Application of the SCVT Orientation Grid to the Simulation of CW EPR Powder Spectra

The orientation grid obtained using the spherical centroidal Voronoi tessellation (SCVT) method is assessed for the simulation of continuous-wave electron paramagnetic resonance (CW EPR) powder spectra. The SCVT spherical code presents less distorted Voronoi cells associated to the points of the grid compared to the regular Igloo, SOPHE and EasySpin grids and similar distortions of the cells to the irregular Repulsion grid. The degree of distribution of the SCVT cells’ areas is smaller than for SOPHE, but higher than for the Igloo and Repulsion grids. All compared spherical codes have nearly the same electrostatic potential energy. Simulated CW EPR powder spectra for rhombic systems of spin S = 1/2 are similar when using the energy minimization SCVT and Repulsion spherical codes and show less intense ripples than the spectra calculated with the SOPHE and Igloo grids, but more intense than those obtained using the EasySpin grid. The classical projection method and a new modified form involving the spectral intensities at the orientations of the grid have been tested for the attenuation of the simulation noise, for grids of relatively reduced size.     

Shape of the ferromagnetic resonance absorption band of textured powder samples of maghemite

The shape of the ferromagnetic resonance absorption band of powder microcrystalline ferrite γ-Fe₂O₃ has been studied. Samples in the form of a ferromagnetic fluid have been subjected to preliminary particle orientation and frozen in a magnetic field. The shape of the absorption bands has been computer processed with allowance for the anisotropy of the shape of particles and their spatial cubic anisotropy, as well as for the contribution from nondispersed fraction of the bulk of the powder. Satisfactory agreement with the experiment has been obtained for several orientations of the measuring magnetic field with respect to the preliminary orientation.     

A numerical scheme for the integration of the Vlasov–Poisson system of equations, in the magnetized case

We present a numerical algorithm for the solution of the Vlasov–Poisson system of equations, in the magnetized case. The numerical integration is performed using the well-known “splitting” method in the electrostatic approximation, coupled with a finite difference upwind scheme; finally the algorithm provides second order accuracy in space and time. The cylindrical geometry is used in the velocity space, in order to describe the rotation of the particles around the direction of the external uniform magnetic field.Using polar coordinates, the integration of the Vlasov equation is very simplified in the velocity space with respect to the cartesian geometry, because the rotation in the velocity cartesian space corresponds to a translation along the azimuthal angle in the cylindrical reference frame. The scheme is intrinsically symplectic and significatively simpler to implement, with respect to a cartesian one. The numerical integration is shown in detail and several conservation tests are presented, in order to control the numerical accuracy of the code and the time evolution of the entropy, strictly related to the filamentation problem for a kinetic model, is discussed.     

PISEMA powder patterns and PISA wheels

Resonance patterns observed in 2D PISEMA (polarization inversion spin exchange at magic angle) spectra from a transmembrane alpha-helix have been demonstrated to yield structural details of the protein. This paper presents a mathematical discussion of the PISEMA powder spectrum as the image in the frequency plane of a quadratic function from the sphere of unit vectors. The simplicity of this function allows easy calculation of the powder spectrum. Based on this analysis of powder patterns, four degeneracies are discussed which arise in determining possible orientations associated with PISA spectra. This paper also gives parametric equations for PISA wheels, which are specific patterns observed in PISEMA spectra of oriented peptides. These wheels are useful both in assigning the resonances and in determining the orientation of the helix with respect to the magnetic field. The union of these PISA wheels gives the entire powder spectrum.     

Influencing the satellite transitions of half-integer quadrupolar nuclei for the enhancement of magic angle spinning spectra

Double frequency sweeps can induce spin transitions in a set of satellites of a half-integer quadrupolar nucleus by simultaneously passing through resonance for a satellite pair. It is shown that by transferring population from the outer spin levels to the inner |1/2 and |−1/2 levels an increased intensity for central transition spectra is obtained. Although Magic Angle Spinning in principle interferes with this process, and the adiabaticity of the passages is different for every crystallite in a powder, enhanced spectra with undistorted line shapes are obtained for I=3/2 (²³Na) and 5/2 (²⁷Al) spins experiencing quadrupolar interactions with ω_Q in the range 0.1–3 MHz. Even at spinning speeds up to 30 kHz significant enhancements are obtained. An analysis of the combined effects of double frequency sweeps (DFS) and MAS indeed shows strongly different effects for different crystallites in powder ranging from no gain at all to the theoretical maximum gain of 2I. As the effects are randomly distributed over all orientations on a sphere this is averaged over the whole line shape. Therefore, undistorted powder patterns are obtained enhanced by the average gain over the individual crystallites. Saturation of the satellite transitions, which can only be achieved if spin–spin relaxation is sufficiently strong, leads to identical results. Optimization of the sweeps should be toward an optimal effect on the population transfer to the central levels and chosen short with respect to spin–lattice relaxation times.     

A rigorous evaluation of spin-Hamiltonian parameters and linewidth from a polycrystalline EPR spectrum.

Details are given of a procedure to evaluate the spin-Hamiltonian (SH) parameters and the linewidth from a polycrystalline EPR spectrum by using a least-squares fitting (LSF) technique in conjunction with numerical diagonalization of the SH matrix. The required resonance line positions are computed rather quickly using a homotopy technique, in which the position at an external magnetic field (B) orientation (theta, phi) is used as the initial value in a LSF procedure to estimate the position at an infinitesimally close B-orientation, (theta + deltatheta, phi + deltaphi). The resonance line positions are calculated successively in this procedure for all orientations of B over a grid of (theta, phi) values for the unit sphere. The eigenvectors of the SH matrix are used to calculate the intensities of the EPR lines exactly for each orientation of B. Details are given of how to compute rigorously the first and second derivatives of the chi(2)-function with respect to the SH parameters and the linewidth using the eigenvalues and eigenvectors of the spin-Hamiltonian matrix for a polycrystalline spectrum required in the LSF procedure. It is explained how this technique is generalized to include two or more magnetically inequivalent paramagnetic species, as well as how it is used for the simulation of other EPR-related spectra. The procedure is illustrated by evaluation of the Mn(2+) SH parameters and Lorentzian linewidth from the 249.9-GHz EPR spectrum of Mn(gamma-picoline)(4)I(2).     

Angular dependence of the photothermally modulated magnetic resonance in Gd thin films

In this paper we use electron spin resonance and photothermally modulated magnetic resonance techniques to investigate gadolinium thin films as a function of the orientation of the film surface with respect to the external magnetic field and of the temperature, around the magnetic phase transition temperature. We observe that, in the ferromagnetic phase, the resonance line is shifted up to higher external magnetic fields when the angle between the film surface and the field increases, revealing the magnetic anisotropy of the sample. At the same time, when the temperature is augmented to values higher than the phase transition temperature, the external field of the resonance collapses back to the expected value in the paramagnetic phase for all orientations. We also demonstrated that, even for the perpendicular orientation (magnetic field perpendicular to the sample surface), the photothermally modulated magnetic resonance signal is maximized near the magnetic phase transition temperature. Furthermore, in the ferromagnetic phase the photothermally modulated magnetic resonance intensity is very sensitive to the orientation, showing a significant enhancement in the perpendicular direction.     

Spatial confinement of ferromagnetic resonances in honeycomb antidot lattices

We report on a theoretical investigation of the magnetic static and dynamic properties of a thin ferromagnetic film with honeycomb lattice of circular antidots using micromagnetic simulations and analytical calculations. The theoretical model is based on the Landau–Lifshitz equations and directly accounts for the effects of the magnetic state nonuniformity. A direct calculation of local dynamic susceptibility tensor yields that the resonance spectra consist of four different quasi-uniform modes of the magnetization precession related to the confinement of magnetic domains by the hole mesh. Three of four resonant modes follow a two-fold variation with respect to the in-plane orientation of the applied magnetic field. The easy axes of these modes are mutually rotated by 60° and combine to yield the apparent six-fold configurational anisotropy. Additionally, a mode with intrinsic six-fold symmetry behavior exists, as well. Micromagnetic calculations of the local dynamic susceptibility tensor allow identifying the magnetic unit cell areas/domains responsible for each resonance mode.     

Efficient orientational averaging by the extension of Lebedev grids via regularized octahedral symmetry expansion

Gaussian spherical quadrature methods in the guise of the Lebedev sampling grids are highly efficient for some orientational ("powder") averaging problems in solid state NMR. However, their applicability is currently restricted, as the sets of orientations are derived analytically and because they are not well adapted to simulate the broad peakshapes encountered, for example, in the NMR on static powders or on half-integer quadrupolar spins subject to second order quadrupolar interactions under magic-angle spinning conditions. We remedy these problems by (i) introducing the recursive procedure regularized octahedral symmetry expansion (ROSE), to which any existing Lebedev set may be subjected. Each recursive step gives a 9-fold enlarged set of orientations. (ii) We demonstrate that ROSE-expanded grids, in conjunction with spectral interpolation, is well suited for calculating broad peakshapes. These advances combine into the apparently most efficient general-purpose two-angle orientational averaging technique proposed to date for solid state NMR applications.     

Local monitoring of proton spin diffusion in static and rotating samples via spy detection

A method is described for investigating local proton “spin diffusion” by means of a ¹³C spin probe. The procedure does not require spectral resolution of proton resonance lines and can be applied in the laboratory frame of reference as well as in the rotating frame. Experimental results are presented for a static single crystal of ferrocene and for a powder sample under magic-angle spinning. The spin-diffusion rate constant is found to be proportional to the spinning speed in the range from 1 to 8 kHz.     

Magnitudes and orientations of the 15N chemical shift tensor of [1-15N]-2'-deoxyguanosine determined on a polycrystalline sample by two-dimensional solid-state NMR spectroscopy.

The magnitudes and orientations of the 15N chemical shift tensor of [1-15N]-2'-deoxyguanosine were determined from a polycrystalline sample using the two-dimensional PISEMA experiment. The magnitudes of the principal values of the 15N chemical shift tensor of the N1 nitrogen of [1-15N]-2'-deoxyguanosine were found to be sigma11 = 54 ppm, sigma22 = 148 ppm, and sigma33 = 201 ppm with respect to (15NH4)2SO4 in aqueous solution. Comparisons of experimental and simulated two-dimensional powder pattern spectra show that sigma33N is approximately collinear with the N-H bond. The tensor orientation of sigma33N for N1 of [1-15N]-2'-deoxyguanosine is similar to the values obtained for the side chain residues of 15Nepsilon1-tryptophan and 15Npi-histidine even though the magnitudes differ significantly.     

Vortex dynamics in single crystal Hg-1201

Anisotropic superconducting materials often show an enhanced pinning along their crystallographic ab-planes. To obtain information about such a behavior of the high-T_c system Hg-1201 (HgBa₂CuO₄) magnetic investigations on a single crystal are performed for the two field orientations, parallel to the c-axis and parallel to the ab-planes. The dependence of the ac magnetization on temperature, magnetic field and frequency is determined. Compared to former results on powder samples of this system no indication of a second peak in the imaginary part of the susceptibility χ′′ is found. It seems to be shifted to higher temperatures overlapping now with the first peak. The corresponding irreversibility lines for both orientations, parallel to c and parallel to ab, are determined and discussed within the framework of a “diffusion” model.     

The orientational dependence of paramagnetic mössbauer spectra on a weak magnetic field

Mössbauer experiments were performed on a single crystal of metmyoglobin at 4.2 K. A. small magnetic field was applied in different orientations. The results show the sensitivity of the Mössbauer spectra to the direction of the field. It was possible to detect the heme normal with respect to the orientation of the myoglobin crystal.     

Numerical solutions for single passage NMR on nuclei experiencing small electric quadrupole interactions

The adiabatic rapid-passage NMR equations are numerically solved for a small additional quadrupole interaction. The full range of the ratio of rf interaction strengths to quadrupole interactions strengths is considered for any electric field gradient orientation. The results forI=1 are particularly easy to describe and are used to predict the single-passage results for different orientations of the electric field gradient with respect to the static magnetic field.     

Temperature dependence of superparamagnetic resonance of iron oxide nanoparticles

Nanoparticles of maghemite (γ-Fe₂O₃) are formed in a sol–gel silicate glass with a molar ratio Fe/Si of 2% by a treatment at 1000°C for 6 h. Electron paramagnetic resonance spectrum at 300 K shows a relatively narrow sharp line at g_eff≈2. As the temperature lowers to 5 K, the apparent resonance field decreases and the linewidth considerably increases. We develop a theoretical formalism based on a distribution of diameters or volumes of the nanoparticles following a lognormal. The nanoparticles are considered as single magnetic domains with random orientations of magnetic moments and thermal fluctuations of anisotropic axes. The individual line shape function is derived from the damped precession equation of Landau–Lifshitz. An appropriate linewidth expression is put forward, which account for the averaging of the fluctuations of orientations of the magnetic moments with respect to the magnetic field and to the magnetic anisotropy axes. A single set of parameters provides good fits to the spectra recorded at the different temperatures. The low-temperature blocking of the nanoparticle magnetic moments has been clearly evidenced in the resonance absorption intensity and the blocking temperature of the assembly of nanoparticles (averaged over the distribution in the nanoparticle volume) has been evaluated as 90 K.     

High-resolution NMR of static samples by rotation of the magnetic field

Mechanical rotation of a sample at 54.7 degrees with respect to the static magnetic field, so-called magic-angle spinning (MAS), is currently a routine procedure in nuclear magnetic resonance (NMR). The technique enhances the spectral resolution by averaging away anisotropic spin interactions thereby producing isotropic-like spectra with resolved chemical shifts and scalar couplings. It should be possible to induce similar effects in a static sample if the direction of the magnetic field is varied, e.g., magic-angle rotation of the B0 field (B0-MAS). Here, this principle is experimentally demonstrated in a static sample of solid hyperpolarized xenon at approximately 3.4 mT. By extension to moderately high fields, it is possible to foresee interesting applications in situations where physical manipulation of the sample is inconvenient or impossible. Such situations are expected to arise in many cases from materials to biomedicine and are particularly relevant to the novel approach of ex situ NMR spectroscopy and imaging.     

A15N-1H dipolar CSA solid-state NMR study of polymorphous polyglycine (-CO-CD2-15NH-)n

The solid-state¹H MAS (magic-angle spinning),²H static,¹⁵N CP (cross polarization)-MAS and¹⁵N-¹H dipolar CSA (chemical shielding anisotropy) NMR (nuclear magnetic resonance) spectra of two different modifications of C_α-deuterated^l5N-polyglycine, namely PG I and PG II (-CO-CD₂-^l5NH-)_n are measured. The data from these spectra are compared to previous NMR, infrared, Raman and inelastic neutron scattering work. The deuteration of C_α eliminates the largest intramolecular¹H-¹H dipolar coupling. The effect of the remaining (N)H-(N)H interaction (～5 kHz) is not negligible compared to the¹⁵N-¹H coupling (about 10 kHz). Its effect on the dipolar CSA spectra, described as a two-spin system, is analyzed analytically and numerically and it is shown that those parts of the powder spectrum, which correspond to orientations with a strong dipolar¹⁵N-¹H interaction, can be described as an effective two-spin system, permitting the measurement of the strength of the¹⁵N-¹H dipolar interaction and the orientation of the dipolar vector with respect to the¹⁵N CSA frame. While in the PG II system the¹⁵N CSA tensor is collinear with the amide plane, in the PG I system the CSA tensor is tilted ca. 16° with respect to the (δ₁₁δ₂₂) CSA plane.     

The effect of orientation on quantification of muscle creatine by 1H MR spectroscopy

Creatine is a central energy metabolite whose N-CH3 group can be detected with 1H MR spectroscopy (1H MRS) with relatively high sensitivity. Prior studies suggest that muscle fiber orientation can influence the appearance of other resonances attributed to total creatine (CR). Our purpose was to determine whether muscle fiber orientation affects muscle CR concentration quantification by 1H MRS with the commonly used N-CH3 resonance at 3.0 ppm. Skeletal muscle CR was quantified with water-referenced 1H MRS in normal subjects with different forearm muscle orientations relative to the static magnetic field at 1.5T. There were no significant differences in mean total [CR] in two different series of experiments separately including two orthogonal orientations and four orientations (0 degrees, 30 degrees, 60 degrees, 90 degrees) of the forearm relative to the static field using either short (TE = 15 ms) or long (TE = 100 ms) echo times for voxels containing or centered on the same tissues. Subtle differences in CR line-width and T2 correction factors were observed with orientation. These observations are consistent with the primary hypothesis that careful water-referenced [CR] quantification, accounting for T2 effects and using the N-CH3 peak at 3.0ppm, is not affected by muscle orientation.     

Magnitudes and Orientations of the N Chemical Shift Tensor of [1-N]-2′-Deoxyguanosine Determined on a Polycrystalline Sample by Two-Dimensional Solid-State NMR Spectroscopy

The magnitudes and orientations of the ¹⁵N chemical shift tensor of [1-¹⁵N]-2′-deoxyguanosine were determined from a polycrystalline sample using the two-dimensional PISEMA experiment. The magnitudes of the principal values of the ¹⁵N chemical shift tensor of the N1 nitrogen of [1-¹⁵N]-2′-deoxyguanosine were found to be ς₁₁ = 54 ppm, ς₂₂ = 148 ppm, and ς₃₃ = 201 ppm with respect to (¹⁵NH₄)₂SO₄ in aqueous solution. Comparisons of experimental and simulated two-dimensional powder pattern spectra show that ς_33N is approximately collinear with the N–H bond. The tensor orientation of ς_33N for N1 of [1-¹⁵N]-2′-deoxyguanosine is similar to the values obtained for the side chain residues of ¹⁵N_ε1-tryptophan and ¹⁵N_π-histidine even though the magnitudes differ significantly.