Advances in large-area graphene synthesis via chemical vapour deposition on metals like copper were instrumental in the demonstration of graphene-based novel, wafer-scale electronic circuits and proof-of-concept applications such as flexible touch panels. Here, we show that graphene grown by chemical vapour deposition on copper is equally promising for spintronics applications. In contrast to natural graphene, our experiments demonstrate that chemically synthesized graphene has a strong spin–orbit coupling as high as 20 meV giving rise to a giantspinHalleffect. The exceptionally large spinHall angle B0.2 provides an important step towards graphene-based spintronics devices within existing complementary metal-oxide-semiconductor technology. Our microscopic model shows that unavoidable residual copper adatom clusters act as local spin–orbit scatterers and, in the resonant scattering limit, induce transverse spin currents with enhanced skew-scattering contribution. Our findings are confirmed independently by introducing metallic adatoms-copper, silver and gold on exfoliated graphene samples.
Conventional electronics intended to build devices and schemes by manipulating the conducting electrons via charge, nowadays this gradually transforms into what we know as spintronics (SPIN-TRansport electrONICS), i.e., the technology which manipulates one more degree of freedom of the electron - the spin. This concept has evolved as a result of strengthening the technological requirements to the conventional electronic devices - first of all, concerning the reduced energy consumption, especially for the high-frequency operating elements, and also concerning the sensitivity of the devices. In turn, this has increased an interest within the academic community in the effects explicitly involved in the electron charge/spin manipulation, as well as in the materials which provide a large magnitude of these effects. The main theoretical description of these effects was given in the early 1970s [1, 2]. It has become clear that the combination of the material characteristics on different scales (e.g. spin-diffusion lengths, relaxation time, etc.) leads to a variety of spin-transport effects, such as giant magnetoresistance (GMR), anomalous Halleffect (AHE), spinHalleffect (SHE), spin accumulation, spin- transfer torque (STT), anomalous Nernst effect (ANE), spin Nernst effect (SNE), etc. All these phenomena constitute a base of spintronics. At the same time, the practical ab-initio numerical models and the technical means for their realistic simulation are still developing. A reliable ab-initio description of these effects in realistic models is a necessary step needed in the Material Science in order to predict and understand the particular features of the spin-phenomena in a given material or combined systems. Development of spintronics is intimately connected with the search of new materials which could combine ferromagnetic properties and properties of semiconductors. On the one hand, such materials could be a source of the spin-polarized electrons and, on the other, could be easily integrated with conventional semiconductor components. To create such a hybrid material - semiconductor with ferromagnetic properties appears to be a complex task, as integrating magnetic atoms into the crystal structure of the semiconductor significantly deteriorates its magnetic properties.
Magnetoresistance plays essential roles in providing both a fundamental understanding of electron transport in magnetic materials and in various technological ap- plications. Anisotropic magnetoresistance (AMR) [1, 2], giant magnetoresistance [3, 4], and tunneling magnetore- sistance [5–8] underpin technologies in sensors, memo- ries, and data storage. Recent studies of thin film bi- layer systems comprised of a normal metal (NM) and a ferromagnetic insulator (FI) revealed a new type of mag- netoresistance called spinHall magnetoresistance (SMR) [9–11], originating from the interplay between the spin accumulation at the NM/FI interface and the magnetiza- tion of the FI layer. When the NM layer has a significant spin-orbit interaction, e.g. Pt, an in-plane charge current j c induces a spin current via the spinHalleffect, which
Cubic ferromagnetic Heusler compounds are a family of materials that often exhibit higher spin polarization at the Fermi level than binary ferromagnetic 3d alloys. 1 Some of the materials are half metals with a gap in the spin-polarized density of states for one spin band which should make them ideal candidates for spin-valves or magnetic tunnel junctions (MTJs). 2–5 Since the prediction by de Groot et al. 6 in 1995 of a half metallic material with two inequivalent magnetic sublattices, whose moments precisely cancel, researchers have striven to fabricate such a material. While electronic structure calculations predicted several candidates, 7–9 most attempts to realize such a material had failed. 8,10,11 Kurt et al. 12 reported the growth of thin films of near-cubic Mn 2 Ru x Ga (MRG), where Mn occupies two inequivalent
We show that the extrinsic spinHalleffect can be engineered in monolayer graphene by decoration with small doses of adatoms, molecules, or nanoparticles originating local spin-orbit perturbations. The analysis of the single impurity scattering problem shows that intrinsic and Rashba spin-orbit local couplings enhance the spinHalleffect via skew scattering of charge carriers in the resonant regime. The solution of the transport equations for a random ensemble of spin-orbit impurities reveals that giantspinHall currents are within the reach of the current state of the art in device fabrication. The spinHalleffect is robust with respect to thermal fluctuations and disorder averaging.
in (4) is the angle made between the vector x y and the -axis; represents anyon density. The effect of the operator phase transformation (3) is to attach m flux quanta to each electron. Composite particles experience the effec- tive magnetic field B ( ) eff x
D ~ 0.1 for OQHE plateaux in the Faraday angle (around n = 4), with wider dc plateaux . The difference between the dc and OQHE plateaux width was assigned by Ikebe et al to the difference in length scales probed by dc Hall measurements and ac THz spectroscopy . A number of factors may contribute to the larger D n reported here: the OQHE plateaux width depends on factors that include the distance travelled by a carrier in one oscillation period of the THz electric ﬁ eld, the characteristic length scale of disorder, and the LL index [ 13 ] . A comparison to the dc plateaux widths was not possible for devices made on these samples, although QHE plateaux have been seen in similar sGe QWs [3, 7, 8].
For SiGe2, since MT measurements did not show any beating in the SdH os- cillations, the evaluation of the Rashba SOI was not possible . A calculation of the SdH beating (using the measured material parameters) resulted in an oscillation of the order of 5% which was not distinguishable because of the instrumental res- olution. Nevertheless, signatures of the Rashba-SOI for SiGe2 have been obtained from the temperature dependence of the MR. From 0.4 K to 3 K, the MR was found to be first negative (associated with the Weak Localisation of carriers, WL) to pos- itive (which is instead associated with the Weak Anti-Localisation, WAL, due to the Rashba-SOI). As this transition is opposite to what is expected, i.e. from WAL to WL, it could be associated with the presence of the Rashba SOI but with an opposite WL/WAL behaviour because of the presence of a further conducting layer. This might arise from the normal modulation doping structure of SiGe2 (see Figure 3.3) where, differently from SiGe1, the B:SiGe supply layer is in between the Hall bar - which was realised to perform MT measurements - and the Ge-QW.
8π ǫ ij ∂ i ¯ l∂ j l. (12) Before proceeding to calculate the Skyrmion dynamics from Eq.(11), let us make a few comments about the comparison of the Skyrmion/spin-wave problem with the polaron/phonon problem . The dynamics of spins is entirely determined by their commutation relations and, importantly, there is no kinetic term in their Hamilto- nian. This results in different dynamics for the Skyrmion and polaron. In the former case, one finds Magnus-force dynamics describing the motion of a Skyrmion perpen- dicular to an applied force. In the latter case, however, the dynamics have a conventional ballistic form. The second consequence is the absence of (multiple) spin- wave Cherenkov processes. Such terms are found in the phonon/polaron case through the collective coordinate expansion of the kinetic terms in the Hamiltonian. They are forbidden by energy conservation in the Skyrmion case, unless one allows for internal modes of the Skyrmion  (which we neglect here, under the assumption that the drift velocity of the Skyrmion is less than the critical velocity derived in Ref. ). These facts were missed in a previous analysis of the Skyrmion problem by Villares Ferrer and Caldeira . Despite these key differences, when Cherenkov processes are neglected, we find that the coherent state representation of the Skyrmion and polaron problems are very similar and that the damp- ing and diffusion of Skyrmions is very similar to that of polarons.
For photovoltaics, switching the p ‐ type dopant in silicon wafers from boron to indium may be advantageous as boron plays an important role in the light ‐ induced degrada- tion mechanism. With the continuous Czochralski crystal growth process it is now pos- sible to produce indium doped silicon substrates with the required doping levels for solar cells. This study aims to understand factors controlling the minority carrier life- time in such substrates with a view to enabling the quantification of the possible ben- efits of indium doped material. Experiments are performed using temperature ‐ dependent Halleffect and injection ‐ dependent carrier lifetime measurements. The recombination rate is found to vary linearly with the concentration of un ‐ ionized indium which exists in the sample at room temperature due to indium's relatively deep acceptor level at 0.15 eV from the valence band. Lifetime in indium doped silicon is also shown to degrade rapidly under illumination, but to a level substantially higher than in equivalent boron doped silicon samples. A window of opportunity exists in which the minority carrier lifetime in degraded indium doped silicon is higher than the equivalent boron doped silicon, indicating it may be suitable as the base material for front contact photovoltaic cells.
In the macrospin model, “damping” and “precessional” magnetization switchings are two mostly considered switching scenarios so far. In the damping switching mode, both the external field and the spin polarization point opposite to the initial state and the magnetization moves towards the new equilibrium gradually along a spiral trajectory which is considered to be reliable but quite slow [13, 68, 9, 6]. Much faster reversals, which are often classified as precessional switchings, have been designed with either the field applied at a certain angle (usually orthogonal) or the spin polar- ization perpendicular to the free layer easy axis [5, 36, 44]. In both cases the effective torque pushes the magnetization out-of-plane, creating a strong demagnetizing field in the direction perpendicular to the easy axis. However those reversal processes require fields or current pulses perfectly fit the precession frequency which increases the error rate and is experimentally hard to control.
A fundamental difference between the quantum Hall and the quan- tum spinHalleffect is that the topological invariant is restricted to the values 0 and 1 in the latter case, meaning either a pair of topologically protected edge states or none at all. The emphasize is here on the topo- logical protection - further edge states may exist but would not be stable. In contrast the quantum Halleffect can realize any integer number of topologically protected edge modes, but they all propagate in the same direction. This ensures the topological protection: if there was a channel in the opposite direction, left and right moving states could scatter into each other and would hybridize, leading to a gap in the spectrum of edge states. In the quantum spinHalleffect this is prevented for a sin- gle pair of time reversed modes since the so-called Kramers degeneracy of the crossing point in the Brillouin zone (see lower panel of Fig. 1.4) is protected by time-reversal symmetry.
Work, represented in this chapter, was motivated by V. S. Pribiag et. al.  (at that moment this paper was not yet published). Authors were per- forming superconducting quantum interference measurements in Joseph- son junctions, made with InAs/GaSb quantum wells. InAs/GaSb is a two-dimensional topological insulator [20, 21], therefore we expect exis- tence of helical quantum spinHall edge modes in the regime, when Fermi energy is inside the topological gap. This means, that SNS junction can be driven by gate from bulk-dominated regime to edge dominated (when the transport happens through the helical modes, and bulk is gapped). This transition was indeed observed in the SQI measurements, alongside with more peculiar phenomenon, displayed on the Fig. 1.3.
The spin polarization of a fractional quantum Hall state shows very interesting properties. The curve of polarization versus magnetic field has wide plateaus. The fractional quantum Halleffect is caused by the Coulomb interaction because the 2D electron system without the Coulomb interac- tion yields no energy gap at the fractional filling factor. Therefore, the wide plateau in the polari- zation curve is also caused by the Coulomb interaction. When the magnetic field is weak, some electrons have up-spins and the others down-spins. Therein the spin-exchange transition occurs between two electrons with up and down spins via the Coulomb interaction. Then the charge dis- tribution before the transition is the same as one after the transition. So these two states have the same classical Coulomb energy. Accordingly, the partial Hamiltonian composed of the spin ex- change interaction should be treated exactly. We have succeeded in diagonalizing the spin ex- change interaction for the first and second nearest electron pairs. The theoretical results repro- duce the wide plateaus very well. If the interval modulations between Landau orbitals are taken into the Hamiltonian, the total energy has the Peierls instability. We can diagonalize the Hamilto- nian with the interval modulation. The results reproduce wide plateaus and small shoulders which are in good agreement with the experimental data.
Spintronics has attracted much attention due to its poten- tial applications in information technology as well as revealing fundamental questions on the physics of elec- tron spin in condensed matter [1–4]. The spinHalleffect (SHE) and its Onsager reciprocal, the inverse spinHalleffect (ISHE), play a significant role in spintronics since they provide an electrical method to convert charge cur- rent into spin current and vice versa, via spin-orbit cou- pling (SOC) [2, 5–8]. The SHE and ISHE have been widely studied in metallic films with heavy elements, such as Pt, Ta, Py, and IrMn, and the emerging topological insula- tors, such as Bi 2 Se 3 and SnTe, due to their strong SOC
oretical speculation. The link between topological and electrical charge densities also produces a curious cou- pling of spinwaves to the disorder potential. Although a planewave spin distortion carries no charge, a wavepacket of spinwaves has an oscillating dipole charge distribution associated with it, due to the non-linear form of the topo- logical density. Spinwaves couple to the disorder poten- tial through this charge distribution. In this work, we investigate the way in which this coupling modifies the conductivity and temperature dependence of magnetiza- tion of the quantum Hall state.
particles in graphene forming a quantum Hall fluid; a strongly correlated sates of matter, which flows just like fluid and without such shearing resistance or dissipation. The viscosity measured in the quantum Hall fluid is what is termed Anomalous (also called Hall or dissipationless) viscosity . Quantum fluids are particularly in- teresting especially due to the remarkable natural phenomenon occurring in superconductivity, superfluidity, ul- tracold atoms. Fractional Quantum Hall (FQH) Effect is yet another example. The ground states of FQH states are holomorphic in nature and gapped. These gapped states are characterized by a universal anomalous viscosity. The viscosity is revealed when stress tensor becomes sensitive to stress preserving deformations of the fluid. In this context, the origin of the anomalous term is due to fluid velocity diverging at microscopic scale which de- forms a metric locally and causes dilatation of particle coordinates. The divergences due to individual particles are collectively manifested at macroscopic scale as an anomalous term. Another important term arising from metric deformations at finite temperature is Hall expansion coefficient. It is well established that graphene can respond to local deformations by producing strain which in turn induces giant pseudo-magnetic fields as much as 10 T in strained graphene  and 300 T in graphene nanobubbles . The induced field allows vortices in the system to feel an effective magnetic field. It is the Hall expansion coefficient that captures the contribution.
of the Majorana resonance. This seems to be an experiment that is fully within reach of existing devices, requiring only the addition of a nanostructured gate electrode and the application of a weak magnetic field. As a longer-term perspective, we have shown how a constriction in the quantum spinHall insulator can reproduce the functionality of a nanowire T
still needs to be associated to such an experimental study. An intriguing prospect for TMD-based vertical transport devices is that of fabricating ultrathin magnetic tunnel junc- tions (MTJs) [13,14]. These may offer the opportunity for realizing low-resistance, high-magnetoresistance devices, i.e., they may become an intriguing materials platform for several spintronics applications both in the magnetic recording and the sensing arena. Furthermore, understanding spin injection from transition metals to TMDs is a crucial step for realizing the vision of spintronics on a flatland beyond graphene, a vision recently energized by the characterization of Schottky barriers at the interface between MoS 2 and ferromagnetic metals