Nonlocal Geometry Research Articles

Measurement of spin-dependent conductivities in a two-dimensional electron gas

Spin accumulation is generated by injecting an unpolarized charge current into a channel of GaAs two-dimensional electron gas subject to an in-plane magnetic field, then measured in a nonlocal geometry. Unlike previous measurements that have used spin-polarized nanostructures, here the spin accumulation arises simply from the difference in bulk conductivities for spin-up and spin-down carriers. Comparison to a diffusive model that includes spin subband splitting in magnetic field suggests a significantly enhanced electron spin susceptibility in the two-dimensional electron gas.

Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 10243 at different times, from t = 0 to t = Te, where Te is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects.

Imaging of lateral spin valves with soft x-ray microscopy

We investigated Co/Cu lateral spin valves by means of high-resolution transmission soft x-ray microscopy with magnetic contrast that utilizes x-ray magnetic circular dichroism (XMCD). No magnetic XMCD contrast was observed at the Cu L$_3$ absorption edge, which should directly image the spin accumulation in Cu. Although electrical transport measurements in a non-local geometry clearly detected the spin accumulation in Cu, which remained unchanged during illumination with circular polarized x-rays at the Co and Cu L$_3$ absorption edges.

Spin-dependent transport in a nanopillar non-local spin valve

We investigate the injection of a pure spin current into a non-magnetic Cu wire in a lateral spin valve. We detect the spin accumulation occurring at the interfaces between the magnetic nanopillars and the non-magnetic wire in the non-local geometry. We confirm that the accumulated spins diffuse equally in the Cu wire irrespective of the presence of a charge current. The inversion of the injector and detector magnetic nanopillars does not affect the spin signal, in agreement with analytical predictions for this system.

Electrical Generation of Pure Spin Currents in a Two-Dimensional Electron Gas

Pure spin currents are generated and detected in micron-wide channels of a GaAs two-dimensional electron gas, using quantum point contacts in an in-plane magnetic field as injectors and detectors. The enhanced sensitivity to spin transport offered by a nonlocal measurement geometry enables accurate spin current measurements in this widely studied physical system. The polarization of the contacts is used to extract the quantum point contact g factor and provides a test for spontaneous polarization at 0.7 structure. The spin relaxation length in the channel is 30-50 microm over the magnetic field range 3-10 T, much longer than has been reported in GaAs two-dimensional electron gases but shorter than that expected from Dyakonov-Perel relaxation.

Local and nonlocal geometry of interplanetary coronal mass ejections: Galactic cosmic ray (GCR) short‐period variations and magnetic field modeling

Energetic galactic cosmic ray (GCR) particles, arriving within the solar system, are modulated by the overall interplanetary field carried in the solar wind. Localized disturbances related to solar activity cause further reduction in intensity, the largest being Forbush decreases in which fluxes can fall ∼20% over a few days. Understanding Forbush decreases leads to a better understanding of the magnetic field structure related to shock waves and fast streams originating at the Sun since the propagation characteristics of the GCR probe much larger regions of space than do individual spacecraft instruments. We examined the temporal history of the integral GCR fluence (≥100 MeV) measured by the high‐sensitivity telescope (HIST) aboard the Polar spacecraft, along with the solar wind magnetic field and plasma data from the ACE spacecraft during a 40‐day period encompassing the 25 September 1998 Forbush decrease. We also examined the Forbush and (energetic storm particles) ESP event on 28 October 2003. It is the use of HIST in a high‐counting‐rate integral mode that allows previously poorly seen, short‐scale depressions in the GCR fluxes to be observed, adding crucial information on the origin of GCR modulation. Variability on time scales within the frequency range 0.001–1.0 mHz is detected. This paper concentrates on investigating four simple models for explaining short‐term reductions in the GCR intensity of both small and large amplitude. Specifically, these models are a local increase in magnetic scattering power, the passage of a shock discontinuity, and the passage of a tangential discontinuity or magnetic rope in the solar wind plasma. Analysis of the short‐scale GCR depressions during a test period in September through October 1998 shows that they are not correlated with changes in magnetic scattering power or fluctuations in solar wind speed or plasma density. However, magnetic field and plasma data during the test period of Forbush decrease strongly suggest the presence of an interplanetary coronal mass ejection (ICME). Use of a non‐force‐free magnetic rope model in conjunction with the energetic particle data allows modeling of the geometry of the ICME in terms of a magnetic cloud topology. It is only this cloud configuration that allows a satisfactory explanation of the magnitude of the Forbush event of 25 September 1998. Calculations made during the test period point to short‐scale GCR depressions being caused by either small‐scale magnetic flux rope structures or possibly tangential discontinuities in the solar wind.

Anisotropic Spin Relaxation in Graphene

Spin relaxation in graphene is investigated in electrical graphene spin valve devices in the nonlocal geometry. Ferromagnetic electrodes with in-plane magnetizations inject spins parallel to the graphene layer. They are subject to Hanle spin precession under a magnetic field B applied perpendicular to the graphene layer. Fields above 1.5 T force the magnetization direction of the ferromagnetic contacts to align to the field, allowing injection of spins perpendicular to the graphene plane. A comparison of the spin signals at B=0 and B=2 T shows a 20% decrease in spin relaxation time for spins perpendicular to the graphene layer compared to spins parallel to the layer. We analyze the results in terms of the different strengths of the spin-orbit effective fields in the in-plane and out-of-plane directions and discuss the role of the Elliott-Yafet and Dyakonov-Perel mechanisms for spin relaxation.

Spin precession in lateral all-metal spin valves: Experimental observation and theoretical description

Mesoscopic all-metal spin-valve devices containing two ferromagnetic permalloy electrodes and an interconnecting aluminum strip have been studied experimentally and theoretically in nonlocal geometry. Spin-valve devices have been fabricated by thermal evaporation of permalloy electrodes, formation of tunnel barriers by natural oxidation in air or in pure oxygen, and subsequent deposition of an aluminum strip on top of the electrodes. Transport measurements at temperatures of liquid helium have been performed. Spin-dependent phenomena, namely the nonlocal spin-valve effect and spin precession, are observed. A theoretical description of spin-dependent transport is presented including spin diffusion, spin relaxation, spin precession, and tunnel barriers at the interfaces between the electrodes and the aluminum strip. From the comparison of the experimentally observed spin precession to the theoretical description, we obtain a spin-relaxation time of 111 ps and a spin-relaxation length of 1034 nm in aluminum.

On the Non-Local Geometry of Turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

On the non-local geometry of turbulence

A multi-scale methodology for the study of the non-local geometry of eddy structures in turbulence is developed. Starting from a given three-dimensional field, this consists of three main steps: extraction, characterization and classification of structures. The extraction step is done in two stages. First, a multi-scale decomposition based on the curvelet transform is applied to the full three-dimensional field, resulting in a finite set of component three-dimensional fields, one per scale. Second, by iso-contouring each component field at one or more iso-contour levels, a set of closed iso-surfaces is obtained that represents the structures at that scale. The characterization stage is based on the joint probability density function (p.d.f.), in terms of area coverage on each individual iso-surface, of two differential-geometry properties, the shape index and curvedness, plus the stretching parameter, a dimensionless global invariant of the surface. Taken together, this defines the geometrical signature of the iso-surface. The classification step is based on the construction of a finite set of parameters, obtained from algebraic functions of moments of the joint p.d.f. of each structure, that specify its location as a point in a multi-dimensional ‘feature space’. At each scale the set of points in feature space represents all structures at that scale, for the specified iso-contour value. This then allows the application, to the set, of clustering techniques that search for groups of structures with a common geometry. Results are presented of a first application of this technique to a passive scalar field obtained from 5123 direct numerical simulation of scalar mixing by forced, isotropic turbulence (Reλ = 265). These show transition, with decreasing scale, from blob-like structures in the larger scales to blob- and tube-like structures with small or moderate stretching in the inertial range of scales, and then toward tube and, predominantly, sheet-like structures with high level of stretching in the dissipation range of scales. Implications of these results for the dynamical behaviour of passive scalar stirring and mixing by turbulence are discussed.

Three dimensional simulations of spin Hall effect in magnetic nanostructures

We investigate the spatial distribution of spin/charge current in a nonlocal geometry of a magnetic nanostructure with Py∕I∕Cu and Cu∕Pt contacts and analyze the spin Hall effects by applying finite element method in three dimensions. We find that the inhomogeneous current distribution appears in the Cu∕Pt connection area, suggesting the possibility of the spin-signal enhancement by controlling the contact shape and the width of the electrodes. The calculated spin Hall voltage is consistent with the experimentally observed Hall resistance.

Calculation of nonlocal baseline resistance in a quasi-one-dimensional wire

Recent spin transport measurements on quasi-one-dimensional wire samples employ a nonlocal geometry. When current is injected at the center of a wire which is grounded at the left end, the portion of the wire to the right of the injector is approximated as having a uniform potential. A voltage measurement between two points on this portion gives a null result. This geometry is useful for studies of spin injection because a spin-sensitive electrode can detect a spin dependent electrochemical potential variation associated with nonequilibrium spin accumulation while contribution from any Ohmic resistance is eliminated. In any real experiment, however, the sample may deviate from the ideal geometry and a small baseline resistance may result. Accurate knowledge of the true baseline is important for the correct interpretation of spin transport experiments. An analytic solution for this nonlocal baseline resistance is found for nonideal injection or detection. The general solution is reduced to a specific case of interest, point injection and detection at the edges of the wire, a result which is compared with experiment.

Formation of multipartite entanglement using random quantum gates

The formation of multipartite quantum entanglement by repeated operation of one- and two-qubit gates is examined. The resulting entanglement is evaluated using two measures: the average bipartite entanglement and the Groverian measure. A comparison is made between two geometries of the quantum register: a one-dimensional chain in which two-qubit gates apply only locally between nearest neighbors and a nonlocal geometry in which such gates may apply between any pair of qubits. More specifically, we use a combination of random single-qubit rotations and a fixed two-qubit gate such as the controlled-phase gate. It is found that in the nonlocal geometry the entanglement is generated at a higher rate. In both geometries, the Groverian measure converges to its asymptotic value more slowly than the average bipartite entanglement. These results are expected to have implications on different proposed geometries of future quantum computers with local and nonlocal interactions between the qubits.

Separating spin and charge transport in single-wall carbon nanotubes

We demonstrate spin injection and detection in single wall carbon nanotubes using a 4-terminal, non-local geometry. This measurement geometry completely separates the charge and spin circuits. Hence all spurious magnetoresistance effects are eliminated and the measured signal is due to spin accumulation only. Combining our results with a theoretical model, we deduce a spin polarization at the contacts of approximately 25 %. We show that the magnetoresistance changes measured in the conventional two-terminal geometry are dominated by effects not related to spin accumulation.

Molecular and Electronic Structures, Brönsted Basicities, and Lewis Acidities of Group VIB Transition Metal Oxide Clusters

The structures and properties of transition metal oxide (TMO) clusters of the group VIB metals, (MO(3))(n) (M = Cr, Mo, W; n = 1-6), have been studied with density functional theory (DFT) methods. Geometry optimizations and frequency calculations were carried out at the local and nonlocal DFT levels with polarized valence double-zeta quality basis sets, and final energies were calculated at nonlocal DFT levels with polarized valence triple-zeta quality basis sets at the local and nonlocal DFT geometries. Effective core potentials were used to treat the transition metal atoms. Two types of clusters were investigated, the ring and the chain, with the ring being lower in energy. Large ring structures (n > 3) were shown to be fluxional in their out of plane deformations. Long chain structures (n > 3) of (CrO(3))(n) were predicted to be weakly bound complexes of the smaller clusters at the nonlocal DFT levels. For M(6)O(18), two additional isomers were also studied, the cage and the inverted cage. The relative stability of the different conformations of M(6)O(18) depends on the transition metal as well as the level of theory. Normalized and differential clustering energies of the ring structures were calculated and were shown to vary with respect to the cluster size. Brönsted basicities and Lewis acidities based on a fluoride affinity scale were also calculated. The Brönsted basicities as well as the Lewis acidities depend on the size of the cluster and the site to which the proton or the fluoride anion binds. These clusters are fairly weak Brönsted bases with gas phase basicities comparable to those of H(2)O and NH(3). The clusters are, however, very strong Lewis acids and many of them are stronger than strong Lewis acids such as SbF(5). Brönsted acidities of M(6)O(19)H(2) and M(6)O(18)FH were calculated for M = Mo and W and these compounds were shown to be very strong acids in the gas phase. The acid/base properties of these TMO clusters are expected to play important roles in their catalytic activities.

Local Hall Effect and Ballistic Transport in Multi-terminal InAs-Based Lateral Spin-Valve Tunnelling Devices

A multi-terminal InAs-based lateral spin-valve tunnelling device is presented, which enables individual electrical characterization of all spin-valve components in two-terminal configuration. Both the spin-valve and the non-local geometry are available for studying spin-dependent transport. Furthermore, we propose a measurement geometry in which the spin-dependent contact resistance of the sensor electrode can be measured in three-terminal configuration. Longitudinal magnetoresistance in spin-valve geometry reveal hysteresis loops of 1 mΩ deflection as known from Hall magnetometry. In non-local geometry a polarity-dependent current–voltage characteristic at 2 K is observed. This can be understood in terms of a superposition of a diffusive resistive component with a polarity-dependent ballistic component.

Nonlinear focusing of acoustic shock waves at a caustic cusp

The present study investigates the focusing of acoustical weak shock waves incoming on a cusped caustic. The theoretical model is based on the Khokhlov-Zabolotskaya equation and its specific boundary conditions. Based on the so-called Guiraud's similitude law for a step shock, a new explanation about the wavefront unfolding due to nonlinear self-refraction is proposed. This effect is shown to be associated not only to nonlinearities, as expected by previous authors, but also to the nonlocal geometry of the wavefront. Numerical simulations confirm the sensitivity of the process to wavefront geometry. Theoretical modeling and numerical simulations are substantiated by an original experiment. This one is carried out in two steps. First, the canonical Pearcey function is synthesized in linear regime by the inverse filter technique. In the second step, the same wavefront is emitted but with a high amplitude to generate shock waves during the propagation. The experimental results are compared with remarkable agreement to the numerical ones. Finally, applications to sonic boom are briefly discussed.

Geometrical effect on spin current in magnetic nanostructures

The spatial distribution of the spin current is studied in the nonlocal geometry of a contact between ferromagnetic and nonmagnetic metals taking into account the finite size effect of the contact area by applying finite element method in two dimensions. The sign and the order of magnitude of the obtained spin accumulation signal are consistent with the experiment. It is shown that, with a tunneling-like contact, the two-dimensional inhomogeneous distribution in spin current is slightly observed, and the one-dimensional analysis is appropriate to evaluate the experimental results.

Detection of spin-polarized electrons injected into a two-dimensional electron gas.

The spin-dependent mean-free path of electrons in a high-mobility InAs two-dimensional electron gas (2DEG) is measured. Ferromagnetic metal/insulator/2DEG junctions are fabricated on a common channel in a nonlocal geometry and used as spin injectors and detectors. For electrons in spin-orbit eigenstates at 4.5 K, lower bounds for the spin mean-free path and relaxation time are Lambda(S) > or = 4.6 microm and tau(s) > or = 3.8 ps, respectively. The temperature dependence is weak over the range 4.5<T<150 K.

Study for realization of spin-polarized field effect transistor in In 0.75Ga 0.25As/In 0.75Al 0.25As heterostructure

For realization of the spin-polarized field effect transistor (spin-FET), we investigated a gated modulation of spin–orbit interaction and a spin-injection from a ferromagnetic metal (FM) to a two-dimensional electron gas (2DEG). Prepared samples were an In 0.75Ga 0.25As/In 0.75Al 0.25As modulation-doped narrow-gap heterojunction grown by molecular beam epitaxy (MBE). For the determination of spin–orbit interaction parameter, α, we measured Shubnikov–de Haas (SdH) oscillations at 1.5 K . We confirmed a modulation of α when a gate voltage was applied. We also carried out spin-injection experiments using a multi-terminal geometry sample, which had two different widths Ni 40Fe 60 electrodes. We observed a spin-valve like effect in a source-drain resistance of ∼0.1% as well as a resistance hysteresis behavior of ∼12% in non-local geometry below 20 K . These results are the first step to realize an active spintronic device, such as spin-FET.