Internuclear distance determination of S = 1, I = 1/2 spin pairs using REAPDOR NMR

A universal function is proposed to describe REAPDOR dephasing curves of an observed spin-1/2 nucleus dipole-recoupled to a spin-1 quadrupolar nucleus ((2)H or (14)N). Previous work had shown that, in contrast to REDOR, the shape of the dephasing curve depends on a large number of parameters including the quadrupolar coupling constant and asymmetry parameter, the sample rotation speed, the RF amplitude, and the relative orientations of the quadrupole tensor and the internuclear vector. Here we demonstrate by numerical simulations that the actual dispersion of REAPDOR dephasing curves is quite small, provided the rotation speed and the RF amplitude applied to the quadrupolar nucleus satisfy an adiabaticity condition. The condition is easily met for (2)H and is also practically achievable for virtually any (14)N-containing compound. This allows the REAPDOR curves to be approximated by a simple universal gaussian-type function, comparison of which with experimental data yields internuclear distances with less than 4% error. The spin dynamics of the recoupling mechanism is discussed. The critical importance of a stable spinning speed for optimizing the signal-to-noise ratio of the (13)C echoes is demonstrated and practical suggestions for achieving high stability are presented. Examples of applications of the universal curve are given for (2)H/(13)C and (14)N/(13)C REAPDOR in alanine.     

Intensity of cross-peaks in hyscore spectra of S = 1/2, I = 1/2 spin systems

The cross-peak intensity for a S = 1/2, I = 1/2 spin system in two-dimensional HYSCORE spectra of single-crystals and powders is analyzed. There is a fundamental difference between these two cases. For single crystals, the cross-peak intensity is distributed between the two (+, +) and (+, -) quadrants of the hyperfine sublevel correlation (HYSCORE) spectrum by the ratio c(2):s(2) (C. Gemperle, G. Aebli, A. Schweiger, and R. R. Ernst, J. Magn. Reson. 88, 241 (1990)). However, for powder spectra another factor becomes dominant and governs cross-peak intensities in the two quadrants. This factor is the phase interference between modulation from different orientations of the paramagnetic species. This can lead to essentially complete disappearance of the cross-peak in one of the two (+, +) or (+, -) quadrants. In the (+, +) quadrant, cross-peaks oriented parallel to the main (positive) diagonal of the HYSCORE spectrum are suppressed, while the opposite is true in the (+, -) quadrant where cross-peaks nearly perpendicular to the main (negative) diagonal of HYSCORE spectra are suppressed. Analytical expressions are derived for the cross-peak intensity profiles in powder HYSCORE spectra for both axial and nonaxial hyperfine interactions (HFI). The intensity is a product of two terms, one depending only on experimental parameter (tau) and the other only on the spin Hamiltonian. This separation provides a rapid way to choose tau for maximum cross-peak intensity in a region of interest in the spectrum. For axial HFI, the Hamiltonian-dependent term has only one maximum and decreases to zero at the canonical orientations. For nonaxial HFI, this term produces three separate ridges which outline the whole powder lineshape. These three ridges have the majority of the intensity in the HYSCORE spectrum. The intensity profile of each ridge resembles that observed for axial HFI. Each ridge defines two principal values of the HFI similar to the ridges from an axial HFI.     

Low-field theory of nuclear spin relaxation in paramagnetic low-symmetry complexes for electron spin systems of S = 1, 3/2, 2, 5/2, 3 and 7/2

(Molecular Physics, 2000, 98, 1617)     

Calculation of pulsed NMR signal in I = 3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.     

Rotor-encoded heteronuclear MQ MAS NMR spectroscopy of half-integer quadrupolar and spin I=1/2 nuclei

A new two-dimensional heteronuclear multiple-quantum magic-angle spinning (MQ MAS) experiment is presented which combines high resolution for the half-integer quadrupolar nucleus with information about the dipolar coupling between the quadrupolar nucleus and a spin I=1/2 nucleus. Homonuclear MQ coherence is initially created for the half-integer quadrupolar nucleus by a single pulse as in a standard MQ MAS experiment. REDOR recoupling of the heteronuclear dipolar coupling then allows the creation of a heteronuclear multiple-quantum coherence comprising multiple- and single-quantum coherence of the quadrupolar and spin I=1/2 nucleus, respectively, which evolves during t1. Provided that the t1 increment is not rotor synchronized, rotor-encoded spinning-sideband patterns are observed in the indirect dimension. Simulated spectra for an isolated IS spin pair show that these patterns depend on the recoupling time, the magnitude of the dipolar coupling, the quadrupolar parameters, as well as the relative orientation of the quadrupolar and dipolar principal axes systems. Spectra are presented for Na2HPO4, with the heteronuclear 23Na-1HMQ MAS experiments beginning with the excitation of 23Na (spin I=3/2) three-quantum coherence. Coherence counting experiments demonstrate that four- and two-quantum coherences evolve during t1. The heteronuclear spinning-sideband patterns observed for the three-spin H-Na-H system associated with the Na(2) site are analyzed. For an IS2 system, simulated spectra show that, considering the free parameters, the spinning-sideband patterns are particularly sensitive to only, first, the angle between the two IS internuclear vectors and, second, the two heteronuclear dipolar couplings. It is demonstrated that the proton localization around the Na(2) site according to the literature crystal structure of Na2HPO4 is erroneous. Instead, the experimental data is consistent with two alternative different structural arrangements, whereby either there is a deviation of 10 degrees from linearity for the case of two identical Na-H distances, or there is a linear arrangement, but the two Na-H distances are different. Furthermore, the question of the origin of spinning-sidebands in the (homonuclear) MQ MAS experiment is revisited. It is shown that the asymmetric experimental MQ sideband pattern observed for the low-C(Q) Na(2) site in Na(2)HPO4 can only be explained by considering the 23Na chemical shift anisotropy.     

Satellite-transition MAS NMR of spin I = 3/2, 5/2, 7/2, and 9/2 nuclei: sensitivity,resolution, and practical implementation

The satellite-transition MAS (STMAS) experiment offers an alternative approach to established methods such as dynamic angle spinning (DAS), double rotation (DOR), and multiple-quantum MAS (MQMAS) for obtaining high-resolution NMR spectra of half-integer quadrupolar nuclei. Unlike the multiple-quantum experiment, STMAS involves two-dimensional correlation of purely single-quantum coherences; satellite transitions in t(1) (or F(1)) and the central transition in t(2) (or F(2)). To date, STMAS has primarily been demonstrated for nuclei with spin quantum numbers I = 3/2 and, to a lesser extent, I > 5/2. However, many chemically relevant nuclei possess I > 3/2, such as (17)O and (27)Al (both I = 5/2), (59)Co (I = 7/2), and (93)Nb (I = 9/2). Here, we discuss the application of STMAS to nuclei with spin quantum numbers from I = 3/2 to 9/2. First, we consider the practical implementation of the STMAS experiment using (87)Rb (I = 3/2) NMR as an example. We then extend the discussion to include nuclei with higher spin quantum numbers, demonstrating (27)Al, (45)Sc (I = 7/2), (59)Co, and (93)Nb STMAS experiments on both crystalline and amorphous samples. We also consider the possibility of experiments involving satellite transitions other than m(I) = +/- 1/2 <--> +/- 3/2 and, using (93)Nb NMR, demonstrate the correlation of all single-quantum satellite transitions up to and including m(I) = +/- 7/2 <--> +/- 9/2. The absolute chemical shift scaling factors in these experiments are discussed, as are the implications for isotropic resolution.     

63Cu, 35Cl, and 1H NMR in the S=1/2 Kagome lattice ZnCu3(OH)6Cl2

ZnCu(3)(OH)(6)Cl(2) (S=1/2) is a promising new candidate for an ideal Kagome Heisenberg antiferromagnet, because there is no magnetic phase transition down to approximately 50 mK. We investigated its local magnetic and lattice environments with NMR techniques. We demonstrate that the intrinsic local spin susceptibility decreases toward T=0, but that slow freezing of the lattice near approximately 50 K, presumably associated with OH bonds, contributes to a large increase of local spin susceptibility and its distribution. Spin dynamics near T=0 obey a power-law behavior in high magnetic fields.     

NMR determination of 2D electron spin polarization at nu = 1/2

Using a "standard" NMR spin-echo technique we determined the spin polarization P of two-dimensional electrons, confined to GaAs quantum wells, from the hyperfine shift of Ga nuclei located in the wells. Concentrating on the temperature ( 0.05 less, similarT less, similar10 K) and magnetic field ( 7 less, similarB less, similar17 T) dependencies of P at Landau level filling factor nu = 1/2, we find that the results are described well by a simple model of noninteracting composite fermions, although some inconsistencies remain when the two-dimensional electron system is tilted in the magnetic field.     

Two-stage spin-flop transitions in the S = 1/2 antiferromagnetic spin chain BaCu(2)Si(2)O(7)

Two-stage spin-flop transitions are observed in the quasi-one-dimensional antiferromagnet BaCu(2)Si(2)O(7). A magnetic field applied along the easy axis induces a spin-flop transition at 2.0 T followed by a second transition at 4.9 T. The magnetic susceptibility indicates the presence of Dzyaloshinskii-Moriya (DM) antisymmetric interactions between the intrachain neighboring spins. We discuss a possible mechanism whereby the geometrical competition between DM and interchain interactions, as discussed for the two-dimensional antiferromagnet La(2)CuO(4), causes the two-stage spin-flop transitions.     

Two-dimensional hyperfine sublevel correlation spectroscopy: powder features for S=1/2, I=1

The lineshapes of two-dimensional magnetic resonance spectra of disordered or partially ordered solids are dominated by ridges of singularities in the frequency plane. The positions of these ridges are described by a branch of mathematics known as catastrophe theory concerning the mapping of one 2D surface onto another. We systematically consider the characteristics of HYSCORE spectra for paramagnetic centers having electron spin S=1/2 and nuclear spin I=1 in terms of singularities using an exact solution of the nuclear spin Hamiltonian. The lineshape characteristics are considered for several general cases: zero nuclear quadrupole coupling; isotropic hyperfine but arbitrary nuclear quadrupole couplings; coincident principal axes for the nuclear hyperfine and quadrupole tensors; and the general case of arbitrary nuclear quadrupole and hyperfine tensors. The patterns of singularities in the HYSCORE spectra are described for each case.     

Bestimmung des (631)K=1/2, I=1/2-Zustandes im U 239

Theγ-ray spectrometer at the DR 3-reactor at Risø was used to investigate the low energyγ-lines of U 239 which are emitted during neutron-capture in U 238. Very closely lying lines have been found between 500 and 650 keV. The big intensity of the 133 keV line and the lack of other transitions of appropriate energy and intensity point out that this line corresponds to the hinderedE 2-transition from the (631)I=1/2⁺ level to the (622)I=5/2⁺ groundstate. A suggestion was made for the decay possibility of the octupole states at 700 keV found by N.Fiebiger.     

N BARYONS(S=0,I=1/2)p,N~+=uud;n,N~0=udd

<正>~~     

Calculation of pulsed NMR signal in I=3/2 quadrupolar spin system

The rf pulse response of I=3/2 spin system experiencing first order quadrupolar splitting is studied using density matrix approach. A general expression is derived in terms of spin populations, quadrupole splitting and duration and amplitude of the rf pulse for calculating the NMR signal arising due to the centre line and satellite resonances for the situation where the impressed rf pulse excites the resonances selectively as well as non-selectively. The necessary 4×4 transformation matrix obtained analytically by diagonalyzing the Hamiltonian are used to get the expression for the centre line response. The satellite signals are obtained in the same way but by using the numerical values of the roots of the related quartics. The widths of the corresponding π/2-pulses are calculated for different initial spin populations. The variations of this pulse-width and the corresponding signal amplitude as a function of satellite splitting are studied.     

Magnetic phase diagram of the dimerized spin S = 1/2 ladder

The ground-state magnetic phase diagram of a spin S=1/2 two-leg ladder with alternating rung exchange J_⊥(n)=J_⊥[1 + (-1)ⁿ δ] is studied using the analytical and numerical approaches. In the limit where the rung exchange is dominant, we have mapped the model onto the effective quantum sine-Gordon model with topological term and identified two quantum phase transitions at magnetization equal to the half of saturation value from a gapped to the gapless regime. These quantum transitions belong to the universality class of the commensurate-incommensurate phase transition. We have also shown that the magnetization curve of the system exhibits a plateau at magnetization equal to the half of the saturation value. We also present a detailed numerical analysis of the low energy excitation spectrum and the ground state magnetic phase diagram of the ladder with rung-exchange alternation using Lanczos method of numerical diagonalizations for ladders with number of sites up to N = 28. We have calculated numerically the magnetic field dependence of the low-energy excitation spectrum, magnetization and the on-rung spin-spin correlation function. We have also calculated the width of the magnetization plateau and show that it scales as δ^ν, where critical exponent varies from ν = 0.87±0.01 in the case of a ladder with isotropic antiferromagnetic legs to ν = 1.82±0.01 in the case of ladder with ferromagnetic legs. Obtained numerical results are in an complete agreement with estimations made within the continuum-limit approach.     

Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain

We study the frustration-induced enhancement of the incommensurate correlation for a bond-alternating quantum spin chain in a magnetic field, which is associated with a quasi-one-dimensional organic compound F5PNN. We investigate the temperature dependence of the staggered susceptibilities by using the density matrix renormalization group, and then find that the incommensurate correlation becomes dominant in a certain range of the magnetic field. We also discuss the mechanism of this enhancement on the basis of the mapping to the effective S=1/2 XXZ chain and a possibility of the field-induced incommensurate long-range order.