Transverse Nuclear Relaxation Research Articles

Monitoring electron spin fluctuations with paramagnetic relaxation enhancement

The magnetic interactions between the spin of an unpaired electron and the surrounding nuclear spins can be exploited to gain structural information, to reduce nuclear relaxation times as well as to create nuclear hyperpolarization via dynamic nuclear polarization (DNP). A central aspect that determines how these interactions manifest from the point of view of NMR is the timescale of the fluctuations of the magnetic moment of the electron spins. These fluctuations, however, are elusive, particularly when electron relaxation times are short or interactions among electronic spins are strong. Here we map the fluctuations by analyzing the ratio between longitudinal and transverse nuclear relaxation times T1/T2, a quantity which depends uniquely on the rate of the electron fluctuations and the Larmor frequency of the involved nuclei. This analysis enables rationalizing the evolution of NMR lineshapes, signal quenching as well as DNP enhancements as a function of the concentration of the paramagnetic species and the temperature, demonstrated here for LiMg1−xMnxPO4 and Fe(III) doped Li4Ti5O12, respectively. For the latter, we observe a linear dependence of the DNP enhancement and the electron relaxation time within a temperature range between 100 and 300 K.

Magnetically induced local lattice anomalies and low-frequency fluctuations in the Mott insulator La2O3Fe2Se2

We report a study of the Mott insulator ${\mathrm{La}}_{2}{\mathrm{O}}_{3}{\mathrm{Fe}}_{2}{\mathrm{Se}}_{2}$ by means of $^{139}\mathrm{La}$ nuclear quadrupole resonance (NQR). The NQR spectra evidence a single La site in the paramagnetic phase and two inequivalent La sites, La1 and La2, in the antiferromagnetic phase. These two sites are characterized by different quadrupole couplings, indicative of distinct lattice configurations segregated in domains. The dependence of the quadrupole coupling for La2 on temperature suggests that the structural distortion is driven by the magnetic order parameter. The nuclear transverse relaxation rate $1/{T}_{2}$ evidences fluctuations in the paramagnetic phase with characteristic frequencies well below the Heisenberg exchange frequency and likely associated with nematic fluctuations.

Paramagnetic NMR Spectroscopy Is a Tool to Address Reactivity, Structure, and Protein–Protein Interactions of Metalloproteins: The Case of Iron–Sulfur Proteins

The study of cellular machineries responsible for the iron–sulfur (Fe–S) cluster biogenesis has led to the identification of a large number of proteins, whose importance for life is documented by an increasing number of diseases linked to them. The labile nature of Fe–S clusters and the transient protein–protein interactions, occurring during the various steps of the maturation process, make their structural characterization in solution particularly difficult. Paramagnetic nuclear magnetic resonance (NMR) has been used for decades to characterize chemical composition, magnetic coupling, and the electronic structure of Fe–S clusters in proteins; it represents, therefore, a powerful tool to study the protein–protein interaction networks of proteins involving into iron–sulfur cluster biogenesis. The optimization of the various NMR experiments with respect to the hyperfine interaction will be summarized here in the form of a protocol; recently developed experiments for measuring longitudinal and transverse nuclear relaxation rates in highly paramagnetic systems will be also reviewed. Finally, we will address the use of extrinsic paramagnetic centers covalently bound to diamagnetic proteins, which contributed over the last twenty years to promote the applications of paramagnetic NMR well beyond the structural biology of metalloproteins.

Application of the LASSO algorithm for fitting the multiexponential data of the NMR relaxometry

The problem of time series fitting by the sum of several exponentials with different decay parameters often arises analyzing the data of a physical experiment. In particular, such a problem arises determining the nuclear transverse relaxation times from the spin-echo decay NMR data. Mathematically, the problem can be formulated as a solution of the Fredholm integral equation of the first kind with an exponential kernel, or an equivalent system of linear equations. To solve this equation, various regularization methods are used, based on the L2-norm in most cases. We report the application of the L1-regularization for the problem, using the LASSO algorithm. A comparison was made between the results of L1- and L2-regularization on model time series, which were the sum of several exponential decays with noise. Also the L1- and L2-regularization were applied to analyze the 1H NMR experimental data of the spin-echo decays of n-hexane adsorbed in the porous volume of aluminium poor MFI-type zeolites known as ZSM-5. It was found out that the L1-regularization is effective method for determination of the transverse relaxation times from NMR data.

NMR as a Probe of Band Inversion in Topologically Nontrivial Half-Heusler Compounds

209Bi nuclear magnetic resonance (NMR) was studied in half-Heusler compounds YPdBi and YPtBi. The observed NMR spectra exhibit low intensity because of short nuclear transverse relaxation time (T2) governed by sizable structural disorder. In both compounds, the frequency shift of the 209Bi bulk nuclei is dominated by the chemical shielding (δcs) contribution. Remarkably, it is positive for topologically trivial YPdBi yet strongly negative for topologically nontrivial YPtBi. At the same time, the spin–lattice relaxation rate (1/T1) is distinctly larger in YPtBi due to stronger spin–orbit coupling and postulated inversion of the electronic bands near the Fermi level. The unique features of δcs and 1/T1 established for YPtBi can be considered as possibly universal fingerprints of topologically nontrivial state in similar materials.

Probing the bulk electronic states of Bi2Se3using nuclear magnetic resonance

We report a nuclear magnetic resonance (NMR) study of Bi${}_{2}$Se${}_{3}$ single crystals grown by three different methods. All the crystals show nine well-resolved peaks in their ${}^{209}$Bi NMR spectra of the nuclear quadrupolar splitting, albeit with an intensity anomaly. Spectra at different crystal orientations confirm that all the peaks are purely from the nuclear quadrupolar effect, with no other hidden peaks. We identify the short nuclear transverse relaxation time (${T}_{2}$) effect as the main cause of the intensity anomaly. We also show that the ${}^{209}$Bi signal originates exclusively from bulk, while the contribution from the topological surface states is too weak to be detected by NMR. However, the bulk electronic structure in these single crystals is not the same, as identified by the NMR frequency shift and nuclear spin-lattice relaxation rate ($1/{T}_{1}$). The difference is caused by the different structural defect levels. We find that the frequency shift and $1/{T}_{1}$ are smaller in samples with fewer defects and a lower carrier concentration. Also, the low-temperature power law of the temperature-dependent $1/{T}_{1}$ ($\ensuremath{\propto}{T}^{\ensuremath{\alpha}}$) changes from the Korringa behavior $\ensuremath{\alpha}=1$ in a highly degenerate semiconductor (where the electrons obey Fermi statistics) to $\ensuremath{\alpha}<1$ in a less degenerate semiconductor (where the electrons obey Boltzmann statistics).

Accurate calibration of a polymer gel dosimeter with a plastic scintillation detector

Three dimensional dose polymer gel dosimetry measurements provide unique information on sophisticated dose distributions. In this study, the authors propose a novel method to improve the accuracy of polymer gel dosimeters by inserting a plastic scintillation detector (PSD) to provide a dose reference. PSD dosimeters were calibrated using chromatic deconvolution and then inserted into polyacrylanide gel (PAG) dosimeters. The gel and the PSDs were immersed into water and irradiated with 6 MV wedge filtered beams to obtain a wide range of dose variation. Calibration vials containing the same gel were also irradiated to generate a standard calibration curve. The distribution of magnetic nuclear transverse relaxation rate (R2) values of the gel was determined with a multislice multiecho MRI sequence at 1.5 T. Another calibration curve was obtained by assigning the R2 values in the gel surrounding the scintillators to the dose determined by the PSDs. A reference calibration point from a PSD located in a low dose gradient area served to correct the standard calibration method yielding three novel calibration methods. The results were compared with EBT2 GAFCHROMIC film measurements acquired in the same condition and with the Pinnacle3 treatment planning dose calculations, The mean absolute error of the standard calibration method ranged from 6.1 to 12.4%. The corresponding gamma index (3%/3 mm distance to agreement) criterion was satisfied for only 56% of the pixels in the middle slice of the gel compared to Pinnacle3 dose calculations and to EBT2 film measurements in the center part of the field. Calibration methods using a PSD reduced the mean absolute error to less than 4%; this value was under 2.6% for one of the three methods. In that case, 98% of the pixels satisfied the gamma index criterion. The accuracy of PAG dosimeters may be highly improved using one reference dose point measurement using a plastic scintillation detector. The best calibration procedure corrected the slope of the calibration curve derived from the calibration vials to match the R2 value around a PSD calibration, while keeping the R2 value at 0 Gy constant.

Communication: Critical dynamics and nuclear relaxation in lipid bilayers

Membrane composition fluctuations affect deuterium nuclear magnetic relaxation in lipid bilayers. The time dependence of the fluctuations depends on lipid diffusion. Near a miscibility critical point this diffusion involves an advective hydrodynamic coupling to the aqueous phase. The corresponding diffusion coefficient depends on both the critical length and the fluctuation wavelength. We calculate the effects of these dynamics on transverse deuterium nuclear relaxation in the 0.1(o)-10(o) range above the critical temperature.

Hydration Pressure Increases in Heat-Damaged Skin:osmotic-Stress and High-Resolution Magnetic Resonance Data Implicate Local Supramolecular Mechanisms

Local forces driving interstitial-fluid transfer affect burns; heat-ablation and remodeling therapies; hemodynamics; and wound healing. We examined hydration/dehydration mechanisms after heating skin ex vivo at 40, 50, and 60°C to induce “denaturing” transitions in three main structures of the interstitial matrix: hyaluronic acid, cells, and collagen.Hydration pressure (HP), swelling rates, water activity, acid-binding capacity (at pH∼7.4) and transverse nuclear-relaxation rate of solvent-water protons (1/T2) were compared using osmotic-stress, gravidometric, saturation vapor-pressure, potentiometric, and magnetic resonance imaging (μMRI, 40μm /pixel resolution) analyses, respectively. Mean HP values were 89, 100, 79, 108 at 4°C and 50, 62, 91, 162 mmHg at 37°C in nonheated control, 40, 50, and 60°C samples, respectively. Swelling kinetic energy increased 1.1, 4.5, and 6.9-fold relative to controls. Acid-binding and water activity increased by 0.3 and 0.4 pH units and 0.020 and 0.033 (at 75% hydration) in 50 and 60°C samples, while in 40°C samples, values remained close to controls'. μMRI changes were obvious only in 60°C samples with 1/T2 gradients (from T2-map contrast), and average 1/T2 in the central dermis decreased 0.1 intensity units/ μm and 66%, respectively.HP and acid-binding data indicate increases in the total solvent-exposed area and, with mutually consistent 1/T2 decreases and water-activity increases, demonstrate qualitative changes in its average hydration properties. Quantitative differences among control and preheated samples and between hydration parameters obtained at 4 versus 37°C confirm temperature-dependent supramolecular reorganization following damage. Together, results provide strong evidence that multiscale interactions among matrix components, independent of vascular, hormonal and neural controls, change key interstitium fluid-transfer properties with heat-damage.

Spin dynamics of the frustrated ferromagnetic-chain system Ca3Co2O6

We report a 59Co NMR study on a quasi-one-dimensional cobalt oxide Ca3Co2O6 having the in-chain ferromagnetic and out-of-chain antiferromagnetic interactions. We have found an increase of the 59Co nuclear transverse relaxation rate 1/T2 at 6.105 T on cooling temperature below 200 K, much higher than the spin freezing temperature of 25 K at 0 T. The result suggests that the unusual slowing down of spin fluctuations in a wide temperature range, probably arising from the spin frustration on the triangular lattice of the ferromagnetic chains. The NMR signals wiped out below 80 K due to the fast relaxation relive below 17 K, the spin freezing temperature measured at the NMR time window.

Dynamics and thermalization of the nuclear spin bath in the single-molecule magnetMn12−ac: Test for the theory of spin tunneling

The description of the tunneling of a macroscopic variable in the presence of a bath of localized spins is a subject of great fundamental and practical interest, and is relevant for many solid-state qubit designs. Most of the attention is usually given to the dynamics of the ``central spin'' (i.e., the qubit), while little is known about the spin bath itself. Here, we present a detailed study of the dynamics of the nuclear spin bath in the ${\mathrm{Mn}}_{12}\text{\ensuremath{-}}\mathrm{ac}$ single-molecule magnet, probed by NMR experiments down to very low temperatures $(T\ensuremath{\simeq}20\phantom{\rule{0.3em}{0ex}}\mathrm{mK})$. The results are critically analyzed in the framework of the Prokof'ev-Stamp theory of nuclear-spin-mediated quantum tunneling. We find that the longitudinal relaxation rate of the $^{55}\mathrm{Mn}$ nuclei in ${\mathrm{Mn}}_{12}\text{\ensuremath{-}}\mathrm{ac}$ becomes roughly $T$ independent below $T\ensuremath{\simeq}0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and can be strongly suppressed with a longitudinal magnetic field. This is consistent with the nuclear relaxation being caused by quantum tunneling of the molecular spin, and we attribute the tunneling fluctuations to the minority of fast-relaxing molecules present in the sample. The transverse nuclear relaxation is also $T$ independent for $T<0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and can be explained qualitatively and quantitatively by the dipolar coupling between like nuclei in neighboring molecules. This intercluster nuclear spin diffusion mechanism is an essential ingredient for the global relaxation of the nuclear spin bath. We also show that the isotopic substitution of $^{1}\mathrm{H}$ by $^{2}\mathrm{H}$ leads to a slower nuclear longitudinal relaxation, consistent with the decreased tunneling probability of the molecular spin. Finally, we demonstrate that even at the lowest temperatures---where only $T$-independent quantum tunneling fluctuations are present---the nuclear spins remain in thermal equilibrium with the lattice phonons, and we investigate the time scale for their thermal equilibration. After a review of the theory of macroscopic spin tunneling in the presence of a spin bath, we argue that most of our experimental results are consistent with that theory, but the thermalization of the nuclear spins is not. This calls for an extension of the spin-bath theory to include the effect of spin-phonon couplings in the nuclear-spin-mediated tunneling process.

Protonless 13C direct detection NMR: Characterization of the 37 kDa trimeric protein CutA1

The major limitation of nuclear magnetic resonance spectroscopy arises from the increase of nuclear transverse relaxation rates with increasing molecular mass. This causes reduction in spectral resolution and coherence transfer efficiency. The use of 2H-labeling to eliminate 1H-mediated relaxation pathways and the constructive use of cross correlation effects (TROSY, CRINEPT) alleviate the phenomenon. An alternative approach is to use direct detection of heteronuclei. Specifically designed 13C direct detection experiments can complement the set of 1H-based NMR experiments commonly used for structure determination providing an additional source of information less affected by the detrimental transverse relaxation effect. We applied this novel methodology to the study of the CutA1 protein (12.3 kDa) from E. coli that forms a homotrimer in solution with a total molecular mass of 37 kDa. In this work we demonstrate that the information available from 13C direct detection experiments makes it possible to completely assign the NMR resonances of the backbone of this 37 kDa trimeric protein without the need of deuteration. The structural and dynamical knowledge obtained for this system may contribute to understand its biological role.

Nuclear magnetic resonance and photomagnetic phenomena in oxygen-deficient ferric borate

Single crystals of ferric borate (FeBO3), annealed in vacuum so as to provide for the oxygen deficiency and the corresponding excess Fe2+ ion concentration, have been studied by 57Fe NMR. The NMR signal intensity and the transverse nuclear relaxation rate in oxygen-deficient ferric borate are significantly increased compared to those in the initial state. The annealed samples also exhibit a giant shift of the resonance frequency under the action of light, which is several times as large as the analogous shift in samples with the equilibrium concentration of Fe2+ ions. The obtained experimental data confirm the model of photomagnetic phenomena in antiferromagnetic materials that is based on the notion of Fe2+-containing complexes playing the role of photosensitive centers.

Nuclear transverse relaxation studies of relaxation anomalies of Ga NQR in the paramagnetic state of the itinerant antiferromagnet [formula omitted

Nuclear transverse relaxation studies of 71 Ga NQR in UGa 3 have confirmed very anomalous onset and development of nuclear quadrupolar relaxation above 240 K found in previous 1 / T 1 measurements.

Spin relaxation of quadrupole nuclei in paramagnetic and magnetically ordered insulators

The longitudinal and transverse spin relaxation through a (generally anisotropic) electron-nucleus interaction in paramagnetic and magnetically ordered insulators is theoretically studied for nuclei with a resolved quadrupole structure. Expressions are derived for the relaxation rates of both the transverse nuclear magnetization components when individual transitions are excited in the quadrupole structure and the total longitudinal nuclear magnetization component. These expressions are reduced to a form that contains the Fourier transforms of the time correlation functions only for the electron spins. Given the specific form of these correlation functions corresponding to different phase states of the electron spins and different origins of their fluctuations, the temperature dependences of the nuclear relaxation rates are ascertained in various cases, including those for dipole and isotropic hyperfine interactions. Calculations are performed for arbitrary electron and half-integer nuclear spins by taking into account the possible quadrupole splitting of the NMR spectrum without any restriction on the smallness of the ratio ℏω s/kBT (ωs is the resonance frequency of the electron spins). The derived expressions are compared with available experimental data on the longitudinal and transverse nuclear relaxation in colossal-magnetoresistance lanthanum manganites in the part of their phase diagram where the corresponding samples are either paramagnetic or magnetically ordered insulators and near the points of transition to an ordered state. Interpretations alternative to the existing ones are offered.

Analysis of the Knight shift data on Li and Zn substituted YBa 2Cu 3O 6+ x

The Knight shift data on Li and Zn substituted YBa 2Cu 3O 6+ x are analyzed using an itinerant model with short-range antiferromagnetic correlations. The model parameters, which are determined by fitting the experimental data on the transverse nuclear relaxation rate T 2 −1 of pure YBa 2Cu 3O 6+ x , are used to calculate the Knight shifts for various nuclei around a nonmagnetic impurity located in the CuO 2 planes. The calculations are carried out for Li and Zn impurities substituted into optimally doped and underdoped YBa 2Cu 3O 6+ x . The results are compared with the 7 Li and 89 Y Knight shift measurements on these materials.

Phase diagram of YBa2Cu3O7−y at T<T c according to transverse nuclear relaxation data for Cu(2)

Two peaks are observed at T=35 and 47 K in the transverse relaxation rate for Cu(2) nuclei in YBa2Cu3O7−y . A comparison of the relaxation rates for isotopes 63Cu(2) and 65Cu(2) at T=47 K indicates the magnetic nature of relaxation. The enhancement of local magnetic field fluctuations perpendicular to CuO2 planes at T=47 K is associated with critical fluctuations of orbital currents. The peak at T=35 K is attributed to the emergence of an inhomogeneous superconducting phase. The obtained experimental results and the available data from the literature made it possible to propose a qualitatively new phase diagram of the superconducting state.

Gradient refractive index of the crystalline lens of the Black Oreo Dory ( Allocyttus Niger): comparison of magnetic resonance imaging (MRI) and laser ray-trace methods

The gradient refractive index of the crystalline lens in the Black Oreo Dory ( Allocyttus Niger) was determined using two methods; an optimisation program based on finite ray-tracing and the path of laser beams through the lens, and magnetic resonance imaging (MRI) and the linear relationship between refractive index and nuclear transverse relaxation rates. The methods showed good agreement in the cortical zone of the lens, but the lack of free water in the core of the lens made MRI measurement impossible in this region. The laser-optimisation method gave mean values of 1.368 and 1.543 for the surface and core refractive indices respectively, with a radial distribution for the gradient refractive index given by n( r)=1.543−0.121 r 2−0.033 r 4−0.021 r 6.

Local vortex mobility below the irreversibility line ofTl2Ba2CaCu2O8:t ATl205NMR study of the transverse relaxation in single crystals

We performed $^{205}\mathrm{Tl}$ NMR on aligned single crystals of the 105-K superconductor ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$ in a field of 4.7 T as a function of angle \ensuremath{\theta} between the field direction and the c axis. Irreversibility temperatures ${\mathrm{T}}_{\mathrm{irr}}$ were determined by comparing the NMR linewidths after field cooling and zero-field cooling. The $^{205}\mathrm{Tl}$ nuclear transverse relaxation rate ${\mathrm{T}}_{2}^{\mathrm{\ensuremath{-}}1}$ shows a well-developed peak caused by vortex motion below ${\mathrm{T}}_{\mathrm{irr}}$. The peak shifts to higher temperatures with increasing \ensuremath{\theta}. The data are analyzed analytically and by computer simulation and the obtained parameters of local vortex motion are discussed.

63Cu-NMR Study in High-Tc Superconductor HgBa2Ca2Cu3O8 + δ

Abstract The 63Cu nuclear transverse relaxation rates have been measured in the normal state on both square and pyramidal CuO2 planes in HgBa2Ca2Cu3O8 + δ with Tc = 133K. The Gaussian component of the spin-echo decay rate, 63(1/T2G), for both sites increases with decreasing temperature, followed by a peak around T* ~ 150 K, indicating that the spin correlation becomes stronger with decreasing temperature. Also, it is found that the magnitude of 63(1/T2G) for a square site is larger than that for a pyramidal one, suggesting that the spin correlation in the square plane is stronger than that in the pyramidal one.