Non-collinear magneto-electronics in nanoscale conditions 

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Fabry-Perot transport regime

Colorscale plots of the conductance as a measure of the source-drain and gate voltages confirm the chessboard like pattern specific to the Fabry-Perot physics. The spacing between the centers of two adjacent rhombs gives access to the spacing of the energy levels inside the quantum dot (QD) which is, experimentallly, determined by, L, the length of the nanotube: E = hvF /L. In our case the spacing between rhombs is 5 mV as highlighted in fig. 1.7, (a), using orange dashed lines and it is consistent with  the lithographically defined length of the nanotube which is about 600 nm. Measurements performed in the linear regime were used to characterize the spin transport in the absence of a source-drain voltage. The signal registered has a hysteretic evolution, with the switchings indicating modifications in the magnetization of the PdNi leads. Measurements done on a large interval of gate voltages show consistent variations in the jumps magnitude up to 4 %.
A striking result obtained here in presented in fig. 1.7, (b). A similar hysteretic curve was obtained in out of equilibrium transport regime for multiple gate voltages values. The hysteretic signal shows magnetization reversal in the electrodes taking place before the external magnetic field applied changes sign. The phenomena was studied both when the field increases and decreases.

The evolution of magneto-electronics

Electrons, as charge carriers, have a property known as spin which is an angular momentum intrinsic to the particle. The quantum mechanical nature of the spin determines that an electron can be described using only two states, with the spin pointing either « up » or « down » (the choice of up and down being arbitrary). An electrical current passing through a macroscopic, non-magnetic conductor is unpolarized due to the fact that spins are randomly oriented.
Things change when ferromagnetic components are incorporated into electronic devices. The particularity of the ferromagnetic materials is that the electron’s magnetic dipoles are aligned in the same direction, their individual magnetic momentum added together creating a measurable macroscopic magnetic moment. In materials with a filled electron shell, the total moment of the electrons is zero because the spins are in up/down pairs. Only atoms with partially filled shells (i.e. unpaired spins) can have a net magnetic moment, so ferromagnetism only occurs in materials with partially filled shells. Ferromagnetism involves an additional phenomenon, though: the dipoles have to align spontaneously, giving rise to a spontaneous magnetization, even when there is no applied field.

The spin field effect transistor

An important brick to todays spintronic devices is the spin field effect transistor (SFET) proposed in 1989 by Supriyo Datta and Biswajit Das [12] that exemplifies very well, still, the relevance of electrical control over the magnetic degrees of freedom as means of spin modulating charge flow. The physical basis for this proposal relies on gate controlling the strength of the Rashba effect (demonstrated by de Andrada e Silva et al. [13]) in a one-dimensional conductor. In other words, in a confining potential (surfaces, asymmetric quantum wells, etc), the spin-orbit coupling may result in a spin splitting of electron states, which has the nature of the so-called Rashba effect [14].
This splitting can be tuned using an additional electric field opening up a pathway for realizing electric-field spin manipulation [15], [16].
In the Datta-Das device (see schematics in fig. 2.6), the current is modulated using the Rashba spin-orbit coupling (SO) between the spin of the polarized current inside the semiconductor material. The electric charge is introduced through an injecting electrode and collected via a drain electrode. A gate is used to generate an electric field that tunes the value of the effective magnetic field, −→BSO, through which the source-drain current can flow. This results in a very small electric field being able to control large currents. The effective magnetic field acting on the spin of an electron moving at velocity v in a region where an electric field E exists, reads (special relativity).

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Transport characteristics in nanotubes/nanoconductors

The originality of low dimensional conductors arises from the enhanced importance of the electron-electron interaction and the quantum coherence in the electronic transport. These two characteristics open the door to individual spin manipulation which is a very hot topic related especially to quantum computing but also to the realization of SFETs.
At such small dimensions, the phenomena taking place are of quantum nature, the transport is of the ballistic type and the physics that reunites all that is the mesoscopic physics. The length scale is in between microscopic and macroscopic systems, and bounded on one side by the de Broglie wavelength of the electron, and on the other, by the length scales for various scattering mechanisms that destroy the electron’s phase coherence or momentum [7].
Starting from the Datta – Das proposition that allows injection/detection of spins and also electrical control over quantum interference, similar to an optic polarizeranalyzer system.
H. T Man et al [18] presented an electronic device analogue to the Fabry-Perot interferometer based on a single wall carbon nanotube, capacitively coupled to a back gate. The nanotube is contacted with two PdNi ferromagnetic leads with different coercive fields, that function as source and drain. A source-drain voltage is used to control the chemical potentials of the two leads. The magnetic moments inside the electrodes lie in the sample plane.

Table of contents :

1 Introduction 
1.1 Main results
1.1.1 PdNi anisotropy
1.1.2 Non-collinear magneto-electronics/Spin dependent transport in quantum dots
1.1.3 Coulomb blockade transport regime
1.1.4 Fabry-Perot transport regime
2 Non-collinear magneto-electronics/Spin dependent transport in quantum dots 
2.1 Spin transfer torque
2.1.1 The evolution of magneto-electronics
2.1.2 The spin field effect transistor
2.1.3 Transport characteristics in nanotubes/nanoconductors
2.1.4 Electron tunneling
2.1.5 Julliere’s model
2.1.6 Magnetic tunnel junctions (MTJ)
2.2 Transport regimes
2.2.1 Quantum spin valves in weak-coupling regime
2.2.2 Magneto-Coulomb effect
2.3 Recent experimental work on spin polarized transport
2.3.1 Effective fields
3 Experimental setup 
3.1 Sample preparation
3.1.1 The substrate
3.1.2 The lithographic process
3.1.3 The resist
3.1.4 The electronic lithography
3.1.5 Development
3.1.6 Thin film deposition
3.1.7 CNT growth
3.1.8 PdNi Hall crosses
3.1.9 Observations on the sample fabrication process
3.2 Measurement techniques
3.2.1 Conductance measurements
3.2.2 MFM characterizations
3.2.3 Extraordinary Hall effect measurements
4 Magnetic anisotropy in PdNi nanostripes 
4.1 General considerations on PdNi anisotropy
4.1.1 General considerations on anisotropy
4.1.2 Particularity of the PdNi nanostripes anisotropy
4.1.3 Normal Hall effect and the extraordinary Hall Effect
4.2 Experimental results
4.2.1 Role of chemical composition
4.2.2 Capping layer effect
4.2.3 Thickness effects on PdNi
4.2.4 Nanometric samples
4.3 Conclusion
5 Non-collinear magneto-electronics in nanoscale conditions 
5.1 Coulomb blockade regime
5.1.1 Spin transport in the linear regime
5.1.2 Out of equilibrium spin-signal
5.1.3 Conclusion
5.2 Fabry-Perot transport regime
5.2.1 Spin transport in the linear regime
5.2.2 Spin transport in non-linear regime
5.2.3 Conclusion
6 Conclusions 


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