Comment on the NMR lineshape in low-dimensional paramagnets

It will be demonstrated that the model used by some workers to describe the NMR lineshape in low-dimensional magnetic systems is of academic interest only. Furthermore, we will show that this model was not treated properly. The NMR lineshape in low-dimensional systems has a normal single-peaked structure.     

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl₂. The spectra were obtained with the sample at 4.2 K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the ²⁷Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from ¹⁵⁵Gd and ¹⁵⁷Gd nuclei.     

Theory of zero-field NMR spectra. Effects of motion

Zero-field NMR spectra of tunnelling methyl group, classically reorienting methyl group and of a pair of spins 1/2 jumping between two perpendicular orientations are calculated. A formula for the second moment of a rigid lattice is derived from a formal analogy between zero-field and high-field spectra. Fast reorientation about a perpendicular axis reduces the intramolecular second moment to 1/4 of its rigid value. The zerofield method seems to be a promising tool for the determination of tunnelling splitting or of jumping rates.     

Deuterium NMR lineshape and relaxation study of a hydrated cross-linked polymer

A combined study of²H nuclear magnetic resonance lineshape and spin-lattice and spin-spin relaxation times as functions of temperature and the amount of hydration water in a cross-linked copolymer of sucrose and 1,4-butadienol diglycidyl ether in the hydrogel phase is reported. The results show strong evidence that the onset of the relaxation mechanisms is driven by anomalous water molecule diffusion depending on both temperature and the hydration degree of the hydrogel. In addition, these results are correlated with the transitions observed by differential thermal analysis.     

Temperature-dependent fourth moment of the relaxation function for cubic Heisenberg paramagnets

Useful expressions, solely in terms of appropriate lattice Green functions, are derived for the fourth moment of the relaxation function of a Heisenberg paramagnet having cubic symmetry (s.c., b.c.c. and f.c.c.) and nearest-neighbour exchange interactions. As is customary, the temperature dependence was estimated on the basis of the spherical model and with a simple random-phase type decoupling of the four-spin correlation functions.     

Calculation of zero-field NMR spectra of the ammonium ion undergoing tunneling motion and fast random reorientation

Zero-field NMR spectra of the ammonium ion in the case of tunneling, tunneling and fast reorientation by 180° jumps around theC ₂ axis, tunneling and fast reorientation by 120° jumps aroundC ₃ axis are calculated.     

NMR lineshape equations for hindered methyl group: a comparison of the semi-classical and quantum mechanical models

The semiclassical and quantum mechanical NMR lineshape equations for a hindered methyl group are compared. In both the approaches, the stochastic dynamics can be interpreted in terms of a progressive symmetrization of the spin density matrix. However, the respective ways of achieving the same limiting symmetry can be remarkably different. From numerical lineshape simulations it is inferred that in the regime of intermediate exchange, where the conventional theory predicts occurrence of a single Lorentzian, the actual spectrum can have nontrivial features. This observation may open new perspectives in the search for nonclassical effects in the stochastic behavior of methyl groups in liquid-phase NMR.     

On the two-scale expansion of the fourth moment of a wave propagating in a random medium

Abstract

A comprehensive and rigorous analysis of the prevalent version of the two-scale expansion used to solve the fourth-moment equation shows that it is not an asymptotic technique. The correct asymptotic version is derived and found to be analytically non-tractable. An elaborated interpretation to the correction terms used before is established and shows that an additional term of the same order was overlooked. The new expression which will improve the result in the scintillation peak is offered. The role of the small parameter of the problem is discussed.     

On the two-scale expansion of the fourth moment of a wave propagating in a random medium

A comprehensive and rigorous analysis of the prevalent version of the two-scale expansion used to solve the fourth-moment equation shows that it is not an asymptotic technique. The correct asymptotic version is derived and found to be analytically non-tractable. An elaborated interpretation to the correction terms used before is established and shows that an additional term of the same order was overlooked. The new expression which will improve the result in the scintillation peak is offered. The role of the small parameter of the problem is discussed.     

High-precision evaluation of the magnetic moment of the helion

NMR spectra of samples containing a mixture of hydrogen deuteride HD with pressure of about 80 atm and helium-3 with partial pressure of about 1 atm are analyzed. The ratio of the resonance frequencies of the nuclei, F(³He)/F(H₂), is determined to be 0.761786594(2), which is equal to the magnetic moment of the helion (bound in a helium atom) in the units of the magnetic moment of a proton (bound in molecular hydrogen). The uncertainty of two digits in the last place corresponds to a relative error of ??[F(³He)/F(H₂)] = 2.6 × 10^?9. The use of the known calculated data on the shielding of nuclei in the helium-3 atom (??(³He) = 59924(2) × 10^?9) and on the shielding of protons in hydrogen (??(H₂) = 26288(2) × 10^?9) yields a value of ??(³He)/?? _p = ?0.761812217(3) for the free magnetic moment of the helion in the units of the proton magnetic moment.     

On the second moment of the multiquantum NMR spectrum of a solid

New experimental data on the time dependence of an increase in the number of correlated spins under the conditions of the observation of the multiquantum NMR spectrum of a solid are processed on the basis of a microscopic theory for describing the growth of the second moment of multiquantum NMR developed by us earlier. As follows from the theory, the growth is an exponential function of time for crystals with quite diverse structures. The results are discussed on the basis of semiphenomenological models.     

N-dependence of the lineshape in nonlinear radiation phenomena

Preliminary experimental results are reported on the investigation of the dependence of the intensity of the second harmonic generated by paramagnets on the number N of spins. A qualitative argument in terms of correlation effects among the spins is tentatively put forward to interpret the results.     

Magnetic dipole moment of127Sb by NMR/ON

The technique of NMR on oriented nuclei has been applied to¹²⁷Sb to measure the magnetic dipole moment of the¹²⁷Sb ground state. Resonant destruction of gamma-ray anisotropy from¹²⁷Sb^g (I =7/2⁺) has been observed at 139.6(2) MHz forB _app=0.30(1) T andat 138.7(1) MHz forB _app=0.25(1) T. The deduced magnetic moment is ||=2.697(6) µ_N.     

Second moment of NMR spectra for oriented partially crystalline polymers

The theory of the second moment of NMR spectra of oriented partially crystalline polymers is developed in this paper. Two phase model of the structure of polymer is considered in deriving of second moment of NMR spectra. Possibilities of characterization of the degree of orientation of macromolecular chains separately in crystalline and noncrystalline regions of the polymer are discussed in this paper.     

Local spin moment distribution in antiferromagnetic molecular rings probed by NMR

The NMR spectra of 19F and 53Cr have been obtained at low temperatures in a heterometallic substituted antiferromagnetic (AF) ring Cr7Cd with an S=3/2 ground state and compared with the spectra in a homometallic Cr8 AF ring with an S=0 ground state. From the analysis of the spectra one can derive directly model independent values of the staggered nonuniform distribution of the local moment in the heterometallic ring Cr7Cd. The experimental values are found to be in excellent agreement with the theoretical values calculated on the basis of an effective spin Hamiltonian which includes crystal field effects.     

NMR frequency and magnetic dipole moment of (3)He nucleus

We present new gas-phase NMR spectra which relate the resonance frequency of (3)He nucleus to the resonance frequency of the proton in tetramethylsilane (TMS). We discuss the dependence of (3)He resonance frequency on the density of the solvent gas, and we consider in detail the absolute shielding scales of both nuclei. Finally, we analyse the accuracy of the results, using the relationship between the resonance frequencies, absolute shielding constants and magnetic dipole moments of (1)H and (3)He nuclei.