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 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

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!

…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 MG 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) 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

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 V 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

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 « 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

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

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

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

Nonlinear differential conductance spectroscopy GL 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

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

Gate modulations of non-local voltage signal MV 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

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)

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).

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, 125422 (2009)

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)

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, 125422 (2009)

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

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

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

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

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

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 ?