Self-diffusion measurements by a constant-relaxation method in strongly inhomogeneous magnetic fields

The simple pulse sequence thetax-tau1-2thetay-tau1+tau2-2thetay-tau2-Hahn echo used to measure the self-diffusion coefficient D under constant-relaxation condition, i.e., for tau1+tau2=const. was investigated in the presence of strongly inhomogeneous static as well as radiofrequency magnetic fields. The encoding of the Hahn-echo amplitude by the pulse flip angle and diffusion was evaluated by taking into account the spatial distribution of the off-resonance field, the strength and orientation of the local field gradients, and the pulse flip angles by a computer simulation program. As input files, this program uses maps of static and radiofrequency fields, and the D coefficient can be evaluated from the time dependence of the Hahn-echo amplitude. The method was applied to a mobile one-sided NMR sensor, NMR-MOUSE with a bar magnet by measuring D for a series of liquids with different viscosities. The method was shown to be particularly useful for measuring D of solvents in elastomers without the need for measurements of the transverse relaxation rates. The self-diffusion coefficient of toluene in a series of crosslinked natural rubber samples was measured and correlated with the crosslink density. Finally, the method was applied to measure the diffusion anisotropy of free water in bovine Achilles tendon.     

Hole-burning NMR in strongly inhomogeneous fields

Different pulse sequences for frequency-selective NMR in the highly inhomogeneous fields of single-sided NMR are explored. A modified Hahn-echo is used to burn a hole in the spectrum of the detected echo. The hole diminishes following molecular dynamics on the scale of the echo time. Preliminary experiments were performed on pure water and natural rubber with the NMR-MOUSE. The results demonstrate the feasibility of hole burning to study slow molecular dynamics by mobile NMR in strongly inhomogeneous magnetic fields.     

The NMR-MOUSE: quality control of elastomers.

New applications of the NMR-MOUSE (mobile universal surface explorer) to non-destructive quality control of elastomers are reported. One example concern the thermal aging of fast clutches which was probed by measurements of 1H transverse relaxation time. Novel methodological developments show that 1H double-quantum filtered NMR signals can be generated in the inhomogeneous fields of the NMR-MOUSE for characterization of residual dipolar couplings. This technique was applied to characterize reference natural rubber samples with different crosslink density and carbon black and silica fillers.     

NMR of multipolar spin states excitated in strongly inhomogeneous magnetic fields

The possibility of exciting and filtering various multipolar spin states in proton NMR like dipolar encoded longitudinal magnetization (LM), double-quantum (DQ) coherences, and dipolar order (DO) in strongly inhomogeneous static and radio-frequency magnetic fields is investigated. For this purpose pulse sequences which label and manipulate the multipolar spin states in a specific way were implemented on the NMR-MOUSE (mobile universal surface explorer). The performance of the pulse sequences was also tested in homogeneous fields on a solid-state high-field NMR spectrometer. The theoretical justification of these procedures was shown for a rigid two-spin 1/2 system coupled by dipolar interactions. Dipolar encoded longitudinal magnetization decay curves, double-quantum and dipolar-order buildup curves, as well as double-quantum decay curves were recorded with the NMR-MOUSE for natural rubber samples with different crosslink density. The possibility of using these multipolar spin states for investigations of strained elastomers by NMR-MOUSE is also shown. These curves give access to quantitative values of the ratio of the total residual dipolar couplings of the protons in the series of samples which are in good agreement with those measured in homogeneous fields.     

Multispin moments edited by multiple-quantum NMR: application to elastomers

The spin system response to the five-pulse sequence used for measurements of double-quantum and triple-quantum buildup curves is evaluated in the initial excitation/reconversion regime. The multispin dipolar network that is present also in many soft solids like elastomers was considered. It is proved rigorously that the relevant quantity for analysis of double-quantum build-up curves in the initial regime is the second van Vleck moment. The higher-order moments edited by double-quantum as well as higher-order coherences in the multiple-quantum build-up experiments are different from van Vleck moments. These results can be applied to compare (1)H residual moments edited by double-quantum and triple-quantum experiments with those measured by other NMR methods. The sensitivity of multiple-quantum coherences to the changes in the values of residual dipolar couplings for cross-linked natural rubber under uniaxial elongation is also discussed. Under such conditions (1)H second van Vleck moments were measured for different elongation ratios of a cross-linked natural rubber. Moreover, (1)H triple-quantum edited moments were also measured for the same sample under uniaxial compression. The dependence of the second van Vleck moment and the time of the maximum of the double-quantum buildup curve on the cross-link density of natural rubber measured at low magnetic field was also investigated.     

Distributions of transverse relaxation times for soft-solids measured in strongly inhomogeneous magnetic fields

The single-sided NMR-MOUSE sensor that operates in highly inhomogeneous magnetic fields is used to record a CPMG ¹H transverse relaxation decay by CPMG echo trains for a series of cross-linked natural rubber samples. Effective transverse relaxation rates 1/T_2,short and 1/T_2,long were determined by a bi-exponential fit. A linear dependence of transverse relaxation rates on cross-link density is observed for medium to large values of cross-link density. As an alternative to multi-exponential fits the possibility to analyze the dynamics of soft polymer network in terms of multi-exponential decays via the inverse Laplace transformation was studied. The transient regime and the effect of the T₁/T₂ ratio in inhomogeneous static and radiofrequency magnetic fields on the CPMG decays were studied numerically using a dedicated C++ program to simulate the temporal and spatial dependence of the CPMG response. A correction factor T₂/T_2,eff is derived as a function of the T₁/T₂ ratio from numerical simulations and compared with earlier results from two different well logging devices. High-resolution T₁–T₂ correlations maps are obtained by two-dimensional Laplace inversion of CPMG detected saturation recovery curves. The T₁–T₂ experimental correlations maps were corrected for the T₁/T₂ effect using the derived T₂/T_2,eff correction factor.     

Selective NMR excitation in strongly inhomogeneous magnetic fields

The NMR-MOUSE is a unilateral and mobile NMR sensor which operates with highly inhomogeneous magnetic fields. To produce a mobile NMR unit, RF excitation is sought, which can be produced with the most simple equipment, in particular nonlinear, low-power amplifiers, and to observe a free induction decay in strongly inhomogeneous fields, the excitation needs to be selective. The possibility to produce selective excitation by sequences of hard low-power radiofrequency pulses in the strongly inhomogeneous magnetic fields of the NMR-MOUSE is explored. The use of the DANTE sequence for selection of magnetization from parts of the sensitive volume was investigated for longitudinal and transverse magnetization by computer simulations and experiments. The spectra of the recorded FIDs and echo signals are in good agreement with those simulated for the excitation, which verifies the concept of the DANTE excitation. The results obtained are an important step towards a low-power operation of the NMR-MOUSE to improve its mobility.     

Double-quantum-filtered NMR signals in inhomogeneous magnetic fields

The possibility of exciting and detecting proton NMR double-quantum coherences in inhomogeneous static and radiofrequency magnetic fields was investigated. For this purpose specialized pulse sequences which partially refocus the strongly inhomogeneous evolution of the spin system and generate double-quantum buildup and decay curves were implemented on the NMR MOUSE (mobile universal surface explorer). The theoretical justification of the method was developed for the simple two-spin-1/2 system. The performances of the same pulse sequences were also tested on a solid-state high-field NMR spectrometer. It was shown that DQ decay curves have a better signal-to-noise ratio in the initial time regime than DQ buildup curves. The double-quantum buildup and decay curves were recorded for a series of cross-linked natural rubber samples. These curves give access to quantitative values of the ratio of proton total residual dipolar couplings which are in good agreement with those measured in homogeneous fields. A linear dependence of these ratios on the sulfur-accelerator content was found.     

Manifestation of basal-plane anisotropy and mechanical boundary conditions in magnetic birefringence of sound in hematite

The angular dependence of the magnetic birefringence of sound in hematite is experimentally investigated as a function of the direction of a magnetic field applied in the basal plane of the hematite crystal. It is found that, at room temperature, the curve of magnetoacoustic oscillations in the magnetic field, i.e., the oscillatory dependence of the amplitude of an acoustic wave transmitted through the crystal on the magnetic field strength, is characterized by hexagonal and uniaxial anisotropy. It is shown that the hexagonal anisotropy is governed by the basal-plane anisotropy of higher orders. The appearance of the uniaxial magnetic anisotropy in the basal plane of the crystal is explained by the mechanical stresses arising in the sample when piezoelectric transducers are glued to the sample ends. This assumption is confirmed by the observed change in the direction of the uniaxial anisotropy axis under variations in the boundary conditions.     

NMR relaxation dispersion of vulcanized natural rubber

The dependence of the 1H spin-lattice relaxation time on the magnetic field strength has been determined for linear and cross-linked polyisoprene for Larmor frequencies between 5 kHz and 20 MHz. Universal power-law relations are found for all temperatures and cross-link densities under investigation and are compared to published results of rotating-frame experiments on similar natural rubber samples. The shape of the individual dispersion functions can be superposed into a master curve using appropriate shift factors. While addition of filler particles even at large weight fractions has only a minor effect on the relaxation times, uniaxial deformation and swelling are demonstrated to alter the molecular dynamics significantly.     

Surface UV aging of elastomers investigated with microscopic resolution by single-sided NMR

Depth profiles taken from the surface of UV irradiated natural rubber sheets have been measured with microscopic resolution using a Profile NMR-MOUSE. An NMR observable related to the sum of the spin echoes in the Carr-Purcell-Meiboom-Gill pulse sequence was used to characterize the cross-link density changes produced by the action of UV radiation in each sheet. The aging process was investigated as function of irradiation time and penetration depth. An exponential attenuation law with a space dependent absorption coefficient describes the change in the NMR observable with penetration depth. An Avrami model is used to describe the dependence of the absorption coefficient on the aging time. The method can be applied to investigate the effect of various aging agents on the surfaces of elastomers.     

Influence of the film thickness and additional elements (Al,O, and N) on the properties of FeCo film structures

The magnetic properties and domain structure of FeCoAlON thin films with thicknesses varying from 55 to 550 nm have been studied, and conditions favoring preparation of FeCoAlON films with uniaxial anisotropy in the direction normal to the film plane, which is required for designing “perpendicular” super-high-density information recording, have been established. In FeCoAlON films with a thickness up to 300 nm, the domain structure consists of cross-linked domain walls, because strong demagnetizing field suppresses formation of stripe domains. After the film thickness has reached 320 nm, cross-linked domain walls transform into stripe domains, with uniaxial anisotropy in the film plane disappearing, to become replaced by uniaxial anisotropy in the direction normal to the film plane, which can be assigned to magnetoelastic stresses induced by nitrogen atoms filling up interstitial space in the (110) plane. A further increase in the film thickness (up to 550 nm) leads to a rotational anisotropy due to the increase of nitrogen concentration in interstitials and the increase of magnetoelastic stresses.     

Spatially modulated antiferromagnetic structures in an easy-plane multiferroic

Possible types of spatially modulated periodic antiferromagnetic structures in a uniaxial rhombohedral multiferroic with BiFeO₃ crystal symmetry have been studied depending on the ratio of the uniaxial anisotropy and magnetoelectric interaction parameters. It has been shown that, along with symmetric cycloid antiferromagnetic structures with zero transverse component of the antiferromagnetism vector, there are changes in the antiferromagnetism vector direction with both right and left nonzero components of the antiferromagnetic moment, which are branched from the high-symmetry spatially modulated distribution. These solutions degenerate into a homogeneous state at a critical value of the normalized easy-plane anisotropy parameter. The existence of the found spatially inhomogeneous antiferromagnetic states with an incommensurate period can lead to additional features in magnetoelectric properties in multiferroics of the type under consideration near magnetic phase transitions in electric and magnetic fields.     

Micromagnetic calculation of the equilibrium distribution of magnetic moments in thin films

A new approach has been proposed for determining an equilibrium configuration of magnetic moments in condensed matter in terms of its discrete model. The solution to this problem is reduced to a system of linear inhomogeneous equations with undetermined Lagrange multipliers. The possibility of numerically solving these systems has been shown using a modified power method. The efficiency of the method has been demonstrated for the model of a thin magnetic film with a nonuniform distribution of the uniaxial magnetic anisotropy over the area. The dependence of the coercive force on the uniaxial anisotropy of nanocrystallites, their exchange interaction, and other parameters of samples has been investigated.     

Enhanced sensitivity to residual dipolar couplings of elastomers by higher-order multiple-quantum NMR

The homonuclear and heteronuclear residual dipolar couplings in elastomers reflect changes in the cross-link density, temperature, the uniaxial and biaxial extension or compression as well as the presence of penetrant molecules. It is shown theoretically that for an isolated methyl group the relative changes in the intensity of the homonuclear double-quantum buildup curves in the initial time regime due to variation of the residual dipolar coupling strength is less sensitive than the changes in the triple-quantum filtered NMR signal when considering the same excitation/reconversion time. For a quadrupolar nucleus with spin I=2 the sensitivity enhancement was simulated for four-quantum, triple-quantum, and double-quantum buildup curves. In this case the four-quantum build-up curve shows the highest sensitivity to changes of spin couplings. This enhanced sensitivity to the residual dipolar couplings was tested experimentally by measuring 1H double-quantum, triple-quantum, and four-quantum buildup curves of differently cross-linked natural rubber samples. In the initial excitation/reconversion time regime, where the residual dipolar couplings can be measured model free, the relative changes in the intensity of the four-quantum buildup curves are about five times higher than those of the double-quantum coherences. For the first time proton four-quantum coherences were recorded for cross-linked elastomers.     

Angle-dependent x-ray magnetic circular dichroism from (Ga,Mn)As: anisotropy and identification of hybridized states

Remarkably anisotropic Mn L2,3 x-ray magnetic circular dichroism spectra from the ferromagnetic semiconductor (Ga,Mn)As are reported. States with cubic and uniaxial symmetry are distinguished by careful analysis of the angle dependence of the spectra. The multiplet structures with cubic symmetry are qualitatively reproduced by calculations for an atomiclike d5 configuration in tetrahedral environment, and show zero anisotropy in the orbital and spin moments within the experimental uncertainty. However, hybridization with the host valence bands is reflected by the presence of a preedge feature with a uniaxial anisotropy and a marked dependence on the hole density.     

Interface biquadratic coupling and magnon scattering in exchange-biased ferromagnetic thin films grown on epitaxial FeF2

The magnetic anisotropy of ferromagnetic (FM) Ni, Co, and Fe polycrystalline thin films grown on antiferromagnetic (AF) FeF(2)(110) epitaxial layers was studied, as a function of temperature, using ferromagnetic resonance. In addition to an in-plane anisotropy in the FM induced by fluctuations in the AF short-range order, a perpendicular (biquadratic) magnetic anisotropy, with an out-of-plane component, was found which increased with decreasing temperature above the AF Neél temperature (T(N) = 78.4 K). This is a surprising result given that the AF's uniaxial anisotropy axis was in the plane of the sample, but is consistent with prior experimental and theoretical work. The resonance linewidth had a strong dependence on the direction of the external magnetic field with respect to in-plane FeF(2) crystallographic directions, consistent with interface magnon scattering due to defect-induced demagnetizing fields. Below T(N), the exchange bias field H(E) measured via FMR for the Ni sample was in good agreement with H(E) determined from magnetization measurements if the perpendicular out-of-plane anisotropy was taken into account. A low field resonance line normally observed at H ≈ 0, associated with domain formation during magnetization in ferromagnets, coincided with the exchange bias field for T < T(N), indicating domain formation with the in-plane FM magnetization perpendicular to the AF easy axis. Thus, biquadratic FM-AF coupling is important at temperatures below and above T(N).     

In-plane uniaxial magnetic anisotropy of thin Fe layers on Si(1 1 1) induced upon grazing deposition of a Si capping layer

We demonstrate that an in-plane uniaxial magnetic anisotropy can be induced in Fe films grown on Si(1 1 1) by means of an appropriate Si capping layer. It is shown that grazing-incidence Si deposition reduces the three-fold symmetry of the body-centered-cubic (BCC) Fe(1 1 1) surface to two-fold, thus generating a surface-type uniaxial in-plane magnetic anisotropy contribution. The relevant magnetic easy axis direction depends in a critical way on the azimuth of the Si evaporation flux with respect to the Fe crystal surface directions. A simple qualitative model based on the change of the Fe surface by inhomogeneous chemical reaction with Si is proposed to interpret the magnetic anisotropy evolution.     

Width and temperature dependence of lithography-induced magnetic anisotropy in (Ga,Mn)As wires

In-plane magnetic anisotropy of 40-μm-long (Ga,Mn)As wires with different widths (0.4, 1.0, and 20 μm) has been investigated between 5 and 75 K by measuring anisotropic magneto-resistance (AMR). The wires show in-plane 〈1 0 0〉 cubic and [−1 1 0] uniaxial anisotropies, and an additional lithography-induced anisotropy along the wire direction in narrow wires with width of 0.4 and 1.0 μm. We derive the temperature dependence of the cubic, uniaxial, and lithography-induced anisotropy constants from the results of AMR, and find that a sizable anisotropy can be provided by lithographic means, which allows us to control and detect the magnetization reversal process by choosing the direction of the external magnetic fields.