Orbitally phase coherent spintronics
C. Feuillet-Palma
Laboratoire Pierre Aigrain,
Ecole Normale Supérieure, Paris
Experiment : T. Delattre, T. Kontos,
J.-M. Berroir, B. Plaçais, G. Fève,D.C. Glattli.
Theory: A. Cottet
Acknowledgment : M. Aprili, A. Thiaville, S. Rohart, H. Jaffrès, G.E.W. Bauer, A. Fert.
Molecular electronics
Hybrid circuit necessarily formed for study of electron transport in molecule
Electronic transport should be sensitive to molecular properties
Quantum effects in electronic transport
Hybrid circuit & Spintronics
Pasupathy et al. Science, 306 (2004)
N. Roch et al. Nature 453, 347 (2008)
Hauptmann et al. Nature Physics 4 (2008)
T. Delattre et al. Nature Physics 5, 208 (2009)
Confinement :
localized eletronic states
Spintronics of localized
electronic states
Magnetic tunnel junction…
N 1h
E
N2i
N1h
EF
eVSD
F1
E
R
N2i
Spin signal
MG
EF
H
I
F2
HcL HcR
Jullière’s model
HcR
HcL
P
VSD
GAP  T 2 N  N 
2
GP  T ( N   N  )
2
2
2
N  N
N  N
RAP  RP
2P 2
MG 

RP
1  P2
Hypothesis: the electron’s phase is not considered!
…with a single wall carbon nanotube (SWNT) :
Simplest spin dependent CNT device
VSD
CG
VG
Field Effect Transistor (FET) geometry analog to optical polarizer\analyzer experiment:
Gate capacitively coupled to NT.
Study as a function of VSD and VG.
Spin FET behavior in SWNTs
R(k)
2500
T= 1.86K
VG= +4.302V
L=500nm
MG
2400
2300
-0,4
-0,2
0,0
B(T)
0,2
0,4
170
R(k)
168
166
164
162
-0,4
T= 1.86K
VG= +4.328V
L=500nm
-0,2
0,0
B(T)
0,2
0,4
Both signs of TMR can be observed.
Oscillations of TMR as a function of gate voltage.
Spin dependent resonant tunneling mechanism (quantitative theory A. Cottet et al.)
How is this picture modified in multi-terminal devices ?
S. Sahoo et al., Nature Phys., 1, 99 (2005), H.T. Man et al., Phys. Rev. B R 73, 241401 (2006),
A. Cottet et al. Semicond. Sci. Tech. 21, S78 (2006), A. Cottet and M.-S. Choi PRB ‘06
Quantum coherent transport vs spintronics
« Theorist’s blob » experiment
C.P. Umbach et al., APL, 50, 1289 (1987)
« Non-local » spin injection
F.D. Jedema et al., Nature, 416, 713 (2002)
See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)
Coherent non-local effects in disordered mesoscopic devices and
non-local spin dependent voltages in disordered incoherent conductors
Quantum coherent transport vs spintronics
« Non-local » spin injection
F.D. Jedema et al., Nature, 416, 713 (2002)
See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)
Hysteretic switching of non-local voltage as a function of magnetic field
Resistor network model for semiclassical spin transport
r1
N
r1
R12
R1
r2
F
r2
R23
R 2
F
r3
r1
r1
R12
r4
V3
R 2
r2
r2
R23
R3
r3
N
r4
R4
R3
V
R1
r3
R34
V4
R4
r3
R34
r4
r4
Model conventionally used in multichannel incoherent spin transport
Non-local spin signal obtained because spin asymmetry
Not valid a priori for coherent few channel conductor
Quantum coherent transport vs spintronics
« Theorist’s blob » experiment
C.P. Umbach et al., APL, 50, 1289 (1987)
h/e modulations due to Aharonov-Bohm effect in the outer loop (not in the
classical path)
Small effect here (1 e2/h over 500 e2/h)
Quantum coherent transport vs spintronics
« Theorist’s blob » experiment
C.P. Umbach et al., APL, 50, 1289 (1987)
« Non-local » spin injection
F.D. Jedema et al., Nature, 416, 713 (2002)
See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)
Few channel regime in NTs make quantum effect a priori prominent.
Use of SWNT
Fabrication of SWNTs devices
Standard Nano-lithography process
Johnson & Silsbee PRL 55 (1985)
C.P. Umbach et al., APL, 50, 1289 (1987)
Device geometry
1
MFM, J.-Y. Chauleau, S. Rohart, A. Thiaville (LPS,Orsay)
2
3
4
VSD
I12
Transverse anisotropy for magnetization of NiPd stripes
Non-local geometry for charge and spin transport
Side gates in addition to back gate to control locally the sections of NT
V34
Coupled Fabry-Pérot electronic interferometers
VGS1
e-
e-
e-
VGS2
e0 V (A.U.)
1
eVSD
Reservoir L
Reservoir R
VSG1
VSG1=0
non
zero
VVSG2
and
non
zero
=0
non zero
=0 and
and
=0VSG2
SG2
Means for characterization
VSG2
Resonances on lines VSG1 +a VSG2 =cste
Nonlinear differential conductance spectroscopy
GR
GL
hvF
E 
2L
eVSD
VSD
DE
Reservoir L
Reservoir R
2DE
VG
VG
Fabry-Pérot electronic interferometer
Direct access to level spacing
0
dI/dV (4e2/h)
1
VSG1
N
H
VSG2
VBG
F
F
Non-local voltage signal
N
INL
G12
V34
0.2
V34(µV)
VSG2 = -6.0 V
VSG1 = -8.76 V
VBG = -11.772 V
0.0
-0.2
-100
-50
0
H(mT)
Tartan pattern for non-local voltage as a function of side gates
Characteristic hysteretic switching of non-local voltage
A priori interplay between non local spin transport and orbital coherence
50
100
Gate modulations of non-local voltage signal
MV=V34P-V34AP
VSG1 = -5 V
VBG = -5.455 V
-48
-56
-100 -50
0
50
100
H(mT)
VSG1
F
N
P
F
H
0.0
-2.5
-5.0
-7.5
Sample III
VBG=-5.455V
VSG1=-5.0V
VSG2
VBG
N
MV (V)
MV
-52
V34 (V)
V34(V)
-44 VSG2 = -5.8 V
INL
VBias
-20
-40
-60
-20
V34
-18
-16
-14
-12
VSG1 (V)
Gate modulation of non local voltage according to tartan pattern
Locally gate controlled MV
-10
-8
-6
VBG
VSG1
N
F
H
VSG2
F
Anomalous hysteresis in the current
N
INL
G12
V34
MG=1-G12AP/G12P
MV=V34P-V34AP
N-F non-local voltage
N-F non-local conductance
0.010
MG
VSG2= 4.8V
V34(µV)
G12(e²/h)
0.625
VSG2= -0.8V
0.600
0.400
MV
VSG2= -0.8V
0.005
VSG2= -9.4V
0.375
-100 -50 0 50 100
H(mT)
-100 -50 0 50 100
H(mT)
MG controlled by remote side gate
Sign change in MV specific to coherent case
Non local spin transitor action in G and V
CFP et al. PRB 81, (2010)
Resistor network model ?
1N
~
r1
R1
VSD
r1
2F
3F
NT12
NT23
R12 ~
r3 r3
r2 r2 R23 ~
Icw1
Icw3
R2
R3
Ic12
R1
Icx1
R2
R3
~
r2
Icx3

~
r3 r3
r1
R12
4N
~
r4
R4
Vc3
Ic12
~
r1
NT34
R 34
r2
R23
r4
Icw4
Vc4
R4
Icx4
R34
Model conventionally used in incoherent spin transport
Non-local spin signal obtained because spin asymmetry
N-F current independent of magnetization relative orientations (also found
In more sophisticated models e.g. Takahashi & Maekawa).
~
r4
r4
Multi-terminal scattering appoach
e i 1 2
t1 p
1N
r1 p
r2 ( p , )
r1 p
t1 p
e i 1 2
t 2 ( p , )
u 2 ( p , )
r ' '2( p , )
I12
e i 3 4
t3( p , )
r3( p , )
r3( p , )
r2 ( p , )
2F
VSD
e i 2 3
t 2 ( p , )
t3( p , )
e i 23
u3( p , )
t4 p
r4 p
e i 3 4
I 0
r4 p
4N
t4 p
r ' '3( p , )
V34
3F
I 0
240
0
210
-5
180
-0.005
23=3
1
0
0
23=3
-0.010
0
2
4
2
4
6
6
The scattering approach provides an explanation for both non local signals in V and G.
Difficult to obtain N-F current magnetic configuration dependent in the diffusive
Incoherent regime
A. Cottet, CFP and T. Kontos Phys. Rev. B 79, 125422 (2009)
VSG1
N
H
VSG2
VBG
F
F
Spectroscopy of conductance
N
INL
G12
V34
Interference fringes observed in the conductance
Multiple Fabry-Perot electronic interferometers physics
Energy scale correspond to one NT section here
CFP et al. PRB 81, (2010)
Magnetic configuration dependent phase shift
F
F
G12
-20
-30
N
2
INL
-10
0.015
P
N
H
VSG2
VBG
G12 (e /h)
VSG1
MG (%)
0
V34
0.010
0.005
-10
-5
0
5
10
VSG2 (V)
Modulations of GP due to Fabry-Perot physics
The orbital phase depends
on magnetic configuration !
Gate modulations of MG phase shifted
Quantitative agreement with scattering theory
CFP et al. PRB 81, (2010)
Orbitally coherent spintronics
Theory : A. Cottet, CFP and T. Kontos Phys. Rev. B 79, 125422 (2009)
« Theorist’s blob » experiment
Aharonov-Bohm
Phase
Quantum
mechanical path
Quantum
mechanical path
Classical
path
Classical
path
Geometric
Phase
« Theorist’s blob » experiment
V34
1 µm
I12
Photo MEB
Nonlinear spectroscopy
4
3
F
2
F
1
N
N
VBG
Nonlinear spectroscopy of Fabry-Perot interferometers in carbon nanotube section
Magnetic switchings
G23 (2e²/h)
1.145
T = 1.65 K
1.140
1.135
1.112
1.110
1.108
T = 4.2 K
-100
0
H (mT)
100
200
0.19
T = 4.2 K
G34 (e²/h)
0.18
0.17
4
3
2
1
T = 1.65 K
2.32
G12 (e²/h)
-200
2.31
T = 4.2 K
2.18
2.16
-200
0.10 T
0.09
= 1.65 K
-100
0
100
H (mT)
Anomalous spin signal in the
conductance N-N
F
F
N
-100
0
H (mT)
100
200
N
VBG
N-N spin spin signal is
temperature dependent
Spin signal temperature dependance
normMG
1.0
0.5
0.0
2.0
2.5
3.0
3.5
4.0
T (K)
No Temperature dependance of spin signal in conductance F-F signal
Spin signal decrepancy in conductance N-N with temperature
Quantitative agreement with theory with no parameters
Conclusion
Observation of local gate controlled “non local” magnetoresistance in mutli-terminal
SWNT devices
Multi-terminal devices are multi-electronic interferometers
Anomalous magnetoresistance between a N contact and a F contact in conductance due
to delocalization of electronic waves
Behaviour qualitatively and quantitatively reproduced within the scattering approach
Orbitally phase coherent spintronics
Perspective : new device with no classical analog to investigate phase coherent
spin polarised electronic wave function
Maybe a new way to couple the orbital and spin degree of freedom ?