Pulsed field gradients in simulations of one- and two-dimensional NMR spectra

A method for the inclusion of the effects of z-axis pulsed field gradients in computer simulations of an arbitrary pulsed NMR experiment with spin (1/2) nuclei is described. Recognizing that the phase acquired by a coherence following the application of a z-axis pulsed field gradient bears a fixed relation to its order and the spatial position of the spins in the sample tube, the sample is regarded as a collection of volume elements, each phase-encoded by a characteristic, spatially dependent precession frequency. The evolution of the sample's density matrix is thus obtained by computing the evolution of the density matrix for each volume element. Following the last gradient pulse, these density matrices are combined to form a composite density matrix which evolves through the rest of the experiment to yield the observable signal. This approach is implemented in a program which includes capabilities for rigorous inclusion of spin relaxation by dipole-dipole, chemical shift anisotropy, and random field mechanisms, plus the effects of arbitrary RF fields. Mathematical procedures for accelerating these calculations are described. The approach is illustrated by simulations of representative one- and two-dimensional NMR experiments.     

On propagation failure in one- and two-dimensional excitable media

We present a nonperturbative technique to study pulse dynamics in excitable media. The method is used to study propagation failure in one-dimensional and two-dimensional excitable media. In one-dimensional media we describe the behavior of pulses and wave trains near the saddle node bifurcation, where propagation fails. The generalization of our method to two dimensions captures the point where a broken front (or finger) starts to retract. We obtain approximate expressions for the pulse shape, pulse velocity, and scaling behavior. The results are compared with numerical simulations and show good agreement.     

On the structure and stability of two-dimensional dynamic solitons in ferromagnets

Dynamic solitons in uniaxial and orthorhombic magnets are investigated. It is shown that centrosymmetric solitons can be unstable with respect to elliptic distortions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 12, 899–903 (25 June 1997)     

Basics of NMR line shape in quasicrystals

The measurement and analysis of broad nuclear magnetic resonance (NMR) spectra of quasicrystals require experimental methods and theoretical interpretations different from NMR investigations of regular periodic crystals. Frequency- and field-sweep methods for recording quasicrystalline NMR spectra are described and compared with the measurement of²⁷Al NMR spectra of icosahedral AlPdMn and decagonal AlNiCo quasicrystals. The nuclear spin interactions that determine the NMR line shape are the same for both types of the above Al-based quasicrystals, where the electric quadrupolar interaction with the broad distribution of its electric field gradient parameters predominantly determines the shape of the broad satellite “background” intensity. The essential observations are an almost isotropic²⁷Al NMR spectrum of the icosahedral quasicrystals and a strong angular dependence of the spectrum of decagonal quasicrystals.     

Excitations in randomly diluted two-dimensional ferromagnets

The dynamics of a randomly diluted Heisenberg ferromagnet on a two-dimensional square lattice is calculated using a CPA procedure introduced by Theumann and Tahir-Kheli. The density of states and frequency-wave-vector-dependent response functions at various symmetry points of the Brillouin zone are presented for several magnetic concentrations. Our results for the density of states are compared with those obtained from computer-experiment calculations of Huber and are found to be in good agreement with them. The spin-wave stiffness coefficient is calculated, and comparison is made with results on two-dimensional resistor networks given by Watson et al.     

Bose-Einstein condensation in one- and two-dimensional gases

We show that the one- and two-dimensional ideal Bose gases undergo a phase transition if the temperature is lowered at constant pressure. At the pressure-dependent transition temperature T_c (P) and in their thermodynamic limit the specific heat at constant pressure c_p and the particle densityn diverge, the entropyS and specific heat at constant volumec _v fall off sharply but continuously to zero, and the fraction of particles in the ground state N₀/N jumps discontinuously from zero to one. This Bose-Einstein condensation provides a remarkable example of a transition which has most of the properties of a second-order phase transition, except that the order parameter is discontinuous. The nature of the condensed state is described in the large but finiteN regime, and the width of the transition region is estimated. The effects of interactions in real one- and two-dimensional Bose systems and recent experiments on submonolayer helium films are discussed briefly.     

NMR line shape in one-dimensional magnet in the finite temperature region

The NMR line width is calculated for the one-dimensional ferro- and antiferro-magnets in the finite temperature region. The NMR line shape turns out to have a structure with double peaks which is quite different from the Lorentzian and the Gaussian type.     

On the spin-flip line shape in CdS

The longitudinal relaxation time of Spin-Flip Raman scattering (SFRS) in n-CdS is explained in terms of the Elliott mechanism. The energy dispersion of spectroscopic factors of the conduction electrons and the Hasegawa model yield a transversal relaxation time different from the longitudinal relaxation time, but do not reproduce the experimental value. The diffusion coefficient, responsible for the SFRS line width behavior with temperature in n-CdS, is explained based upon hopping effects in the low temperature region.     

On the line shape of EELS-spectra

The influence of anharmonic coupling between vibrations of an adsorbate parallel and perpendicular to the surface on electron energy loss spectra is investigated. Although in most cases vibrations parallel to the surface are not directly observable in EELS, this anharmonic coupling can be the origin of satellites in the loss spectra.     

Dynamics of topological solitons in two-dimensional ferromagnets

Dynamical topological solitons are studied in classical two-dimensional Heisenberg easy-axis ferromagnets. The properties of such solitons are treated both analytically in the continuum limit and numerically by spin dynamics simulations of the discrete system. Excitation of internal mode causes orbital motion. This is confirmed by simulations.     

Boundary conditions and cluster property in two-dimensional Ising ferromagnets

Using the Sherman theorem on paths, the cluster property, and the second GKS inequality, we obtain some results in favor of the nonexistence of non-translation-invariant equilibrium states for twodimensional Ising models with ferromagnetic short-range interactions in the low-temperature region. With a constraint on the interaction strength at the boundary, we prove that for the two-dimensional Ising model, all boundary conditions yield the unique translation-invariant correlation functions _X²,+, for |X| even.Supported by the Fonds National Suisse de la Recherche Scientifique.     

Measurement of longitudinal relaxation times in crowded 1H NMR spectra using one- and two-dimensional maximum quantum (MAXY) NMR spectroscopy

Methods for measuring longitudinal relaxation times of protons in heavily overlapped ¹H NMR spectra are introduced and exemplified using a solution of cholesteryl acetate. The methods are based on 1-dimensional and 2-dimensional maximum quantum NMR spectroscopy (MAXY), which makes possible the selective detection of CH, CH₂ and CH₃ ¹H NMR resonances. A modification of the BIRD pulse sequence to achieve selective inversion of protons bonded to either ¹²C or ¹³C is given. The approach should find application in studies of molecular dynamics where isotopic enrichment is not possible and the level of available sample dictates the use of ¹H NMR spectroscopy.     

NMR line shape in anisotropic superconductors in a tilted magnetic field

NMR line shape has been constructed for anisotropic type-II superconductors in tilted magnetic fields, with inclusion of vortex-lattice magnetic-field nonuniformities and of the skin effect near the superconductor surface. The NMR line shape parameters are shown to change considerably when the external magnetic field changes direction. This makes it possible to obtain more detailed information about the characteristics of a superconductor, in particular, its anisotropy parameter. Fiz. Tverd. Tela (St. Petersburg) 40, 993–997 (June 1998)     

Spin-wave interaction in two-dimensional ferromagnets with dipolar forces

We discuss the spin-wave interaction in two-dimensional (2D) Heisenberg ferromagnet (FM) with dipolar forces at T_C?T?0 using 1/S expansion. A comprehensive analysis is carried out of the first 1/S corrections to the spin-wave spectrum. In particular, we obtain that the spin-wave interaction leads to the gap in the spectrum ε_k renormalizing greatly the bare gapless spectrum at small momenta k. Expressions for the spin-wave damping Γ_k are derived self-consistently and it is concluded that magnons are well-defined quasi-particles in both quantum and classical 2D FMs at small T. We observe thermal enhancement of both Γ_k and Γ_k/ε_k at small momenta. In particular, a peak appears in Γ_k and Γ_k/ε_k at small k and at any given direction of k. If S∼1 the height of the peak in Γ_k/ε_k is not larger than a value proportional to T/D?1, where D is the spin-wave stiffness. In the case of large spins S?1 the peak in Γ_k/ε_k cannot be greater than that of the classical 2D FM found at k=0 whose height is small only numerically: Γ₀/ε₀≈0.16 for the simple square lattice.     

Resonance absorption of gamma-quanta in one- and two-dimensional crystals

The resonance absorption of gamma-quanta in undisturbed one- and two-dimensional crystals is studied, the form of the resonance lines is determined and the question of the possibility of the existence of the Mössbauer effect in such models is studied. It is found that for one-dimensional crystals the Mössbauer effect is zero with the exception of the case of the perpendicular incidence of gamma-rays on the linear chain and for two-dimensional crystals this effect would be possible in addition only at absolute zero temperature.The authors would like to thank Dr. . Muziká for suggesting the work and for many discussions.     

Influence of magnetic dipolar interaction on one- and two-magnon scattering of light in ferromagnets

It is shown that the presence of magnetic dipolar interaction in a ferromagnetic medium changes the polarization selection rules of light scattered by magnons. In addition it provides a new mechanism for two-magnon scattering.