Theoretical Study of Dipolar Relaxation of Coupled Nuclear Spins at Variable Magnetic Field

A theoretical study was made of magnetic field-dependent dipolar relaxation in two- and three-spin systems. The results for the nuclear magnetic relaxation dispersion (NMRD) curves were compared with those for the simpler model of fluctuating local fields. For both models it was found that at low fields spins tend to relax with a common T ₁-relaxation time. Sharp features in the NMRD curves coming from nuclear spin level anti-crossings are also predicted by both models. However, the simple model fails to describe the behavior of so-called long-lived spin states (LLS). We have studied the LLS as function of magnetic field and molecular geometry and simulated experimental results for the LLS in histidine amino acid obtained at the laboratory of Prof. H.-M. Vieth (Free University Berlin, Germany). In addition, we described polarization transfer in a three-spin system where two spins are protons, which are initially hyperpolarized by para-hydrogen induced polarization (PHIP), while the third spin is a spin ½ hetero-nucleus, which acquires polarization in the course of cross-relaxation.     

Solid state 33S NMR of inorganic sulfides

Solid state 33S NMR spectra of a variety of inorganic sulfides have been obtained at magnetic field strengths of 4.7 and 17.6T. Spectra acquired with magic angle spinning show considerable improvements in sensitivity and resolution when compared with static spectra. Multiple factors are considered when analyzing the spectral line widths, including; magnetic field inhomogeneity, dipolar coupling, chemical shift anisotropy, chemical shift dispersion (CSD), T(2) relaxation, and quadrupolar coupling. Quadrupolar coupling was expected to be the dominant line broadening mechanism. However, for most of the samples CSD was the prevailing line broadening mechanism. Thus, for many of the metal sulfides studied at a high magnetic field strength, the line widths were actually larger than those observed in the spectra at low field. This is atypical in solid state 33S NMR. Solid state 33S spin-lattice (T(1)) and spin-spin (T(2)) relaxation rates were measured for the first time and are discussed. This information will be useful in future efforts to use 33S NMR in the compositional and structural analysis of sulfur containing materials.     

Nuclear spin relaxation in paramagnetic systems (S>/=1) under fast rotation conditions

A new theoretical model for nuclear spin relaxation in paramagnetic systems in solution has been developed. Fast rotational motion is included in the model, both as a source of modulation of the static zero-field splitting, which provides a mechanism for electron spin relaxation, and as an origin of the stochastic variation of the electron spin-nuclear spin dipole-dipole interaction leading to nuclear spin relaxation. At the limit of low magnetic field, the model is essentially identical to the earlier formulations from our laboratory, but new closed-form expressions are given for the inner- and outer-sphere relaxation at the high-field limit. Numerical comparisons with a general theory are reported for the inner-sphere case. In addition, some nuclear magnetic relaxation dispersion (NMRD) profiles from the literature are considered for systems where experiments have been done with both low-molecular weight paramagnetic complexes and their adducts with proteins. Previously developed theories are used to interpret data for the slowly rotating protein adducts, and good fits of the fast-rotating counterparts are obtained by further adjustment of one or two additional parameters.     

Transverse relaxation mechanisms in articular cartilage

Relaxation rates in the rotating frame (R1rho) and spin-spin relaxation rates (R2) were measured in articular cartilage at various orientations of cartilage layer to the static magnetic field (B0), at various spin locking field strengths and at two different static magnetic field strengths. It was found that R1rho in the deep radial zone depended on the orientation of specimens in the magnet and decreased with increasing the spin locking field strength. In contrast, R1rho values in the transitional zone were nearly independent of the specimen orientation and the spin locking field strength. Measurements of the same specimens at 2.95 and 7.05 T showed an increase of R1rho and most R2 values with increasing B0. The inverse B0 dependence of some R2 values was probably due to a multicomponent character of the transverse magnetization decay. The experiments revealed that the dominant T1rho and T2 relaxation mechanism at B0 < or = 3 T is a dipolar interaction due to slow anisotropic motion of water molecules in the collagen matrix. On average, the contribution of scalar relaxation due to rapid proton exchange in femoral head cartilage at 2.95 T is about 6% or less of the total R1rho at the spin locking field of 1000 Hz.     

Paramagnetic proton nuclear spin relaxation theory of low-symmetry complexes for electron spin quantum number S = 52

A generalization of the modified Solomon-Bloembergen-Morgan (MSBM) equations has been derived in order to describe paramagnetic relaxation enhancement (PRE) of paramagnetic complexes characterized by both a transient (DeltaZFSt) and a static (DeltaZFSs) zero-field splitting (ZFS) interaction. The new theory includes the effects of static ZFS, hyperfine coupling, and angular dependence and is presented for the case of electron spin quantum number S = 52, for example, Mn(II) and Fe(III) complexes. The model gives the difference from MSBM theory in terms of a correction term delta which is given in closed analytical form. The theory may be important in analyzing the PRE of proton spin-lattice relaxation dispersion measurements (NMRD profiles) of low-symmetry aqua-metal complexes which are likely to be formed upon transition metal ions associated with charged molecular surfaces of biomacromolecules. The theory has been implemented with a computer program which calculates solvent water proton T1 NMRD profiles using both MSBM and the new theory.     

Designing spin-spin interactions with one and two dimensional ion crystals in planar micro traps

We discuss the experimental feasibility of quantum simulation with trapped ion crystals, using magnetic field gradients. We describe a micro structured planar ion trap, which contains a central wire loop generating a strong magnetic gradient of about 20 T/m in an ion crystal held about 160 μm above the surface. On the theoretical side, we extend a proposal about spin-spin interactions via magnetic gradient induced coupling (MAGIC) [J. Phys. B At. Mol. Opt. Phys. 42, 154009 (2009)]. We describe aspects where planar ion traps promise novel physics: spin-spin coupling strengths of transversal eigenmodes exhibit significant advantages over the coupling schemes in longitudinal direction that have been previously investigated. With a chip device and a magnetic field coil with small inductance, a resonant enhancement of magnetic spin forces through the application of alternating magnetic field gradients is proposed. Such resonantly enhanced spin-spin coupling may be used, for instance, to create Schrödinger cat states. Finally we investigate magnetic gradient interactions in two-dimensional ion crystals, and discuss frustration effects in such two-dimensional arrangements.     

The oral administration of MnCl2: A potential alternative to IV injection for tissue contrast enhancement in magnetic resonance imaging

Mn⁺² (as MnCl₂) was administered to rabbits intravenously and orally (a route of administration which based upon our previous experiments in rats⁷ promises to give selective hepatobiliary enhancement with less systemic toxicity). Nuclear magnetic relaxation dispersion or T₁ (NMRD) was performed on selected tissues (heart, liver, kidney, serum, and bile) in both animal groups to examine possible qualitative and semiquantitative differences in T₁ relaxation at equivalent sacrifice times. One animal was given an oral dose of MnCl₂ (620 micromoles/kg) and imaged sequentially (T₁ weighted sequence, .12T) for 30 minutes. The NMRD curves for organ tissues show an increase in relaxation efficacy in the 10–20MHz range characteristic of Mn-macromolecular complexes and are similar irrespective of the route of administration. The lack of increased relaxation enhancement for bile in this frequency range reflects cleavage of this complex upon excretion. Decreased overall relaxation in the liver is observed when oral Mn⁺² is compared to IV Mn⁺² due to the small fraction of administered dose that is absorbed. However, the images document a significant increase in the intensity of liver signal after the oral dose. We suspect this dose may ultimately be adjusted downward to give selective hepatobiliary effects.     

The influence of the stoichiometry on the Eu nuclear spin-spin relaxation in EuO single crystals

The ¹⁵³Eu spin-spin relaxation for two spherical EuO single crystals of different composition has been measured for two saturating field values of 2 and 6 T. The relaxation can be described by two time constants, a short one increasing with the magnetic field, arising from the Suhl-Nakamura coupling and a long one, due to the dipolar coupling, which is field independent. It is shown that the number of nuclei which are relaxed due to the dipolar coupling increases at increasing magnetic fields, in agreement with the Suhl-Nakamura theory. For the sample which is nearly stoichiometric the relative number of nuclei which is relaxed due to the SN coupling is much larger than for the sample which contains an excess of Eu atoms.     

Extensive NMRD studies of Ni(II) salt solutions in water and water-glycerol mixtures

Aqueous solutions of simple nickel(II) salts are a classical test case for theories of the paramagnetic relaxation enhancement (PRE) and its dependence on the magnetic field (nuclear magnetic relaxation dispersion, NMRD), going back to late fifties. We present here new experimental data, extending the NMRD range up to 21T (900 MHz). In addition to salt solutions in (acidified) water, we have also measured on solutions containing glycerol. The aqueous solution data do not show any significant changes compared to the earlier experiments. The interpretation, based on the general ("slow-motion") theory is also similar to the earlier work from our laboratory. The NMRD-data in mixed solvents are qualitatively different, indicating that the glycerol not only changes the solution viscosity, but may also enter the first coordination sphere of the metal ion, resulting in lower symmetry complexes, characterized by non-vanishing averaged zero-field splitting. This hypothesis is corroborated by molecular dynamics simulations. A strategy appropriate for interpreting the NMRD-data for the chemically complicated systems of this type is proposed.     

Low energy spin waves and magnetic interactions in SrFe2As2

We report inelastic neutron scattering studies of magnetic excitations in antiferromagnetically ordered SrFe2As2 (T_{N}=200-220 K), the parent compound of the FeAs-based superconductors. At low temperatures (T=7 K), the magnetic spectrum S(Q,Planck's omega) consists of a Bragg peak at the elastic position (Planck's omega=0 meV), a spin gap (Delta< or =6.5 meV), and sharp spin-wave excitations at higher energies. Based on the observed dispersion relation, we estimate the effective magnetic exchange coupling using a Heisenberg model. On warming across T_{N}, the low-temperature spin gap rapidly closes, with weak critical scattering and spin-spin correlations in the paramagnetic state. The antiferromagnetic order in SrFe2As2 is therefore consistent with a first order phase transition, similar to the structural lattice distortion.     

Slice with angulated non-parallel boundaries

The explosive hexahydro-1,3,5-trinitro-s-triazine (CH2-N-NO2)3, commonly known as RDX, has been studied by 14N NQR and 1H NMR. NQR frequencies and relaxation times for the three ν+ and ν- lines of the ring 14N nuclei have been measured over the temperature range 230-330 K. The 1H NMR T1 dispersion has been measured for magnetic fields corresponding to the 1H NMR frequency range of 0-5.4 M Hz. The results have been interpreted as due to hindered rotation of the NO2 group about the N-NO2 bond with an activation energy close to 92 kJ mol(-1). Three dips in the 1H NMR dispersion near 120, 390 and 510 kHz are assigned to the ν0, ν- and ν+ transitions of the 14NO2 group. The temperature dependence of the inverse line-width parameters T2? of the three ν+ and ν- ring nitrogen transitions between 230 and 320 K can be explained by a distribution in the torsional oscillational amplitudes of the NO2 group about the N-NO2 bond at crystal defects whose values are consistent with the latter being mainly edge dislocations or impurities in the samples studied. Above 310 K, the 14N line widths are dominated by the rapid decrease in the spin-spin relaxation time T2 due to hindered rotation of the NO2 group. A consequence of this is that above this temperature, the 1H T1 values at the quadrupole dips are dominated by the spin mixing time between the 1H Zeeman levels and the combined 1H and 14N spin-spin levels.     

Electrical control of spin relaxation in a quantum dot

We demonstrate electrical control of the spin relaxation time T1 between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W identical withT1(-1) by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T1 exceeds 1 s.     

Surface dynamics of liquids in porous media.

We report remarkable differences in the 1H nuclear magnetic relaxation dispersion data (NMRD) between water and other common aprotic solvents such as acetone when in contact with high surface area calibrated microporous chromatographic silica glasses that contain trace paramagnetic impurities located at or close to the pore surface. All these differences have been related to the particular chemical behaviors and dynamics of these liquids at the pore surface. We apply this technique to probe the structure and dynamics of water and oil at the surface of calibrated macroporous systems, where similar surface dynamics effects have been observed. This technique is also applied to follow the first hydration stage of a white cement-paste. Last, we present an analysis of the magnetic field dependence of 1H nuclear relaxation data to exhibit the microporosity of ultra high performance concretes.     

The dependence of nuclear magnetic resonance (NMR) image contrast on intrinsic and pulse sequence timing parameters

In Nuclear Magnetic Resonance (NMR) the image pixel value is governed by at least three major intrinsic parameters: the spin density N (H), the spin-lattice relaxation time T1, and the spin-spin relaxation time T2. The extent to which the signal is weighted toward one or several parameters is related to the history of the spin system preceding detection. On the simplifying, though not generally warranted assumption that the spin density does not vary significantly in soft tissues, relative tissue contrast can be predicted quantitatively provided the relaxation times are known. Signal intensities and contrast were computed on the basis of the Bloch equations and experimentally determined relaxation times as a function of pulse timing parameters and the data compared with those in images recorded at 0.5T field strength. Significant deviations from the equal density hypothesis were found for gray and white substance. Notably partial saturation but also spin echo and inversion-recovery images are not in full accordance with predictions made on the basis of relaxation times alone.     

Features of low-frequency spin dynamics in manganite LaMnO3 according to 139La NMR data

The spin-lattice and spin-spin relaxation times of ¹³⁹La are measured in manganite LaMnO₃. Analysis of the frequency dependence of the spin-lattice relaxation rate in the paramagnetic temperature range shows that this quantity is determined by magnetic fluctuations. The magnitude of the fluctuating field is estimated. It is shown that the correlation time for spin fluctuations varies with temperature in accordance with the Arrhenius law. The high value of the spin-spin relaxation rate in the paramagnetic region can be due to strong anisotropy of fluctuating magnetic fields at La nuclei.     

Enhanced signal intensities obtained by out-of-phase rapid-passage EPR for samples with long electron spin relaxation times

To understand the signals that are observed under rapid-passage conditions for samples with long electron spin relaxation times, the E' defect in irradiated vitreous SiO(2) was studied. For these samples at room temperature, T(1) is 200 mciro s and T(2) ranged from 35 to 200 micro s, depending on spin concentration. At X band with 100-kHz modulation frequency and 1-G modulation amplitude there was minimal lineshape difference between the low-power, in-phase spectra and high-power spectra detected 90 degrees out-of-phase with respect to the magnetic field modulation. Signal enhancement, defined as the ratio of the intensities of the out-of-phase to the in-phase signals when B(1) for both observation modes is adjusted to give maximum signal, was 3.4 to 9.5 at room temperature. The origin of the out-of-phase signal was modeled by numerical integration of the Bloch equations including magnetic field modulation. The waveforms for the E' signal, prior to phase sensitive detection, were simulated by summing the contributions of many individual spin packets. Good agreement was obtained between experimental and calculated waveforms. At low B(1) the experimental values of T(1) and T(2) were used in the simulations. However, at higher B(1), T(2) was adjusted to match the experimental signal intensity and increased with increasing B(1). At high B(1), T(2)=T(1), consistent with Redfield's and Hyde's models. For the spin concentrations examined, the out-of-phase signals at very high power (B(1) approximately 0.33 G) displayed a linear relationship between peak-to-peak signal amplitude and spin concentration. Under the conditions used for spin quantitation the signal-to-noise for these spectra was up to 5 times higher than for the in-phase signal, which greatly facilitates quantitation for these types of samples. For samples in which T(2) is dominated by electron spin-spin interaction, lower spin concentration results in longer T(2) and the enhancement is increased.     

Determination of the effective correlation time modulating 1H NMR relaxation processes of bound water in protein solutions

The relaxation in protein solutions has mainly been studied by nuclear magnetic relaxation dispersion (NMRD) techniques. NMRD data have mostly been analyzed in terms of fast chemical exchange of water between free water and water bound to proteins. Several approaches were used for the estimation of correlation time modulating the relaxation mechanism of bound water. On the other hand, in a nuclear magnetic resonance experiment, the relaxation rates of protein solutions (1/T1 and 1/T2) and also those of free water (1/T1f and 1/T2f) are measurable. However, the relaxation rates of bound water (1/T1b and 1/T2b) are not. Despite this, equating (1/T1-1/T1f)/2(1/T2-1/T2f) to (1/T1b)/2(1/T2b) leads to an expression involving only an effective tau that is related to the rotational correlation time (tau r) of proteins. Equating the ratios may therefore give a simple alternative method for the determination of tau r even if this method is limited to a single resonance frequency. In this work, a formula was derived for the solution of the effective tau. Then, the 1/T1 and 1/T2 in solutions of two globular proteins (lysozyme and albumin) and one nonglobular protein (gamma-globulin) were measured for different amounts of each protein. Next, the values of 1/T1 and 1/T2 were plotted vs. protein concentrations, and then the slopes of the fits were used in the derived equation for determining the effective tau values. Finally, the rotational correlation time tau r, calculated from tau, was used in the Stokes-Einstein relation to reproduce relevant radii. The effective tau values of lysozyme, albumin and gamma-globulin were found to be 5.89 ns, 7.03 ns and 8.8 ns, respectively. tau r values of albumin and lysozyme produce their Stokes radii. The present data suggest that use of the measurable ratio in the derived formula may give a simple way for the determination of the correlation times of lysozyme and albumin.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Quest for frustration driven distortion in Y2(Mo2)O(7)

We investigated the nature of the freezing in the geometrically frustrated Heisenberg spin glass Y2(Mo2)O(7) by measuring the temperature dependence of the static internal magnetic field distribution above the spin-glass temperature, Tg, using the muon spin relaxation technique. The evolution of the field distribution cannot be explained by changes in the spin susceptibility alone and suggests a lattice deformation. This possibility is addressed by numerical simulations of the Heisenberg Hamiltonian with magnetoelastic coupling at T > 0.