Spin Diffusion Coefficient Research Articles

Inelastic-light-scattering in Cdf 0.95Mn 0.05Se:In near the metal-to-insulator transition

Inelastic-light-scattering measurements on Cd 1−xMn xSe:In, x=0.05, near the metal-to-insulator transition are made in a dilution refrigerator down to T-0.25 K. The electron spin splitting increases dramatically for decreasing temperature, and at low fields can be expressed as an effective g-factor increasing to a value of g∼500. Spectral linewidths in back scattering (large q-vector) are broader than for forward scattering, demonstrating the diffusive character of the delocalized electrons. Comparison of these linewidths give values for the spin-relaxation time T 2 and spin-diffusion coefficients D s. We discuss the temperature and field dependencies of these quantities on the metallic side of the metal-to-insulator transition.

Magnetic relaxation in superfluid 3HeB

We present new experimental and theoretical studies of magnetic relaxation in 3HeB. Methods are developed for the measurement of relaxation using either CW or Pulsed NMR. Both methods make use of the properties of the Homogeneously Precessing Domain. Terms corresponding to intrinsic (Leggett-Takagi), spin diffusion and surface relaxation are distinguished. Theoretical results for the spin diffusion coefficient and the Leggett-Takagi relaxation time, which display nonhydrodynamic anomalies, are compared with experiment.

Universal long-time relaxation of nuclear spins in a disordered conductor

The influence of fluctuations of the local density of states in dirty metal on the kinetics of nuclear magnetization is investigated. The large-scale fluctuations of the Korringa relaxation rate lead to a deviation from the typical exponential law. The nuclear spin diffusion promotes a new universal exponential regime at long times, when the exponent is independent of the constant of electron-nuclear interaction and is determined by the nuclear spin diffusion coefficient D s and by the electron diffusion coefficient D.

Spin Wave Spectroscopy of Spin Polarized Atomic Hydrogen: Measurement of the Longitudinal Spin diffusion Coefficient

Abstract We describe the measurement of the longitudinal spin diffusion coefficient D0 in spin polarized atomic hydrogen through a detailed spectroscopic study of the small tipping angle, pulsed NMR frequency spectrum. Measurements are discussed for temperatures between 160 and 537 mK and for densities between 7×1015 and 5 × 1016cm−3 and are in good agreement with the theory. At low densities (

Spin wave spectroscopy of spin polarized atomic hydrogen: Measurement of the longitudinal spin diffusion coefficient

We describe the measurement of the longitudinal spin diffusion coefficient D 0 in spin polarized atomic hydrogen through a detailed spectroscopic study of the small tipping angle, pulsed NMR frequency spectrum. Measurements are discussed for temperatures between 160 and 537 mK and for densities between 7×1015 and 5 × 10 16 cm −3 and are in good agreement with the theory. At low densities (< 10 16 cm −3 ), results are consistent with expected inertial corrections.

Measurement of the spin diffusion rate by depolarization of rare spins in CP MAS NMR

The proton spin diffusion rate in solid-state samples can be directly measured by using depolarization of rare spins in CP MAS NMR. In the slow decaying stage of the depolarization process, the magnetization of rigid protonated rare spins changes mono-exponentially. This behavior can be reasonably described by using a one-dimensional random walk model. The mean flip-flop time of protons can be deduced from the exponential decay, and the spin diffusion coefficient can thus be estimated. In some typical rigid organic solids and crystallized polymers, the mean flip-flop time is found to be about 700 μs.

Spin-diffusion coefficient in gaseous helium between 1 and 0.5 K.

We report on measurements of the nuclear-spin diffusion coefficient in gaseous helium below 1 K. Both ${D}_{33}$ (self-diffusion in $^{3}\mathrm{He}$) and ${D}_{34}$ (diffusion of $^{3}\mathrm{He}$ in $^{4}\mathrm{He}$) are obtained from ${T}_{2}$ measurements in applied magnetic gradients. We operate at low densities, where transport properties are governed by two-body collisions. Predictions from various helium-helium potentials have been computed and are compared with the experimental results. A rough agreement is obtained, although theoretical values for ${D}_{33}$ seem somewhat too small. Relative variations with temperature are well described by theory between 4.2 and 0.5 K (within 10%).

NMR in pure3He films on a Nuclepore substrate

The properties of3He films on a Nuclepore substrate have been measured by pulsed NMR at a Larmor frequency of 10 MHz between 1.3 and 4.2 K. The3He film thickness was varied from 0.14 to 2 layers. The spin-spin relaxation timeT2 agrees well with previous measurements of3He films on Mylar and Vycor glass at low temperatures. The spin-lattice relaxation timeT1 for submonolayer films shows a strong temperature dependence consistent with a thermally activated process. This behavior has not previously been observed on amorphous substrates. The spin diffusion coefficient was measured for the thickest films at 4.2 and 2.6 K and found to be consistent with free atom motion of the3He in the vapor. In thin films or at low temperatures, the diffusion was too small to be observed. The magnetic coupling between the3He nuclei in a film and the protons in the Nuclepore substrate was determined from the effect of the3He on the proton-lattice relaxation time. It is about 100 times weaker than the interaction between3He and the fluorine nuclei in a Teflon substrate.

On Anisotropy of Nuclear Spin‐Diffusion Coefficient

AbstractThe anisotropy of the spin diffusion coefficient for the simple cubic lattice is investigated. The analysis is based on using the non‐equilibrium statistical operator method. The form of the correlation function, which determines the spin diffusion coefficient, is treated by the momentum method. Exact expressions for the second and fourth moments are obtained. It is shown that usually using the Gaussian form of the correlation function as usually is unsatisfactory. Therefore, the known conclusion about the absence of anisotropy of the spin diffusion coefficient does not take place. Values of the spin diffusion coefficients are presented.

1H nuclear magnetic resonance and spin–lattice relaxation in solid, high-density polyethylene

1 H spin–lattice relaxation, in both laboratory and on-resonance rotating frames, are reported for five samples of a high-density, linear polyethylene prepared so as to produce a range of lamellar crystalline widths. The samples are also characterised by measurements of density, Raman longitudinal acoustic modes (LAM) crystallinity (DSC) and small-angle X-ray scattering (SAXS). The laboratory-frame spin–lattice relaxation (LFSLR) is well represented by a single process, and the relaxation rates are linearly related to the crystalline fraction (DSC), which is consistent with the prediction of the fast-diffusion limit of the two-region, spin-diffusion-coupled model of relaxation in these systems. The rotating-frame relaxation (RFSLR) is, as found in previous studies, a multi-exponential process. It is shown that a fit to four components is optimum in terms of quality of fit and signal-to-noise ratio and that this leads to accurate values for the amplitude and time constant of the dominant, longest relaxation-time component. It is also shown that the use of a solid-echo refocussing pulse, following the spin-locking substantially increases the total signal observed but has a much smaller effect on the amplitudes and time constants. The values of the relaxation times and amplitudes for the two longest relaxation time components for each sample are compared with the predictions of the slow-diffusion limit of the spin-diffusion model. The longest relaxation-time component is found to be proportional to the square of the lamellar thickness determined from Raman LAM, and this is used to deduce a value for the spin-diffusion coefficient in the crystalline region, D2≈ 2 × 1016 m2 s–1. Assuming the slow-diffusion limit, the amplitudes of the long-time components in the RFSLR are used to derive values for the size of the disordered region, l1, using both the Raman and NMR derived values of l2, the size of the crystalline region. The l1 and l2 values obtained from the RFSLR are used to derive densities for regions 1 and 2 from the measured sample densities. The values of (l1+l2) from NMR are compared with those obtained from SAXS, and good agreement is found. The validity of the spin-diffusion model is further supported by the data reported here. The relaxation processes (both LF and RF) seem to imply a higher degree of ‘crystallinity’ than revealed by DSC or X-ray diffraction. The LFSLR and RFSLR are internally self-consistent, and this suggests that for SLR the crystalline component includes a fraction of the material characterised as non-crystalline by other methods (XRD, DSC).

Magnetic spin lattice relaxation in the presence of spin-diffusion

The equations describing the spin-diffusion-coupled nuclear magnetic spin-lattice relaxation behaviour of a one-dimensional, two-region system are solved exactly. The solutions allow the calculation of the relaxation times and their associated amplitudes in terms of the values of the sizes, spin-diffusion coefficients and intrinsic relaxation times of each region. The morphology of the roots of the equation are represented graphically in a manner which illustrates their behaviour as a function of the system parameters. The results obtained from these exact calculations are compared with numerically simulated data which mimic experimental measurements and which are fitted to a maximum of four exponential processes. Good agreement is demonstrated, particularly for the longer relaxation components when there are several roots with significant amplitude. Preliminary consideration is given to the inverse problem of deriving system parameters from the observed relaxation behaviour.

Theory of spin diffusion of dilute, polarized fermions for all temperatures

We describe the solution of the transport equation over the entire range of temperature from the Boltzmann to fully degenerate regimes for dilute, polarized Fermi systems. Since spin-polarized systems can show unusual quantum effects involving spin rotation in both Boltzmann and degenerate regimes, a solution of the kinetic equation over the whole temperature range is expected to be useful. Our results for the longitudinal spin diffusion coefficient reduce to the known limits in the Boltzmann and degenerate regimes and also to the expected form in the peculiar high-polarization regime in which one spin species is degenerate and the other described by classical statistics (the degenerate-classical case). We derive numerical results for the spin-rotation quality parameter μ over the full temperature range. Unlike experimental results that show μ diminishing anomalously as the temperature decreases toward the degenerate regime, our value for μ is monotonically increasing. However, the transition to the degenerate-classical regime is found to occur with a rounded-step jump in μ as a function of polarization.

Measurement of Spin-Diffusion Coefficient in Gaseous Helium between 2 K and 0.5 K

Spin-diffusion coefficient D in 3He gas and in 3He–4He mixtures has been measured by NMR techniques between 2 K and 0.5 K. The samples were polarized by optical pumping. The experimental values of D33 (spin self-diffusion in 3He) and D34 (diffusion of 3He in 4He) seems to be twenty percent higher than the theoretical predictions computed from currently used interatomic potentials.

Measurement of the Longitudinal Spin Diffusion Coefficient in Spin Polarized Atomic Hydrogen

We report on the measurement of the longitudinal spin diffusion coefficient in doubly spin polarized atomic hydrogen. Measurements were made using pulsed nuclear magnetic resonance to probe the transport of magnetization between a sealed container and a large reservoir. Results are presented for densities between 1.4×1015 and 4.8×1016 cm-3 at temperatures between 246 and 470 mK in a magnetic field of 7.7 Tesla and are found to be in reasonable agreement with theoretical calculations by Lhuillier.

Measurements of the spin diffusion coefficient of normal3He in bulk liquid and a restricted geometry

In this paper we present reliable measurements of the pressure variation of the spin diffusion coefficient of normal liquid3He in the limiting low-temperature Fermi fluid regime. Deviations from the bulk liquid behavior are observed for a sample confined to a 5-µm glass capillary array in which the mean free path of the3He quasiparticles is of the order of the capillary diameter. These deviations are believed to indicate that the spin momentum specular reflection coefficient is less than unity but greater than zero in this system.

The effects of morphology on 1H NMR spectra and relaxation in semicrystalline polyolefins

AbstractA brief résumé is given of the role of structural heterogeneity, magnetic dipolar couplings, molecular structure, and molecular motion in determining the 1H NMR spectra and relaxation properties of heterogeneous solids such as semicrystalline polymers. Measurements of 1H spin‐lattice relaxation in laboratory (T1) and rotating frames (T) are reported for a number of solid polyolefin samples. These include solution‐crystallized and melt‐crystallized polyethylene, annealed and quenched isotactic polypropene, and isotactic polybut‐1‐ene. In addition, broad‐line 1H spectra, both normal and partially (T) relaxed, are reported for these materials as well as a number of pulsed NMR experiments having the philosophy of the so‐called Goldman–Shen experiment. Spin‐lattice relaxation (T1) for all samples is a single exponential process, whereas rotating‐frame relaxation comprises three exponential processes both on‐resonance (θ = 90°) and off‐resonance at the magic angle (θ = 54.7°), with the latter generally being much slower. The spectra show clearly the existence of components having differing degrees of mobility and, with the exception of the solution‐crystallized polyethylene, the partially (T) relaxed spectra indicate a correlation between breadth of resonance line and magnitude of T1ρ. The Goldman–Shen‐type experiments indicate a spin‐diffusional transport of magnetization between the different spectral and (T) components. A computer program has been used to simulate the NMR behavior of a three‐region system comprising repeating units of infinite lamellae of different widths, each region having different intrinsic relaxation times and spin diffusion coefficients. The results demonstrate that the observed 1H NMR behavior of these samples can be interpreted in terms of this model and that, inter alia, the long‐time T behavior reflects, qualitatively, the time taken for magnetization to diffuse a distance of the order of the dimensions of the region to which it corresponds.

Spin diffusion in ferromagnetic superconductors

The influence of spin diffusion on the superconducting transition temperature is studied for systems containing a periodic array of ferromagnetic coupled spins as well as for amorphous ferromagnets. The susceptibilities of the spin systems are subject to a sum rule which allows the determination of the spin diffusion coefficient. Detailed numerical calculations of the renormalized gap functions and self-energies on the imaginary frequency axis are performed. With the help of these quantities the superconducting transition temperature is determined. The results show a relatively small decrease of T/sub c/ in comparison to static limit calculations.

Dynamic Recovery of Magnetism in Collision Cascades: MnF2

The time dependence of the hyperfine field at $^{19}\mathrm{F}$ nuclei following implantation into Mn${\mathrm{F}}_{2}$ has been studied by the perturbed angular distribution technique. The data show a partial destruction of the magnetic order in the collision cascade, attributed to electronic energy loss processes. The recovery of this magnetism defect can be accounted for by spin diffusion from the undisturbed regions of the crystal. The temperature dependence of the spin-diffusion coefficient is consistent with a critical exponent of 0.7.

Spin Diffusion in a Two-Dimensional Degenerate Fermi Liquid

The spin-diffusion coefficient $D$ of a polarized two-dimensional degenerate Fermi fluid is evaluated as a model of adsorbed $^{3}\mathrm{He}$. Because in two dimensions, for zero or weak polarization, the only allowed scattering angles are 0 and $\ensuremath{\pi}$, the transport coefficients become expressible in terms of Landau parameters without approximation. For unpolarized and weakly polarized systems it is shown that ${D}^{\ensuremath{-}1}\ensuremath{\sim}{T}^{2}\mathrm{ln}T$ and ${T}^{2}\mathrm{ln}(\mathrm{polarization})$, respectively. The two-dimensional kinetic equation is found to be exactly solvable.

Magnetic field effect on the critical EPR-dynamics of the cubic ferromagnets CdCr 2Se 4 and CdCr 2S 4

We present measurements of the critical behaviour of the EPR linewidths at frequencies 9.21 and 35.5 GHz. In the exchange critical region above T c (4π x ⪡ 1) the strong field dependence of the linewidths is observed, even when the field variation of susceptibility x is small. This phenomenon is explained by the spin diffusion effect on the linewidth. The spin diffusion coefficients D for CdCr 2Se 4 and CdCr 2S 4 are determined from the linewidths data. The temperature dependence D is found to be consistent with the predictions of the dynamical scaling theory.