1. 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.

2. 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

3. Hybrid circuit & Spintronics
N. Roch et al. Nature 453, 347 (2008)
Pasupathy et al. Science, 306 (2004)
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

4. Magnetic tunnel junction…EF
N1h
N2i R
N1h E
N2i
Spin signal MG
eVSD EF F1 I F2 H
HcR
HcL
HcR
HcL
Jullière’s model
VSD
Hypothesis: the electron’s phase is not considered!

5. …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.

6. Spin FET behavior in SWNTsMG
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, (2006),
A. Cottet et al. Semicond. Sci. Tech. 21, S78 (2006), A. Cottet and M.-S. Choi PRB ‘06

7. Quantum coherent transport vs spintronics
« Theorist’s blob » experiment
C.P. Umbach et al., APL, 50, 1289 (1987)
F.D. Jedema et al., Nature, 416, 713 (2002)
See also M. Johnson and R. H. Silsbee, PRL 55, 1790 (1985)
« Non-local » spin injection
Coherent non-local effects in disordered mesoscopic devices and
non-local spin dependent voltages in disordered incoherent conductors

8. 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

9. Resistor network model for semiclassical spin transportV V3 V4 R1 R4
R12
R23
R34 r1 r4 N F
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

10. 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)

11. Quantum coherent transport vs spintronics
« Theorist’s blob » experiment
« 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)
C.P. Umbach et al., APL, 50, 1289 (1987)
Few channel regime in NTs make quantum effect a priori prominent.
Use of SWNT

12. Fabrication of SWNTs devices
Johnson & Silsbee PRL 55 (1985)
C.P. Umbach et al., APL, 50, 1289 (1987)
Standard Nano-lithography process

13. Transverse anisotropy for magnetization of NiPd stripes
Device geometry
VSG1 1 4 2 3
VSD
I12
VSG2
V34
MFM, J.-Y. Chauleau, S. Rohart, A. Thiaville (LPS,Orsay)
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

14. Coupled Fabry-Pérot electronic interferometers
VGS1
VGS2 e- e- e- e-
V (A.U.) 1
eVSD
Reservoir L
Reservoir R
VSG1
VSG2
Resonances on lines VSG1 +a VSG2 =cste
VSG1 =0 and VSG2=0
VSG1=0 and VSG2non zero
VSG1 non zero and VSG2=0
VSG1 non zero and VSG2 non zero
Means for characterization

15. Nonlinear differential conductance spectroscopyGL GR
eVSD
VSD DE
Reservoir L
Reservoir R
2DE VG VG
Fabry-Pérot electronic interferometer
Direct access to level spacing
dI/dV (4e2/h) 1

16. Non-local voltage signal
VSG1
VSG2
VBG N F F N H
INL
G12
V34
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

17. Gate modulations of non-local voltage signalMV
MV=V34P-V34AP
VSG1
VSG2
VBG N F F N H
INL
VBias
V34
Gate modulation of non local voltage according to tartan pattern
Locally gate controlled MV

18. Anomalous hysteresis in the current
VBG
Anomalous hysteresis in the current
VSG1
VSG2 N F F N H
INL
MG=1-G12AP/G12P
MV=V34P-V34AP
G12
V34
N-F non-local conductance
N-F non-local voltage MG MV
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)

19. Resistor network model ?
VSD
Vc3
Vc4
1 N
2 F
3 F
4 N
NT12
NT23
NT34
Ic12
Icw1
Icw3
Icx3
Icw4
Icx4
Icx1
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).

20. Multi-terminal scattering appoach
2 F
3 F
VSD
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, (2009)

21. Spectroscopy of conductance
VSG1
VSG2
VBG N F F N H
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)

22. Magnetic configuration dependent phase shift
VSG1
VSG2
VBG N F F N H
INL
G12
V34
Modulations of GP due to Fabry-Perot physics
The orbital phase depends
on magnetic configuration !
Gate modulations of MG phase shifted
CFP et al. PRB 81, (2010)
Quantitative agreement with scattering theory
Orbitally coherent spintronics
Theory : A. Cottet, CFP and T. Kontos Phys. Rev. B 79, (2009)

23. « Theorist’s blob » experiment
Geometric
Phase
Aharonov-Bohm
Classical
path
Quantum
mechanical path

24. « Theorist’s blob » experiment
VSD
V34
I12
1 µm
Photo MEB

25. Nonlinear spectroscopy
VBG N F 1 2 3 4
Nonlinear spectroscopy of Fabry-Perot interferometers in carbon nanotube section

26. Magnetic switchings Anomalous spin signal in the conductance N-N
VBG N F 1 2 3 4
Anomalous spin signal in the conductance N-N
N-N spin spin signal is temperature dependent

27. Spin signal temperature dependance
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

28. 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 ?