Quadrupolar Spin Research Articles

Efficient rotational echo double resonance recoupling of a spin-1/2 and a quadrupolar spin at high spinning rates and weak irradiation fields

A modification of the rotational echo (adiabatic passage) double resonance experiments, which allows recoupling of the dipolar interaction between a spin-1/2 and a half integer quadrupolar spin is proposed. We demonstrate efficient and uniform recoupling at high spinning rates ( ν r ), low radio-frequency (RF) irradiation fields ( ν 1), and high values of the quadrupolar interaction ( ν q ) that correspond to values of α = ν 1 2 / ν q ν r , the adiabaticity parameter, which are down to less than 10% of the traditional adiabaticity limit for a spin-5/2 (α = 0.55). The low-alpha rotational echo double resonance curve is obtained when the pulse on the quadrupolar nucleus is extended to full two rotor periods and beyond. For protons (spin-1/2) and aluminum (spin-5/2) species in the zeolite SAPO-42, a dephasing curve, which is significantly better than the regular REAPDOR experiment (pulse length of one-third of the rotor period) is obtained for a spinning rate of 13 kHz and RF fields down to 10 and even 6 kHz. Under these conditions, α is estimated to be approximately 0.05 based on an average quadrupolar coupling in zeolites. Extensive simulations support our observations suggesting the method to be robust under a large range of experimental values.

MATS and LaSpec: High-precision experiments using ion traps and lasers at FAIR

Nuclear ground state properties including mass, charge radii, spins and moments can be determined by applying atomic physics techniques such as Penning-trap based mass spectrometry and laser spectroscopy. The MATS and LaSpec setups at the low-energy beamline at FAIR will allow us to extend the knowledge of these properties further into the region far from stability. The mass and its inherent connection with the nuclear binding energy is a fundamental property of a nuclide, a unique “fingerprint”. Thus, precise mass values are important for a variety of applications, ranging from nuclear-structure studies like the investigation of shell closures and the onset of deformation, tests of nuclear mass models and mass formulas, to tests of the weak interaction and of the Standard Model. The required relative accuracy ranges from 10−5 to below 10−8 for radionuclides, which most often have half-lives well below 1 s. Substantial progress in Penning trap mass spectrometry has made this method a prime choice for precision measurements on rare isotopes. The technique has the potential to provide high accuracy and sensitivity even for very short-lived nuclides. Furthermore, ion traps can be used for precision decay studies and offer advantages over existing methods. With MATS (Precision Measurements of very short-lived nuclei using an A_dvanced Trapping System for highly-charged ions) at FAIR we aim to apply several techniques to very short-lived radionuclides: High-accuracy mass measurements, in-trap conversion electron and alpha spectroscopy, and trap-assisted spectroscopy. The experimental setup of MATS is a unique combination of an electron beam ion trap for charge breeding, ion traps for beam preparation, and a high-precision Penning trap system for mass measurements and decay studies. For the mass measurements, MATS offers both a high accuracy and a high sensitivity. A relative mass uncertainty of 10−9 can be reached by employing highly-charged ions and a non-destructive Fourier-Transform Ion-Cyclotron-Resonance (FT-ICR) detection technique on single stored ions. This accuracy limit is important for fundamental interaction tests, but also allows for the study of the fine structure of the nuclear mass surface with unprecedented accuracy, whenever required. The use of the FT-ICR technique provides true single ion sensitivity. This is essential to access isotopes that are produced with minimum rates which are very often the most interesting ones. Instead of pushing for highest accuracy, the high charge state of the ions can also be used to reduce the storage time of the ions, hence making measurements on even shorter-lived isotopes possible. Decay studies in ion traps will become possible with MATS. Novel spectroscopic tools for in-trap high-resolution conversion-electron and charged-particle spectroscopy from carrier-free sources will be developed, aiming e.g. at the measurements of quadrupole moments and E0 strengths. With the possibility of both high-accuracy mass measurements of the shortest-lived isotopes and decay studies, the high sensitivity and accuracy potential of MATS is ideally suited for the study of very exotic nuclides that will only be produced at the FAIR facility.Laser spectroscopy of radioactive isotopes and isomers is an efficient and model-independent approach for the determination of nuclear ground and isomeric state properties. Hyperfine structures and isotope shifts in electronic transitions exhibit readily accessible information on the nuclear spin, magnetic dipole and electric quadrupole moments as well as root-mean-square charge radii. The dependencies of the hyperfine splitting and isotope shift on the nuclear moments and mean square nuclear charge radii are well known and the theoretical framework for the extraction of nuclear parameters is well established. These extracted parameters provide fundamental information on the structure of nuclei at the limits of stability. Vital information on both bulk and valence nuclear properties are derived and an exceptional sensitivity to changes in nuclear deformation is achieved. Laser spectroscopy provides the only mechanism for such studies in exotic systems and uniquely facilitates these studies in a model-independent manner.The accuracy of laser-spectroscopic-determined nuclear properties is very high. Requirements concerning production rates are moderate; collinear spectroscopy has been performed with production rates as few as 100 ions per second and laser-desorption resonance ionization mass spectroscopy (combined with β-delayed neutron detection) has been achieved with rates of only a few atoms per second.This Technical Design Report describes a new Penning trap mass spectrometry setup as well as a number of complementary experimental devices for laser spectroscopy, which will provide a complete system with respect to the physics and isotopes that can be studied. Since MATS and LaSpec require high-quality low-energy beams, the two collaborations have a common beamline to stop the radioactive beam of in-flight produced isotopes and prepare them in a suitable way for transfer to the MATS and LaSpec setups, respectively.

Determination of the local inhomogeneity of a crystal lattice using a two-frequency nuclear quadrupole resonance method

Nonuniform line broadening in quadrupole spin systems is analyzed. It is shown theoretically that this broadening is of the tensor type. This forms the basis of the method for analyzing the distribution of local inhomogeneities in the crystal lattice, which is verified experimentally on a sodium nitride sample.

Novel Geometrical Frustration Effects in the Two-Dimensional Triangular-Lattice Antiferromagnet NiGa2S4 and Related Compounds

Geometrical frustration may suppress conventional magnetic long-range order and possibly promote a novel type of ordering associated with a higher order degree of freedom than spin dipolar-moment such as vector spin chirality and spin quadrupole moment. After a brief overview of such phenomena due to vector spin chirality, we focus on the two-dimensional (2D) frustrated magnetism in the layered chalcogenide Mott insulator NiGa 2 S 4 and related compounds. NiGa 2 S 4 provides the unique example of a S = 1 2D antiferromagnet on a regular exact triangular lattice. Extensive studies using high-purity samples of NiGa 2 S 4 have revealed that Ni 2+ S = 1 Heisenberg spins exhibit resonant critical slowing down at T * = 8.5 K without forming a magnetic long-range order, signaling a viscous spin-liquid state. The critical spin-fluctuation regime extends over almost an order of magnitude in temperature both above and below T * . Even well below T * , the spin–spin correlation remains short-ranged at an incommensurate wave vector close to (1/6, 1/6, 0), corresponding to a 120° correlation with 2 a period. Interestingly, however, a 2D linearly dispersive magnetic mode and a quasi-static spin component exist in the low temperature limit. Possibly relevant scenarios including topological phase transition associated with Z 2 vortex due to vector spin chirality, spin quadrupolar nematic correlation, and C 3 bond-ordering are reviewed.

The quadrupole enhanced 1H spin–lattice relaxation of the amide proton in slow tumbling proteins

An analysis, based on the stochastic Liouville approach, is presented of the R(1)-NMRD or field dependent spin-lattice relaxation rate of amide protons. The proton relaxivity, displayed as R(1)-NMRD profiles, is calculated for a reorienting (1)H-(14)N spin group, where the inter spin coupling is due to spin dipole-dipole coupling or the scalar coupling. The quadrupole nucleus (14)N has an asymmetry parameter eta = 0.4 and a quadrupole interaction which is modulated by the overall reorientational motion of the protein. In the very slow reorientational regime, omega(Q)tau(R) >> 1 and tau(R) > or = 2.0 micros, both the dipole-dipole coupling and the scalar coupling yield a T(1)-NMRD profile with three marked peaks of proton spin relaxation enhancement. These peaks appear when the proton Larmor frequency, omega(I), matches the nuclear quadrupole spin transition frequencies: omega(1) = omega(Q)2eta/3, omega(2) = omega(Q)(1-eta/3) and omega(3) = omega(Q)(1 + eta/3), and the quadrupole spin system thus acts as a relaxation sink. The relative relaxation enhancements of the peaks are different for the dipole-dipole and the scalar coupling. Considering the dipole-dipole coupling, the low frequency peak, omega(1), is small compared to the high field peaks whereas for the scalar coupling the situation is changed. For slow tumbling proteins with a correlation time of tau(R) = 400 ns, omega(2) and omega(3) are not resolved but become one relatively broad peak. At even faster reorientation, tau(R) < 60 ns, the marked peaks disappear. In this motional regime, the main effect of the cross relaxation phenomenon is a subtle perturbation of the main amide proton T(1) NMRD dispersion. The low field part of it can be approximately described by a Lorentzian function: R(DD,SC)(0.01)/(1 + (omega(I)tau(R)3/2)(2)) whereas the high field part coincides with R(DD,SC)(0.01)/(1 + (omega(I)tau(R))(2)).

Synthesis and solid state characterization of molecular rotors with steroidal stators: ethisterone and norethisterone

In this article we describe the synthesis and dynamic behavior of two new molecular rotors with 1,4-diethynylphenylene rotators axially linked to two conformationally rigid steroidal norethisterone acetate or ethisterone frames. The resulting 1,4-bis(19-nor-17alpha-ethynyltestosterone-17beta-acetate)benzene (1) and 1,4-bis(17alpha-ethynyltestosterone)benzene (2) were fully characterized in solution and in the solid state, and the rotational dynamics of the central phenylene were explored with the help of (13)C NMR with cross polarization and magic angle spinning (CPMAS), and with quadrupolar echo variable temperature (VT) (2)H NMR in the case of 1. Splitting of signals from the aromatic ring on the (13)C CPMAS NMR and a broad quadrupolar spin echo (2)H spectrum of polycrystalline samples indicated that the rotation of the central aromatic ring in these compounds was limited at ambient temperature in the solid state. Variable temperature (2)H NMR experiments at 350 K in the case of 1-d(4) suggested a 2-fold rotational exchange with upper frequency limit of ca. 10 kHz. Single crystal X-ray analysis of this compound revealed that a crowded environment around the prospective phenylene rotator is responsible of the restricted rotation in the solid state.

High-field QCPMG NMR of large quadrupolar patterns using resistive magnets

Spectroscopy in a high magnetic field reduces second-order quadrupolar shift while increasing chemical shift. It changes the scale between quadrupolar and chemical shift of half-integer quadrupolar spins. The application of QCPMG multiple echo for acquiring large quadrupolar pattern under the high magnetic field of a 25 T resistive magnet is presented for acquiring large quadrupolar patterns. It shows that temporal field fluctuations and spatial homogeneity of the Keck magnet at the NHMFL contribute about ±20 ppm in line broadening. NMR patterns which have breadths of hundreds to thousands of kilohertz can be efficiently recorded using a combination of QCPMG and magnetic field stepping with negligible hindrance from the inhomogeneity and field fluctuations of powered magnets.

Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensate

We study tunneling properties of collective excitations in spin-1 Bose-Einstein condensates. In the absence of magnetic fields, the total transmission in the long wavelength limit occurs in all kinds of excitations but the quadrupolar spin mode in the ferromagnetic state. The quadrupolar spin mode alone shows the total reflection. A difference between those excitations comes from whether the wavefunction of an excitation corresponds to that of the condensate in the long wavelength limit. The correspondence results in the total transmission as in the spinless BEC.

Q-shear transformation for MQMAS and STMAS NMR spectra

The multiple-quantum magic-angle spinning (MQMAS) and satellite-transition magic-angle spinning (STMAS) experiments refocus second-order quadrupolar broadening of half-integer quadrupolar spins in the form of two-dimensional experiments. Isotropic shearing is usually applied along the indirect dimension of the 2D spectra such that an isotropic projection free of anisotropic quadrupolar broadening can be obtained. An alternative shear transformation by a factor equal to the coherence level (quantum number) selected during the evolution period is proposed. Such a transformation eliminates chemical shift along the indirect dimension leaving only the second-order quadrupolar-induced shift and anisotropic broadening, and is expected to be particularly useful for disordered systems. This transformation, dubbed Q-shearing, can help avoid aliasing problems due to large chemical shift ranges and spinning sidebands. It can also be used as an intermediate step to the isotropic representation for expanding the spectral window of rotor-synchronized experiments.

Supercycled symmetry-based double-quantum dipolar recoupling of quadrupolar spins in MAS NMR: I. Theory

Using average Hamiltonian (AH) theory, we analyze recently introduced homonuclear dipolar recoupling pulse sequences for exciting central-transition double-quantum coherences (2QC) between half-integer spin quadrupolar nuclei undergoing magic-angle-spinning. Several previously observed differences among the recoupling schemes concerning their compensation to resonance offsets and radio-frequency (rf) inhomogeneity may qualitatively be rationalized by an AH analysis up to third perturbation order, despite its omission of first-order quadrupolar interactions. General aspects of the engineering of 2Q-recoupling pulse sequences applicable to half-integer spins are discussed, emphasizing the improvements offered from a diversity of supercycles providing enhanced suppression of undesirable AH cross-terms between resonance offsets and rf amplitude errors.

Quenching of Gamow-Teller strength due to tensor correlations inZr90andPb208

We performed self-consistent Hartree-Fock plus random-phase approximation (HF+RPA) calculations for charge-exchange ${1}^{+}$ states in $^{90}\mathrm{Zr}$ and $^{208}\mathrm{Pb}$ by using Skyrme interactions with tensor terms. We employed a parameter set in which the tensor terms are added to the SGII interaction. It is pointed out that Gamow-Teller (GT) states can couple strongly with the spin-quadrupole (SQ) ${1}^{+}$ states in the high-energy region above ${E}_{x}=30$ MeV due to the tensor interactions. As a result of this coupling, more than $10%$ of the GT strength is shifted to the energy region above 30 MeV, and the main GT peak is moved 2 MeV downward. At the same time, the main SQ ${1}^{+}$ peak is moved upward by more than 10 MeV due to the tensor correlations. Schematic separable interactions are proposed to elucidate the quenching mechanism induced by the tensor interaction on the GT state.

Influence of relaxation processes on amplitude and shape of echo signals

A theory of signal-processing analog devices that use the phenomenon of spin, light, or nuclear quadrupole echo is considered with allowance for noise immunity. Main equations describing these phenomena are solved by multiplicative integration. Such an approach makes it possible to calculate echo signals of arbitrary amplitude and structure in a general form.

Prevention of spinning induced sample deterioration during long time solid state NMR experiments of quadrupolar spin systems

A simple solution is proposed to prevent a solid state polycrystalline sample from deterioration during long time high speed spinning experiments in solid state NMR. It is found that if a certain percentage (∼40% volume) of polyethylene glycol (PEG, (HO–CH 2–(CH 2–O–CH 2–) n –CH 2–OH) n ) is mixed with the sample that are subject to deterioration, the quality of the sample can be maintained for a long time under high speed spinning for a few days or longer, sufficient for multi-dimensional and/or low-sensitivity experiments. Both 1D and 2D experimental results are shown to support this idea.

Determination of NMR cogwheel phase cycle with XML

The selection of correct coherence transfer pathways is an essential component of an NMR pulse sequence. This article describes a new method based on the use of web tools (eXtensible Markup Language and eXtensible Stylesheet Language Transformation) to generate a cogwheel phase cycle for selecting coherence transfer pathways. We illustrate this method with the three-pulse phase-modulated shifted-echo or split- t 1 MQMAS sequences for triple-quantum spin-3/2 systems. After generalization to the different half-integer quadrupole spins, we use the SIMPSON program to confirm our results. Finally, we apply our method to the case of the z-filter 3QMAS sequence for I=3/2 systems.

Determination of absolute quadrupolar tensor orientations by double-quantum NMR on powders

We introduce a new nuclear magnetic resonance (NMR) approach for determining electric field gradient (‘quadrupolar’) tensor orientations directly from polycrystalline powders. It involves a homonuclear 2D experiment that correlates (two-spin) double-quantum and single-quantum coherences of half-integer quadrupolar spin nuclei undergoing magic-angle-spinning. The 2D NMR spectrum is sensitive both to the relative orientations between the correlated quadrupolar tensors and to their orientations relative to the dipolar vector of the spin-pair. A novel strategy to calculate 2D spectra from multi-spin systems is used to extract the tensor orientations. We demonstrate the method by estimating the three 23Na quadrupolar tensor orientations in Na 2 SO 3 .

Field cycling methods as a tool for dynamics investigations in solid state systems: Recent theoretical progress

In this paper physical mechanisms and theoretical treatments of polarization transfer and field-dependent relaxation in solid state systems, containing mutually coupled spins of spin quantum numbers I = 1 2 (spins 1 2 ) and S⩾1 (quadrupolar spins), are presented. First, theoretical descriptions of these effects are given in detail for an illustrative, simple system. Next, it is shown how to generalize the theories to much more complex spin systems. The polarization transfer and relaxation effects are illustrated by several examples. Typical misunderstandings regarding their physical origins are clarified. This paper reviews recent theoretical descriptions of the polarization transfer and relaxation phenomena. Its goal is to popularize the proper theoretical treatments with the intention to establish them as standard tools for analyzing field cycling data.

Quadrupole-enhanced proton spin relaxation for a slow reorienting spin pair: (I)–(S). A stochastic Liouville approach

The field dependence of the proton (I) spin–lattice relaxation rate is calculated for a dipole–dipole coupled spin pair, (I = 1/2) − (S = 1), where the quadrupole nucleus (S) is 2H or 14N with asymmetry parameter η = 0. The observed relaxation profile shows a marked enhancement for equal proton Larmor and quadrupole spin frequencies (i.e. ω I = ωQ). This phenomenon is referred to as the quadrupole dip, and has been observed, for instance, in 14N−1H amide groups of immobilized proteins. In this work, an analysis of the observed relaxation enhancement is presented when the dipole–dipole coupling and the quadrupole interaction are modulated by the overall re-orientational motion. A characteristic low field dispersion is observed when (3/2) τRω I ≥ 1, where τR is the rotational correlation time and ω I is the proton Larmor frequency. At higher fields, the relaxation peak exhibits a Lorentzian-like line shape, , which is centred at the quadrupole frequency. The quadrupole spin system shows a spin–lattice T 1Q and a spin–spin relaxation time T 2Q that become equal in the zero field limit. In the slow tumbling limit, the quadrupole spin relaxation times, T 1Q, T 2Q, are equal to (3/2)τR.

Recent advances in solid-state NMR spectroscopy of quadrupolar nuclei

Nuclear magnetic resonance (NMR) spectroscopy of quadrupolar nuclei (i.e., those with a spin quantum number I > 1/2) has always been viewed as "difficult" owing to the presence of an anisotropic broadening arising from the interaction of the nuclear electric quadrupole moment with the electric field gradient. This quadrupolar interaction can be considerable, resulting in broadening of the spectral resonances often over many MHz. Furthermore, magic-angle spinning (MAS), a conventional approach for increasing the resolution in solid-state NMR, is often unable to remove the broadening completely and high-resolution spectra are generally not obtained. Despite the vast amount of information contained in the anisotropic linewidths and lineshapes, the resolution and sensitivity challenges have, until recently, somewhat limited the application of solid-state NMR for quadrupolar nuclei. In general, structural information, such as that obtained through recoupling techniques or from two-dimensional correlation spectroscopy, is much more difficult to extract easily and accurately. However, recent advances in magnet design, probe hardware and pulse sequence development have significantly improved the ease with which quadrupolar spins can be studied and high-resolution spectra can be obtained, and recent applications are beginning to exploit the wealth of information available. In this discussion, we highlight just a few of the recent developments in this area, including new state-of-the art correlation experiments, the expanding study of nuclei with low gyromagnetic ratio, gamma, the increasing application of first-principles calculations in the solid state, and methods which exploit the quadrupolar broadening to provide information on dynamics. Whilst not a complete review, it is hoped that this brief overview of some of the more exciting recent developments can provide insight into the challenges, and the rewards, involved in the NMR study of quadrupolar nuclei.

209Bi NQR studies of low-temperature spin–lattice relaxation in Bi 4Ge 3O 12 single crystal

Unusual influence of weak external magnetic fields on quadrupole spin–spin relaxation was earlier found for Bi 4Ge 3O 12 which exhibited, like some other compounds of composition Ba kBi lA mO n (A=Al, B, Ge, Br, Cl), a dramatic increase in the 209Bi NQR line intensities upon switching the magnetic field. The measuring of the nuclear quadrupole interaction parameters gave an evidence for the presence in the compound of local magnetic fields of the order of 20–30 G. The existence of several low-lying crystal field levels for the p-electrons can be admitted in Bi 4Ge 3O 12 which contributes to the anomalies in the 209Bi NQR spectra of this crystal. The present work was carried out to identify the contribution of such paramagnetic centers to the nuclear spin − lattice relaxation. This contribution resulted in the low-temperature minimum on the curve of the nuclear spin–lattice relaxation rate T 1 − 1 vs. temperature, measured for the transition Δ m = 3 / 2 − 5 / 2 in the 209Bi NQR spectrum of the Bi 4Ge 3O 12 single crystal.

QCPMG using adiabatic pulses for faster acquisition of ultra-wideline NMR spectra

A previously reported quadrupolar spin–echo experiment using adiabatic pulses, which can achieve uniform excitation of quadrupolar nuclei across a wide bandwidth, has been extended to a QCPMG-like sequence exhibiting the same uniform, broadband excitation as the echo experiment but with the advantage of a significant increase in S/N. This WURST–QCPMG sequence is used to obtain static wideline 71Ga (spin-3/2) and 91Zr (spin-5/2) spectra with linewidths in excess of 500 kHz, on a standard probe at 9.4 T without any transmitter frequency or field adjustment. The sequence is also used to observe the 59Co (spin-7/2) central transition and inner satellite transitions.