic field
(present generation of MRAM,
nonlocal, risk of « cross-talk »
limits integration)
Current
pulse
2) «Electronic» reversal by spin transfer
from current
(ST-MRAM: next generation of MRAM, with
demonstrations by Sony, Hitachi, NEC, etc)
Spin Transfer Oscillators (STO)
(communications, microwave pilot)
Advantages:
-direct oscillation in the microwave range (5-40 GHz)
f/ff  18000
-agility: control of frequency by dc current amplitude,
(frequency modulation , fast switching)
- high quality factor
- small size ( 0.1m) (on-chip integration)
-oscillations without applied field
-Needed improvements
- - increase of power by synchronization of a
large of number N of STO ( x N2 )
Rippart et al,
PR B70, 100406,
2004
Experiments of STO synchronization by electrical connection
(B.Georges, AF et al, CNRS/Thales and LPN-CNRS, preliminary results)
trilayer 2
Idc +
Ihf1+
trilayer 1
hf circuit
Idc
Ihf2
0.6
0.5
0.4
increasing I
0.3
0.2
0.1
- 9 mA
0.0
1.0
1.1
1.2
1.3
frequency (GHz)
0.6
power (pW/GHz/mA2)
Ihf1+ Ihf2
power (pW/GHz/mA2)
-12.4 mA
-11.00mA
-9.80mA
0.5
0.4
0.3
0.2
0.1
0.0
1.0
1.1
1.2
frequency (GHz)
1.3
Spintronics with semiconductors
and molecules
Spintronics with semiconductors
Magnetic metal/semiconductor
hybrid structures
Example: spin
injection from
Fe into LED
(Mostnyi et al,
PR. B 68, 2003)
Ferromagnetic
semiconductors (FS)
GaMnAs (Tc170K) and R.T. FS
Electrical control of ferromagnetism
TMR, TAMR, spin transfer (GaMnAs)
Field-induced metal/insulator transition
Spintronics with semiconductors
Magnetic metal/semiconductor
hybrid structures
Spin Field Effect Transistor ?
Example: spin
injection from
Fe into LED
(Mostnyi et al,
PR. B 68, 2003)
Ferromagnetic
semiconductors (FS)
GaMnAs (Tc170K) and R.T. FS
Electrical control of ferromagnetism
TMR, TAMR, spin transfer (GaMnAs)
Field-induced metal/insulator transition
V
F1
F2
Semiconductor
channel
Semiconductor lateral channel between
spin-polarized source and drain
transforming spin information into
large(?) and tunable (by gate voltage)
electrical signal
Nonmagnetic lateral channel between spin-polarized source and drain
F1
Semiconductor channel:
P
AP
Semiconductor channel
F2
« Measured effects of the order of 0.1-1% have been reported for the change in
voltage or resistance (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)
Nonmagnetic lateral channel between spin-polarized source and drain
F1
Semiconductor channel:
P
AP
Semiconductor channel
F2
« Measured effects of the order of 0.1-1% have been reported for the change in
voltage or resistance (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
Carbon nanotubes:
R/R  60-70%, VAP-VP  20-60 mV
nanotube
1.5 m
LSMO
LSMO = La2/3Sr1/3O3
LSMO
MR  72%
Nonmagnetic lateral channel between spin-polarized source and drain
F1
Semiconductor channel:
P
AP
Semiconductor channel
F2
« Measured effects of the order of 0.1-1% have been reported for the change in
voltage or resistance (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)
Carbon nanotubes:
L.Hueso, N.D. Mathur,A.F. et al, Nature 445, 410, 2007
AP
60%
R/R  60-70%, VAP-VP  20-60 mV
nanotube
1.5 m
LSMO
LSMO
P
LSMO = La2/3Sr1/3O3
P
Two interface
spin transport
problem
(diffusive
regime)
0612495, +
IEEE Tr.El.Dev*.
54,5,921,2007
*calculation. for
Co and GaAs
at RT
Condition
spin injection
dwell time n < spin lifetime sf
window
L
dwell time
1
L rb*
n 

*
v
tr v
2
2
2L
tN=20nm
N
lSF=2µm
1.6
0.30
R
0.25
1.2
0.20
RP
0.8
0.15
for  n  rb*   sf
0.4
0.05
10
tL
N=2µm
-4
10
-2
10
L / lsfN
V
F2
Semiconductor
channel
L
Window only for lsf(N) > L
 /(1   )

1   n /  sf
drops to zero as 1 / rb*
tN
L=200nm
0.10 L=20nm
0.0
0.00
F1
lsf
0.35
PP
R/R
R/R
AF and Jaffrès
PR B 2001*
+cond-mat
Condition for
0
10
*
r r
rb* /brNN
2
lsfN / L
10
4
Interface resistance rb*
in most experiments
 n   sf
rb*  unit area interface resist.  1/trans.co eff t *r
  spin asymmetry of the interface resistance
rN   N l sfN
Transport between SP source and drain : τ n  dwell time, τ sf  spin lifetime, γ  injection SP
: the contrast between P (on) and AP (off ),
R
RP
 2 /(1   2 )

, is large if  n   sf
1   n /  sf
Nanotubes (also graphene, other molecules) :
small spin  orbit  spin lifetime  sf is long ( 5  50ns )
2L
high velocity v   n 
can be relatively short ( 60ns*   sf )
v tr
Semiconductors:
 sf can be as long as in CNT ( for n  1017 el / cm3 )
but v is sm aller  long  n 
*
2L
 sf
v tr
CNT : τ n  60ns from L, v of CNT and t r derived from interface resistance
Transport between SP source and drain : τ n  dwell time, τ sf  spin lifetime, γ  injection SP
: the contrast between P (on) and AP (off ),
R
RP
 2 /(1   2 )

, is large if  n   sf
1   n /  sf
Nanotubes (also graphene, other molecules) :
small spin  orbit  spin lifetime  sf is long ( 5  50ns )
2L
high velocity v   n 
can be relatively short ( 60ns*   sf )
v tr
Semiconductors:
 sf can be as long as in CNT ( for n  1017 el / cm3 )
but v is sm aller  long  n 
2L
 sf
v tr
Solution for semiconductors:
shorter L ?, larger transmission tr ?
Transport between SP source and drain : τ n  dwell time, τ sf  spin lifetime, γ  injection SP
: the contrast between P (on) and AP (off ),
R
RP
 2 /(1   2 )

, is large if  n   sf
1   n /  sf
Nanotubes (also graphene, other molecules) :
small spin  orbit  spin lifetime  sf is long ( 5  50ns )
2L
high velocity v   n 
can be relatively short ( 60ns*   sf )
v tr
Semiconductors:
 sf can be as long as in CNT ( for n  1017 el / cm3 )
but v is sm aller  long  n 
2L
 sf
v tr
Solution for semiconductors:
shorter L ?, larger transmission tr ?
Potential of molecular
spintronics (nanotubes,
graphene and others)
Transport between SP source and drain : τ n  dwell time, τ sf  spin lifetime, γ  injection SP
: the contrast between P (on) and AP (off ),
R
RP
 2 /(1   2 )

, is large if  n   sf
1   n /  sf
Nanotubes (also graphene, other molecules) :
small spin  orbit  spin lifetime  sf is long ( 5  50ns )
2L
high velocity v   n 
can be relatively short ( 60ns*   sf )
v tr
Semiconductors:
 sf can be as long as in CNT ( for n  1017 el / cm3 )
but v is sm aller  long  n 
2L
 sf
v tr
Solution for semiconductors:
shorter L ?, larger transmission tr ?
Potential of molecular
spintronics (nanotubes,
graphene and others)
Next challenge for molecules:
spin control by gate
Summary
¤Already important
aplications of GMR/TMR
(HDD, MRAM..) and now
promising new fields
-Spin transfer for
magnetic
switching and
microwave
generation
-Spintronics with
semiconductors,
molecules or
nanoparticles
SILICON
ELECTRONICS
SPINTRONICS
Acknowledgements to
M. Anane, C. Barraud, A. Barthélémy, H. Bea, A. BernandMantel, M. Bibes, O. Boulle, K.Bouzehouane, O. Copi, V.Cros,
C. Deranlot, B. Georges, J-M. George, J.Grollier, H. Jaffrès, S.
Laribi, J-L. Maurice, R. Mattana, F. Petroff, P. Seneor, M. Tran
F. Van Dau, A. Vaurès
Université Paris-Sud and Unité Mixte de Physique CNRS-Thales, Orsay, France
P.M. Levy, New York Un., A.Hamzic, M. Basletic Zagreb University
B. Lépine, A. Guivarch and G. Jezequel
Unité PALMS, Université de Rennes , Rennes, France
G. Faini, R. Giraud, A. Lemaître: CNRS-LPN, Marcoussis, France
L. Hueso, N.Mathur, Cambridge
J. Barnas, M. Gimtra, I. Weymann, Poznan University
Two interface
spin transport
problem
(diffusive
regime)
L
dwell time
1
L rb*
n 

*
v
tr v
2
2
2L
0.35
tN=20nm
N
lSF=2µm
1.6
0.30
0.25
1.2
0.20
tN
L=200nm
0.10 L=20nm
0.4
0.05
10
40
30
0.8
0.15
0.0
0.00
-4
10
Semiconductor
channel
L
Window only for lsf(N) > L
GaAs QW=6nm
RP
T=4K
10
0
-2
L / lsfN
F2
a R
20
-300
tL
N=2µm
V
F1
lsf
MR (%)
*calculation. for
Co and GaAs
at RT
dwell time n < spin lifetime sf
10
0
10
*
r r
rb* /brNN
2
10
50
lsfN / L
MR ( % )
IEEE Tr.El.Dev*.
54,5,921,2007
spin injection

 /(1   )
1   n /  sf
drops to zero as 1 / rb*
as in this example
-200
-100
0 AF
100 et
200
(Mattana,
al)300
Magnetic field (Oe)
4
GaMnAs/AlAs/GaAs/AlAs/GaMnAs
vertical
structure
40
GaAs QW=6nm
b
T=4K
30
20
10
0
1E-3
)
0612495, +
Condition
window
PP
R/R
R/R
AF and Jaffrès
PR B 2001*
+cond-mat
Condition for
1.45nm
1.7nm
0.01
* AR ( .cm2 )2~ t
rb
(
cm
)N
AP
1.95nm
0.1
VSD
Usual
conditions:
small bias
voltage
experiments
LSMO/CNT/LSMO:
higher voltage
experiments thanks to
large interface
resistances and small
V2/R heating at large V
VG
eV = 25-500 meV
>> Coulomb energy,
level spacing,
spin-orbit spliting,
4.2 K< T <120 K
E+Uc
Uc=e2/2C
eV  1 meV
source
drain
nanotube
Oscillatory variation of the conductance,
different signs of theMR depending on the
bias voltage and from sample to sample
source
drain
nanotube
Quasi-continuous DOS, same conditions
as for semiconductor or metallic channel
Deviations from
J-J
J+J

 rF   rb*
rF  rN  rb*
at large current density (drift effect)
= low current limit
= deviations from
the low current limit
(nondegenerate
semiconductor)
from Jaffrès and A.F.
(see also Yu and Flatté)
current density
Condition for
Condition
spin injection
dwell time n < spin lifetime sf
window
0.35
N
1
L
dwell time
 n  2 L /(v t r )  rb*
tN=20nm
II
lSF=2µm
1.6
0.30
lsf
R  2 /(1   2 )

R P 1   n /  sf
PP
R/R
R/R
0.25
1.2
0.20
R (), r ()=
0.8
0.15
0.10 L=20nm
0.4
0.05
interface
resistance
I
(equal for source
and drain)
0.0
0.00
10
-4
I
Unpolarized current in the
semiconductor
(depolarization in the
source and repolarization
in the drain)
R/R = 0
drops to 0 as 1/rb*
tN
L=200nm
III
tL
N=2µm
10
-2
10
0
for  n  rb*   sf
10
2
10
rb* / rN
4
*
r
R
r
R
rII
rN
b
V/2
r
R
R
r
Optimal R/R
P
AP
r
R
r
R
III
V/2
r
R
R
r
R/R = 0
P
V/Vbias for local (2 types) and non-local geometries
2.0
N
1.8 l
1.6
V/V
P
1.4
=10 µm
SF
tN=100 nm
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-4
10
10
-3
10
-2
10
-1
10
0
*
10
rb /rN
1
10
2
10
3
10
4
Non-local
Diffusive transport
Ballistic*transport
0.35
-1
10
lSF=2µm
tN
L=200nm
0.10 L=20nm
0.4
0.05
0.0
0.00
10
tN=20nm
1.0
lSF=2µm
10
'
2
2
3
10
4
10
10
0.5
tL
N=2µm
-4
10
1.5
P
0.8
0.15
rb /r
N
R/R
PP
R/R
R/R
0.25
1.2
0.20
1
10
2.0
tN=20nm
N
1.6
0.30
0
-2
W
rb*   *
N tN
w
10
0
10
2
10
4
0.0
*
(l N ) 2
* rb rN *
rb / rN rb   *N sf W
t
w
-3
10
-2
10
-1
0
10
10
 n /  sf /rb*
N
N
+ additional geometrical parameters
when the number of conduction
channels is different for the injection and
in the channel (W  w in the example)
W/w
SF
1
10
2
10
MR of LSMO/Alq3/Co structures (preliminary results)
Collaboration CNRS/Thales [C. Barraud, P. Seneor et al) and CNR Bologna (Dediu et al)]
Co
resist
1- 4 nm
Alq3 (50nm)
LSMO
Co nanocontact
Alq3
LUMO
10 nm
Alq3 =  - conjugated 8-hydroxy-quinoline aluminium
LSMO
HOMO
Co