Electron Spin Diffusion Research Articles

Electron spin diffusion and transport in graphene

We investigate the spin diffusion and transport in a graphene monolayer on SiO${}_{2}$ substrate by means of the microscopic kinetic spin Bloch equation approach. The substrate causes a strong Rashba spin-orbit coupling field $~0.15$ meV, which might be accounted for by the impurities initially present in the substrate or even the substrate-induced structure distortion. By surface chemical doping with Au atoms, this Rashba spin-orbit coupling is further strengthened as the adatoms can distort the graphene lattice from ${\mathit{sp}}^{2}$ to ${\mathit{sp}}^{3}$ bonding structure. By fitting the Au doping dependence of spin relaxation from Pi et al.[Phys. Rev. Lett. 104, 187201 (2010)], the Rashba spin-orbit coupling coefficient is found to increase approximately linearly from 0.15 to 0.23 meV with the increase of Au density. With this strong spin-orbit coupling, the spin diffusion or transport length is comparable with the experimental values. In the strong scattering limit (dominated by the electron-impurity scattering in our study), the spin diffusion is uniquely determined by the Rashba spin-orbit coupling strength and insensitive to the temperature, electron density, as well as scattering. With the presence of an electric field along the spin injection direction, the spin transport length can be modulated by either the electric field or the electron density. It is shown that the spin diffusion and transport show an anisotropy with respect to the polarization direction of injected spins. The spin diffusion or transport lengths with the injected spins polarized in the plane defined by the spin-injection direction and the direction perpendicular to the graphene are identical, but longer than that with the injected spins polarized vertical to this plane. This anisotropy differs from the one given by the two-component drift-diffusion model, which indicates equal spin diffusion or transport lengths when the injected spins are polarized in the graphene plane and relatively shorter lengths when the injected spins are polarized perpendicular to the graphene plane.

Room temperature spin diffusion in (110) GaAs/AlGaAs quantum wells

Transient spin grating experiments are used to investigate the electron spin diffusion in intrinsic (110) GaAs/AlGaAs multiple quantum well at room temperature. The measured spin diffusion length of optically excited electrons is about 4 μm at low spin density. Increasing the carrier density yields both a decrease of the spin relaxation time and the spin diffusion coefficient Ds.

Induced voltage due to time-dependent magnetisation textures

We determine the induced voltage generated by spatial and temporal magnetisation textures (inhomogeneities) in metallic ferromagnets due to the spin diffusion of non-equilibrium electrons. Using time dependent semi-classical theory as formulated in Zhang and Li [1] and the drift-diffusion model of transport it is shown that the voltage generated depends critically on the difference in the diffusion constants of up and down spins. Including spin relaxation results in a crucial contribution to the induced voltage. We also show that the presence of magnetisation textures results in the modification of the conductivity of the system. As an illustration, we calculate the voltage generated due to a time dependent field driven helimagnet by solving the Landau–Lifshitz equation with Gilbert damping and explicitly calculate the dependence on the relaxation and damping parameters.

Measurement of interlayer spin diffusion in the organic conductor [formula omitted], [formula omitted], Br

In organic conductors the overlap integral between layers is small, in-plane momentum scattering is rapid and transport perpendicular to the layers is expected to be blocked. We present a high frequency conduction electron spin resonance (CESR) study in the layered organic metals κ ‐ ( BEDT ‐ TTF ) 2 Cu [ N ( CN ) 2 ] X , X = Cl , Br, which verifies that the inter-layer spin hopping is effectively blocked. The method relies on resolving the CESR lines of adjacent layers in which the orientation of the g-factor tensors differs. We find that at ambient pressure and in the metallic phase the electron spin diffusion is two dimensional in both the X = Cl and Br compounds, i.e. electrons diffuse longer than the spin lifetime within a single molecular layer without inter-layer hopping. Application of pressure at 250 K increases rapidly the inter-layer hopping rate of spins.

Study of electron spin diffusion transport in intrinsic GaAs quantum wells by time- and space-resolved absorbtion spectroscopy

A time- and space-resolved circularly polarized pump-probe spectroscopy and its theory are developed, and are used experimentally to study electron spin diffusion transport in intrinsic GaAs quantum wells. The ambipolar spin diffusion coefficient of Ｄas=37.5±15 cm2/s is obtained at room temperature, and is smaller than that in a doped GaAs quantum well obtained by spin grating. The difference is explained based on “hole Coulomb drag" effect which slows the diffusion transport of electron spin packet.

Diffusive to drift-diffusion crossover of spin transport in the low-field regime

Electric field-dependent electron spin diffusion in GaAs is investigated experimentally. We consider the three spin transport regimes, namely diffusive, drift-diffusion crossover, and drift. Of them, spin transport in the diffusive and drift-diffusion crossover regimes is studied in more detail. We also estimate the drift-diffusion crossover field (Ex) and the intrinsic spin diffusion length (δs) in the nondegenerate regime. The estimated value of δs is found to be 1.74μm, a factor of 0.87 lower than that reported in the literature. The technique, however, demonstrates it as a convenient and useful tool to measure Ex and δs in semiconductors.

Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment

We consider the decoherence of a single localized electron spin due to its coupling to the lattice nuclear spin bath in a semiconductor quantum computer architecture. In the presence of an external magnetic field and at low temperatures, the dominant decoherence mechanism is the spectral diffusion of the electron spin resonance frequency due to the temporally fluctuating random magnetic field associated with the dipolar interaction induced flip-flops of nuclear spin pairs. The electron spin dephasing due to this random magnetic field depends intricately on the quantum dynamics of the nuclear spin bath, making the coupled decoherence problem difficult to solve. We provide a formally exact solution of this non-Markovian quantum decoherence problem which numerically calculates accurate spin decoherence at short times, which is of particular relevance in solid-state spin quantum computer architectures. A quantum cluster expansion method is developed, motivated, and tested for the problem of localized electron spin decoherence due to dipolar fluctuations of lattice nuclear spins. The method is presented with enough generality for possible application to other types of spin decoherence problems. We present numerical results which are in quantitative agreement with electron spin echo measurements in phosphorus doped silicon. We also present spin echo decay results for quantum dots in GaAs which differ qualitatively from that of the phosphorus doped silicon system. Our theoretical results provide the ultimate limit on the spin coherence (at least, as characterized by Hahn spin echo measurements) of localized electrons in semiconductors in the low temperature and the moderate to high magnetic field regime of interest in scalable semiconductor quantum computer architectures.

Spatially resolved and integral measurements of the electron spin diffusion properties of an organic quasi 1-D conductor

The radical cation salt (Fluoranthen) 2PF 6 is an organic quasi-1d conductor showing a Peierls transition at T P = 186 K. Model calculations predicted that the Peierls transition is suppressed by an increased density of defects which can be influenced by irradiating the crystals with high-energetic protons (E P = 25 MeV). This prediction could be verified by microwave conductivity measurements investigating a homogeneously irradiated crystal. In order to eliminate possible sample dependence, a high quality crystal was irradiated through a periodic grid to result in a stripy pattern. A detailed spatially resolved X-band-pulse-ESR-analysis quantifies the resulting defect concentration and proves that the Peierls transition can be nonuniformly suppressed.

Anisotropy of charge and spin motion in perylene hexafluoroarsenate salts

Conduction electron spin echo attenuation in well defined magnetic field gradients providesmore accurate values of the anisotropy of electron spin motion than microwave conductivitymeasurements. The electron spin diffusion coefficient for motion along the perylene (PE)radical cation stack, , in the PE hexafluoroarsenate salt is influenced temperature dependently byperpendicular-to-stack motion and reflects the varying average unrestricted chain length,. The anisotropy of is larger than 7300:1 at 250 K.

Influencing the spin diffusion of (Fluoranthene)2 PF6 single crystals by volume structuring

From the restricted quasi-ld conduction electron spin diffusion of (Fluoranthene) 2 PF 6 single crystals quasi-microscopic structural details could be derived with electron spin echo methods. A predetermined geometrical structure impressed into the crystals with high energetic protons (Ep = 25 MeV) could be visualised by two dimensional spatially resolved electron spin density and dynamic imaging. The influence of this microstructuring on the diffusive process is discussed.

Magnetic resonance study of the two-dimensional spin diffusion in the Heisenberg paramaget (C 18H 37NH 3) 2MnCl 4

1H nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) techniques were employed to study the perovskite-type layered structure compound (C 18H 37NH 3) 2MnCl 4 undergoing structural phase transitions. The spin relaxation was found to sensitively reflect the two-dimensional electron spin diffusion.

Electron-spin diffusion in proton-irradiation microstructured (fluoranthene)2PF6

The properties of the quasi-one-dimensional organic conductor (fluoranthene)${}_{2}{\mathrm{PF}}_{6}$ are modified by proton irradiation ${(E}_{p}=25\mathrm{MeV},$ ${n}_{p}=5.4\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\ensuremath{-}2}).$ The crystals are characterized by measurement of static magnetic susceptibility, cw--electron spin resonance, static magnetic-field gradient pulsed electron spin resonance and especially by one- and two-dimensional electron-spin-resonance imaging. Electron-spin diffusion constant parallel to the stacking direction is reduced by one order of magnitude, whereas the perpendicular direction remains essentially unchanged, for homogeneous proton irradiation. A well-defined periodic $100\ensuremath{-}\ensuremath{\mu}\mathrm{m}$ structure is impressed using appropriate metal grids in the proton beam. Thus the diffusion constant, as well as the concentration of localized defects, is spatially modulated. Experimental evidence of the coherence phenomena of the diffusing electron spins moving between the artificially created reflecting walls is presented.

Spintronics: spin accumulation in mesoscopic systems.

In spintronics, in which use is made of the spin degree of freedom of the electron, issues concerning electrical spin injection and detection of electron spin diffusion are fundamentally important. Jedema et al. describe a magneto-resistance study in which they claim to have observed spin accumulation in a mesoscopic copper wire, but their one-dimensional model ignores two-dimensional spin-diffusion effects, which casts doubt on their analysis. A two-dimensional vector formalism of spin transport is called for to model spin-injection experiments, and the identification of spurious background resistance effects is crucial.

Spin diffusion of optically oriented electrons and photon entrainment in n-gallium arsenide

An experimental and theoretical study of spin transport in the n-GaAs semiconductor is reported. Transport of average electron spin from the photoexcited crystal surface is shown to be determined by the spin diffusion process. At the same time the transport of photoexcited carriers takes place primarily through photon entrainment, which transfers nonequilibrium carriers into the bulk of the semiconductor to distances considerably in excess of the electron spin diffusion length. A comparison of the experimental results with theory permits one to determine the average-spin diffusion length and electron-spin relaxation time.

Variable-Temperature High-Resolution Proton NMR Study of Laboratory-Frame and Rotating-Frame Spin−Lattice Relaxation in Coals

We have carried out the first systematic in situ variable-temperature (25-180 °C) high-resolution proton NMR study of laboratory-frame and rotating-frame proton spin-lattice relaxation of coal samples, based on the CRAMPS technique. For coal samples that have been exposed to air, we confirmed the fact that paramagnetic oxygen is the main source of laboratory-frame proton spin-lattice relaxation (T 1 ). We demonstrate that paramagnetic oxygen trapped in coal can be used as a sensitive probe for monitoring structural and dynamical changes in coal as the temperature is varied. High-temperature spin-lattice relaxation experiments help to reveal the structural heterogeneity of coal because of reduced proton and electron spin-diffusion rates at high temperature. Large domains, on the order of 200-800 A, with distinctively different paramagnetic oxygen concentrations, were found in all three coal samples studied, consisting of one low-volatile and two high-volatile bituminous coals from the Argonne Premium Coal bank. In particular, we found that aliphatic-rich domains with a length-scale larger than 500 A exist in Premium Coal 601. The observed dependences of the rotating-frame 1 H spin-lattice relaxation time T 1p on the strength of the spin-lock field and temperature support the view that the main relaxation mechanism is time-dependent 1 H- 1 H dipolar interactions in coals. From these dependences, we estimate that the correlation time of molecular motion responsible for rotating-frame proton spin-lattice relaxation in coals is on the order of 5 μs, which is in agreement with conclusions drawn from previous proton dipolar-dephasing studies. Two T 1p values were identified for each of the three coal samples studied, indicating the existence of structural heterogeneity in coal on a spatial scale of at least 50 A. The sizes of heterogeneous domains in coal are estimated on the basis of measured spin-lattice relaxation times and the analysis of proton spin-diffusion processes.

Spin Conductivity and Spin-Charge Separation in the High-TcCuprates

We address the question of how to experimentally test spin-charge separation in the high- ${T}_{c}$ cuprates. We demonstrate that a comparison between the temperature dependences of the electrical resistivity and spin resistivity can be used for this purpose. Given the known linear in temperature dependence of the electrical resistivity, the spin resistivity should also be linear in temperature in the absence of spin-charge separation and under conditions appropriate for the optimally doped cuprates, but is in general not so in the presence of spin-charge separation. We demonstrate the quantitative feasibility of applying the spin-injection technique to measure the electron-spin diffusion constant.

Spin-dependent tunneling phenomena in insulating granular systems

We studied giant magnetoresistance (GMR) and the related properties in Co-Al-O insulating granular films prepared by reactive sputtering. Microstructural observation revealed that the films were composed of Co base metallic granules and Al 2O 3 base insulating network-like boundaries. The GMR varied as a function of oxygen content (or Co/Al 2O 3 ratio) and it took a maximum of 8% at room temperature and 17% at 4.2 K for a Co 52Al 20O 28 film, accompanying huge specific electrical resistivities of the order of 10 5–10 6 μΩ cm. It has been considered that the observed GMRs are attributed to a spin-dependent tunneling and that the spin diffusion of electrons during tunneling plays an important role of the composition dependence of GMR. In addition, it has been noted that the temperature dependence of GMR is smaller than the T −1 dependence predicted theoretically by Helman et al. but rather close to the theory by Inoue et al.

Nuclear spin-lattice relaxation mechanisms in kaolinite confirmed by magic-angle spinning

Spin-lattice relaxation mechanisms in kaolinite have been reinvestigated by magic-angle spinning (MAS) of the sample. MAS is useful to distinguish between relaxation mechanisms: the direct relaxation rate caused by the dipole-dipole interaction with electron spins is not affected by spinning while the spin diffusion-assisted relaxation rate is. Spin diffusion plays a dominant role in 1H relaxation. MAS causes only a slight change in the relaxation behavior, because the dipolar coupling between 1H spins is strong. 29Si relaxes directly through the dipole-dipole interaction with electron spins under spinning conditions higher than 2 kHz. A spin diffusion effect has been clearly observed in the 29Si relaxation of relatively pure samples under static and slow-spinning conditions. 27Al relaxes through three mechanisms: phonon-coupled quadrupole interaction, spin diffusion and dipole-dipole interaction with electron spins. The first mechanism is dominant, while the last is negligibly small. Spin diffusion between 27Al spins is suppressed completely at a spinning rate of 2.5 kHz. We have analyzed the relaxation behavior theoretically and discussed quantitatively. Concentrations of paramagnetic impurities, electron spin-lattice relaxation times and spin diffusion rates have been estimated.

19F NMR relaxation time T1 and interchain spin diffusion in polyaniline trifluoromethanesulfonate, [(−C 6H 4NH−)(CF 3SO 3) 0.5·0.5H 2O] n

The relaxation time T 1 of 19F NMR and that of 1H NMR were determined for the polyaniline trifluoromethanesulfonate, [(−C 6H 4NH−)(CF 3SO 3) 0.5·0.5H 2O] n in a temperature range 4.2–300 K. The 1H T 1 was practically temperature-independent except for temperatures near 4.2 K, and was governed by a quasi-one-dimensional diffusion of electron spins. The 19F T 1 of the dopant was explained by a combined effect of the F-F dipolar interaction and the nucleus-electron spin coupling. The latter paramagnetic relaxation term was temperature-dependent in contrast to the 1H T 1, and was explained by an interchain spin diffusion with an activation energy of 1.6 kJ mol −1 and a diffusion velocity of the order of 10 11 rad s −1. The interchain diffusion of the spin carriers is expected to occur via close face-to-face contacts of aniline groups.

19F NMR relaxation time T1 and spin diffusion in polyaniline trifluoromethanesulfonate, [(-C 6H 4NH-)(CF 3SO 3) 0.5·0.5H 2O] n

The relaxation time T 1 of 19F NMR and that of 1H NMR were determined for the polyaniline trifluoromethanesulfonate, [(-C 6H 4NH-)(CF 3SO 3) 0.5·0.5H 2O] n in a temperature range of 4.2–300 K. The 1H T 1 value was practically temperature-independent except for temperatures near 4.2 K, and was governed by a quasi-one-dimensional diffusion of electron spins. The 19F T 1 value of the dopant was explained by a combined effect of the F-F dipolar interaction and the nucleus-electron spin coupling. The latter paramagnetic relaxation term was temperature-dependent in contrast to the 1H T 1, and was explained by an interchain spin diffusion with an activation energy of 1.6 kJ mol −1 and a diffusion velocity of the order of magnitude of 10 11 rad s −1. The interchain diffusion of the spin carriers is expected to occur via close face-to-face contacts of aniline groups.