Finite pulse width artifact suppression in spin-1 quadrupolar echo spectra by phase cycling

A phase cycling scheme for suppressing spectral artifacts introduced in quadrupolar echo spectroscopy of spin-1 nuclei due to finite pulse width effects is presented. The phase cycling scheme is developed using the formalism of average Hamiltonian theory and fictitious spin-1 operators. A simulation and experiment on deuterated polyethelene is performed highlighting the spectral artifact introduced by finite pulse widths and successful removal with the proposed phase cycling scheme.     

Spin-locking mechanism of spin I = 3/2 quadrupolar nuclei undergo magic angle spinning

The spin-locking mechanism of the spin I=3/2 quadrupolar nuclei under magic angle spinning (MAS) has been theoretically and experimentally investigated, and the criterion of adiabatic passage around zero-crossings of the quadrupole splitting was inferred from the time-dependent Shrödinger equation in this article. The theory, numerical simulations, and experiments conducted in this work all indicated that second-order quadrupole interaction and off-resonance play important roles in the spin-locking of the quadrupolar nuclei, and they were responsible for the great loss of the spin-locking signals. The spin-locking for a spin I=3/2 nucleus might be achieved by minimizing the effect of the second-order quadrupole interaction by using a radio frequency (RF) offset. This offset was realized by setting the RF to the opposite position of the isotropic second-order quadrupolar shift of single quantum coherences.     

Kosterlitz-Thouless transition for the finite-temperatured=2+1,U(1) Hamiltonian lattice gauge theory

We prove that in thed=2+1,U(1) Hamiltonian (continuous time) lattice gauge theory the confining potential between two static external charges grows logarithmically with their distance, at sufficiently high temperatures. As it is known that for zero or low temperatures and large coupling constant the model confines linearly, we have therefore established the existence of a Kosterlitz-Thouless transition. Our results are based on a Mermin-Wagner type of argument combined with correlation inequalities and known results for the two-dimensional (spin) Villain model.     

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.     

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)     

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.     

Theoretical investigations on the spin Hamiltonian parameters and local structures for the trigonal Ni2+ centers in CsMgX3 (X=Cl,Br, I)

The spin Hamiltonian parameters (zero-field splitting and the anisotropic g factors) and the local structures for the trigonal Ni²⁺ centers in CsMgX₃ (X=Cl, Br, I) are theoretically investigated from the perturbation formulas of these parameters for a 3d⁸ ion in trigonally distorted octahedra, by including the ligand s-orbital contributions. Based on the studies, the local impurity-ligand bond angles β related to the C ₃ axis in the Ni²⁺ centers are found to be about 2° larger than the corresponding angles, β_H, in the hosts, due to the size mismatching substitution of Mg²⁺ by Ni²⁺. The theoretical results based on the inclusion of the ligand s-orbital contributions show an improvement when compared with those in the absence of the above contributions, especially for the ligand I^?.     

Quadrupole effects of spin-3/2 nuclei on the solid-state magic-angle spinning nuclear magnetic resonance spectra of spin-1/2 nuclei Deviations from first-order theory and implications concerning the sign of the indirect coupling constant

The effect of the interaction between spin-3/2 and spin-1/2 nuclei on solid-state magic-angle spinning nuclear magnetic resonance (MAS NMR) spectra of the latter is studied in cases where deviations from first-order theory are expected. A comparison is made between the exact and first-order perturbation approaches. Both dipolar and indirect (iso- and anisotropic) coupling interactions are considered. Implications regarding ¹³C,^35,37Cl, ³¹P,^63,65Cu and ¹¹⁹Sn,^35,37Cl cases are discussed. It is shown that in the latter two cases the sign of the indirect coupling constant J can be derived.     

Theoretical investigations of the local structure distortion and the spin Hamiltonian parameters of Cr ions at tetragonal charge-compensation defect CrF5O site in Cr: KMgF3 crystals

The local structure distortion and the spin Hamiltonian (SH) parameters, including the zero-field splitting (ZFS) parameter D and the Zeeman g-factors g_‖ and g_⊥, are theoretically investigated by means of complete diagonalization method (CDM) and the microscopic spin Hamiltonian theory for tetragonal charge compensation CrF₅O defect center in Cr³⁺:KMgF₃ crystals. The superposition model (SPM) calculations are carried out to provide the crystal field (CF) parameters. This investigation reveals that the replacement of O²⁻ for F⁻ and its induced lattice relaxation Δ₁(O²⁻) combined with an inward relaxation of the nearest five fluorine Δ₂(F⁻) give rise to a strong tetragonal crystal field, which in turn results in the large ZFS and large anisotropic g-factor Δg. The experimental SH parameters D and Δg can be reproduced well by assuming that O²⁻ moves towards the central ion Cr³⁺ by Δ₁(O²⁻)=0.172R₀ and the five F⁻ ions towards the central ion Cr³⁺ by Δ₂(F⁻)=0.022R₀. Our approach takes into account the spin-orbit (SO) interaction as well as the spin-spin (SS), spin-other-orbit (SOO), and orbit-orbit (OO) interactions omitted in previous studies. This shows that although the SO interaction is the most important one, the contributions to the SH parameters from other three magnetic interactions are appreciable and should not be omitted, especially for the ZFS parameter D.     

Transition probabilities of lines with origin in the 3d′(5/2)2, 3d′(5/2)3 and 3d′(3/2)1 levels of Ne(I).

Relative transition probabilities for twenty near-i.r. electric dipole lines and for three forbidden lines of Ne(I) with origin in the 3d′(5/2)₂, 3d′(5/2)₃ and 3d′(3/2)₁ levels have been measured. The calculated lifetime in jK coupling of the 3d′(5/2)₂ and 3d′(5/2)₃ levels was used to put on an absolute scale the transition probabilities of fourteen lines. The values of the present work are compared with theoretical calculations obtained by use of the Coulomb approximation and the intermediate-coupling scheme.     

E2 transitions in the SU(3) formalism for N = Z nuclei of the sd and pf shells

We show that the SU(3) coupling scheme reproduces the data for E2 transitions in N = Z even-even nuclei both of the sd and the pf shells. The SU(3) results are compared with large-scale shell model calculations. Along the ground-state band-like structures, the increase of the B(E2) values with spin toward a maximum value and the subsequent fall with further increasing spin are reproduced rather well. The role of the quadrupole-quadrupole term of the nuclear residual interaction is stressed.     

The influence of the radiofrequency excitation and conversion pulses on the lineshapes and intensities of the triple-quantum MAS NMR spectra of I = 3/2 nuclei

A rigorous examination of the various multiple-quantum magic angle spinning sequences is carried out with reference to sensitivity enhancement in the isotropic dimension and the lineshapes of the corresponding MAS peaks in the anisotropic dimension. An echo efficiency parameter is defined here, which is shown to be an indicator of the performance aspects of the various sequences. This can be used in the design of further new experiments in this field. A consequence of such a systematic analysis has been the combination of a spin-lock pulse for excitation of multiple-quantum coherences and an amplitude-modulated pulse for their conversion to observable single-quantum coherences. This approach has resulted in an improved performance over other sequences with respect to both the anisotropic lineshapes and the isotropic intensities.     

Inelastic cross-sections and natural lifetimes for the 62D3/2, 5/2 and 82S1/2 states of Rb

The results of an experimental study of population dynamics following excitation of [0pt] and [0pt] states of rubidium are reported. Excitation transfer and quenching cross-sections in collisions with ground state rubidium atoms, and natural lifetimes have been measured. The experiment was performed in a vapour cell, using pulsed two-photon excitation and photon counting detection. The analysis of time dependent signals was based on a rate equation model in which transitions induced by thermal radiation have been accounted for. The measurements yielded following results: (1) [0pt] state J-mixing cross-section: [0pt] ; (2) cross-sections for [0pt] excitation transfer process: [0pt] ; (3) quenching cross-sections: [0pt] , [0pt] , [0pt] ; [0pt](4) radiative lifetimes: [0pt] ns, [0pt] ns, [0pt] ns. Received 1st December 1998 and Received in final form 17 May 1999     

Mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice within the effective-field theory

An effective-field theory with correlations is developed for a mixed spin-1 and spin-3/2 Ising system with two alternative layers of a honeycomb lattice. Spin-1 atoms and spin-3/2 atoms are distributed in alternative layers of a honeycomb lattice. We consider that the nearest-neighbor spins of each layer are coupled ferromagnetically and the interaction between the vertically aligned spins and adjacent spins are coupled either ferromagnetically or antiferromagnetically depending on the sign of the bilinear exchange interactions. We investigate the temperature dependence of the total magnetization to find the compensation points and to determine the type of compensation behavior. We present the phase diagrams in different planes for h=0, and the phase diagrams contain the paramagnetic, nonmagnetic and ferrimagnetic phases. The system also presents a tricritical behavior besides multicritical point (A), isolated critical point (C) and double critical end point (B) depending on the interaction parameters.     

The parallel magnetic susceptibility and specific heat of the antiferromagnetic Ising linear-chain system with spin S = 2, 52, and 3

The parallel magnetic susceptibility and specific heat of the antiferromagnetic Ising linear-chain system with spin S = 2, $\text{5}\text{2}$, and 3 are calculated using the matrix approach. The results for spin $\text{S =}\text{1}\text{2}$, 1, $\text{3}\text{2}$, and 2 are checked against known results for these cases.     

Spectroscopic properties of Fe ions at tetragonal sites—Crystal field effects and microscopic modeling of spin Hamiltonian parameters for Fe (S=2) ions in K2FeF4 and K2ZnF4

Magnetic and spectroscopic properties of the planar antiferromagnet K₂FeF₄ are determined by the Fe²⁺ ions at tetragonal sites. The two-dimensional easy-plane anisotropy exhibited by K₂FeF₄ is due to the zero field splitting (ZFS) terms arising from the orbital singlet ground state of Fe²⁺ ions with the spin S=2. To provide insight into the single-ion magnetic anisotropy of K₂FeF₄, the crystal field theory and the microscopic spin Hamiltonian (MSH) approach based on the tensor method is adopted. Survey of available experimental data on the crystal field energy levels and free-ion parameters for Fe²⁺ ions in K₂FeF₄ and related compounds is carried out to provide input for microscopic modeling of the ZFS parameters and the Zeeman electronic ones. The ZFS parameters are expressed in the extended Stevens notation and include contributions up to the fourth-order using as perturbation the spin-orbit and electronic spin-spin couplings within the tetragonal crystal field states of the ground ⁵D multiplet. Modeling of the ZFS parameters and the Zeeman electronic ones is carried out. Variation of these parameters is studied taking into account reasonable ranges of the microscopic ones, i.e. the spin-orbit and spin-spin coupling constants, and the energy level splittings, suitable for Fe²⁺ ions in K₂FeF₄ and Fe²⁺:K₂ZnF₄. Conversions between the ZFS parameters in the extended Stevens notation and the conventional ones are considered to enable comparison with the data of others. Comparative analysis of the MSH formulas derived earlier and our more complete ones indicates the importance of terms omitted earlier as well as the fourth-order ZFS parameters and the spin-spin coupling related contributions. The results may be useful also for Fe²⁺ ions at axial symmetry sites in related systems, i.e. Fe:K₂MnF₄, Rb₂Co_1−xFe_xF₄, Fe²⁺:Rb₂CrCl₄, and Fe²⁺:Rb₂ZnCl₄.