Quadrupolar Spin Systems Research Articles

Satellite nutation of half integer quadrupolar nuclei: Theory and practice.

For quadrupolar spin systems, interpretation of solid state NMR spectra can be hampered by the presence of resonances from both satellite and central transitions. This is particularly true for disordered systems, where many different quadrupolar sites exist, which can have strongly different quadrupolar coupling constants. If second order effects are too strong for obtaining meaningful MAS, MQMAS or STMAS spectra, an approach is needed to successfully separate central and satellite transitions. In this work, we provide a rigorous treatment of 2D quadrupolar nutation NMR for the study of central and satellite transitions in quadrupolar systems. Using this SATURN experiment (SAtellite Transition nUtation of quadRupolar Nuclei) spectral intensity can be assigned to contributions from either central or satellite transitions. We show that the experiment can be applied to any half-integer spin (3/2, 5/2, 7/2 and 9/2), and that spectra can be obtained that closely match simulations. We furthermore show that distributions in quadrupolar parameters do not hamper the assignment of central and satellite transitions from a SATURN experiment.

AFNMR/NQR signal enhancement via population transfer

Antiferromagnetic nuclear magnetic resonance (AFNMR) and nuclear quadrupole resonance (NQR) are useful techniques to characterize materials in bulk volumes without applying external static magnetic fields. For industrial materials characterization applications, it is crucial to maximize signal‐to‐noise ratio in the available time. We simulate the AFNMR and NQR signal enhancement via population transfer in single crystals and powders and predict the enhancement factors for half‐integer quadrupolar nuclei spin systems. Differences to conventional high‐field NMR population transfer experiments are emphasized. We restrict our discussion to electric field gradients with axial symmetry = 0. Triple resonance tuned crossed coil experiments on CuFeS2 and In2O3 powders support the numerical results. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 43A: 147–156, 2015.

Spin coherent states in NMR quadrupolar system: experimental and theoretical applications

Working with nuclear magnetic resonance (NMR) in quadrupolar spin systems, in this paper we transfer the concept of atomic coherent state to the nuclear spin context, where it is referred to as pseudo-nuclear spin coherent state (pseudo-NSCS). Experimentally, we discuss the initialization of the pseudo-NSCSs and also their quantum control, implemented by polar and azimuthal rotations. Theoretically, we compute the geometric phases acquired by an initial pseudo-NSCS on undergoing three distinct cyclic evolutions: (i) the free evolution of the NMR quadrupolar system and, by analogy with the evolution of the NMR quadrupolar system, that of (ii) single-mode and (iii) two-mode Bose-Einstein Condensate like system. By means of these analogies, we derive, through spin angular momentum operators, results equivalent to those presented in the literature for orbital angular momentum operators. The pseudo-NSCS description is a starting point to introduce the spin squeezed state and quantum metrology into nuclear spin systems of liquid crystal or solid matter.

Preparing Pseudo-Pure States in a Quadrupolar Spin System Using Optimal Control

Pseudo-pure state (PPS) preparation is crucial in nuclear magnetic resonance quantum computation. There have been some methods in spin-1/2 systems and a few attempts in quadrupolar spin systems. As optimal control via gradient ascent pulses engineering (GRAPE) has been widely used in quantum information science, we apply this technique to PPS preparation in quadrupolar spin systems. This approach shows an effective and fast quantum control method for both the state preparation and the realization of quantum gates in quadrupolar systems.

Concept of effective Hamiltonians for transitions in multi-level systems

Employing the concept of effective Hamiltonians, an analytical theory is introduced to describe transitions in a multi-level system in nuclear magnetic resonance (NMR) spectroscopy. Specifically, the discussion is centered towards the treatment of selective and non-selective excitations in static quadrupolar spin (I > 1/2) systems. To this end, effective radiofrequency (RF) Hamiltonians based on the spherical tensor formalism are proposed for describing transitions in both integral (I = 1, 2 and 3) and half-integral (I = 3/2, 5/2 and 7/2) quadrupolar spins. The optimum conditions desired for selective excitation in a multi-level system are derived pedagogically from first principles and presented through analytical expressions. Employing suitable model systems, the derived optimum conditions are substantiated through rigorous numerical simulations based on the spherical tensor formalism. The theory presented provides a framework for describing selective and non-selective RF pulses and could improve our understanding of multiple-pulse experiments involving quadrupolar nuclei.

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1/2 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1/2, are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover's algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3/2 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1/2 and quadrupolar spin 3/2 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.

ESTIMATION OF DOMAIN SIZE IN NANO-FERROELECTRICS FROM NMR T1 MEASUREMENTS

ABSTRACT The spin lattice relaxation of I = 3/2 quadrupolar spin system due to domain walls in order-disorder ferroelectrics has been studied and a general method is proposed for the measurement of domain width in nano ferroelectrics. Based on the fact that electric polarization undergoes spiral orientation as one moves from one domain to the other, it is assumed that at low temperatures the spins at and near domain walls undergo relaxation due to possible easy reorientation of electric polarization in domain walls even though such a relaxation in the main body of the domain has almost ceased. The spins present inside the domain undergo relaxation through transfer of magnetization to the domain walls through a spin diffusion process by nearest neighbour interaction. Rate equations for spin populations are formed by representing the ferroelectric domain by a one-dimensional chain of equidistant spins having dipolar coupling. Spin populations are calculated as a function of time for different ratios of quadrupolar to dipolar transition probabilities for a sample subjected to selective rf pulse. Expression for spin- lattice relaxation time T 1 is derived in terms of domain width and ratio of quadrupolar to dipolar transition probabilities. It is found that the domain width can be estimated provided the value of spin lattice relaxation time T 1 is known for the corresponding crystal with normal sized grains. The results are quite general and can be applied to any order disorder ferroelectric with nano sized domains and having spin I = 3/2 nuclei.

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.

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)).

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.

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.

Some aspects of spin-locking effect in nitrogen-14 quadrupolar spin-system

The following is a study of some aspects of the spin-locking effect in pure NQR. It was proved that the spin-locking effect similar to that obtained in NMR and based on the use of the frequency offset condition can be obtained in NQR. It was shown that the modified multi-pulse technique enable the observation of a long train of the spin-echo signals. The experimental results are presented for 4-cyanopyridine at room temperature.

Cross-polarisation method for improvement of 14N NQR signal detectability

This is a study of the cross-polarization effects in the case of 14N quadrupolar spin-system with a long spin–lattice relaxation time. Two important benefits of the cross-polarization technique were demonstrated for PETN: (i) a polarization transfer resulting in increased NQR single shot signal response and (ii) a dynamic reduction in recovery time of the NQR system allowing scan repetition on a much shorter timescale. It was proved that this technique can reduce the optimal waiting time between pulse sequences up to 60 times through a significant reduction of the relaxation time of the quadrupolar spin-system. All experiments were carried out at room temperature using spin-locking multi-pulse sequences and small external magnetic field.

Some aspects of steady-state of nitrogen-14 quadrupolar spin-system

The behaviour of nuclear quadrupole resonance (NQR) signal was studied after applying additional RF pulses to the spin-system which was previously prepared to be in the equilibrium or steady-state. The experiments revealed some peculiarities in the behaviour of the signals which are important for the understanding of the dynamic properties of the quadrupolar spin-system. The experimental results are presented for 4-cyanoperidine and sodium nitrite.

New opportunities for double rotation NMR of half-integer quadrupolar nuclei

A combined approach is presented which expands the applicability of double rotation (DOR) by overcoming its most prominent disadvantages: spinning stability and sensitivity. A new design using air-bearings for the inner rotor and a computer-assisted start-up procedure allows DOR operation over in principle unlimited time at outer rotor speeds of up to 2000 Hz. Sensitivity enhancement of the DOR experiment is achieved by applying amplitude-modulated adiabatic pulses such as the double frequency sweep (DFS) before pulse excitation. Repeating the DFS enhancement and signal readout several times without allowing for spin–lattice relaxation leads to sensitivity enhancements of a factor 3 for 27Al in various minerals. As a result, it becomes possible to study low sensitivity quadrupolar nuclei and various long duration 2D measurements can be performed routinely. Spinning is adequate to suppress residual homonuclear dipolar couplings in the spectral dimension of typical quadrupolar spin systems. In 2D-exchange spectroscopy, however, homonuclear correlation can still be established through dipolar–quadrupolar cross-terms.

Some Aspects of Dynamics of Nitrogen-14 Quadrupolar Spin-System

This is a study of the behaviour of nuclear quadrupole resonance (NQR) signals in the “observation windows” of multi-pulse sequence for a nitrogen-14 spin-system. Obtained results revealed steady state (SS) and spin echo (SE) components of the signal. The results contribute to the understanding the dynamic properties of the quadrupolar spin-system.

Multiple rotary echoes in nitrogen-14 quadrupolar spin-system

This is a study of the influence of multi-pulse sequences consisting of blocks of short-repetition pulses on the nitrogen-14 NQR spin-system. The experiment demonstrated that the application of such sequences generates multiple rotary echo signals in the effective field of the pulse sequence similar to those generated by conventional spin-locking multi-pulse sequences. The detected RE signals were analysed and the obtained results presented, adding to the understanding of the dynamic properties of the quadrupolar spin-system. The experimental results are obtained for polycrystalline NaNO 2.

Characterization of quantum algorithms by quantum process tomography using quadrupolar spins in solid-state nuclear magnetic resonance

NMR quantum computing with qubit systems represented by nuclear spins (I=12) in small molecules in liquids has led to the most successful experimental quantum information processors so far. We use the quadrupolar spin-32 sodium nuclei of a NaNO3 single crystal as a virtual two-qubit system. The large quadrupolar coupling in comparison with the environmental interactions and the usage of strongly modulating pulses allow us to manipulate the system fast enough and at the same time keeping the decoherence reasonably slow. The experimental challenge is to characterize the "calculation" behavior of the quantum processor by process tomography which is here adapted to the quadrupolar spin system. The results of a selection of quantum gates and algorithms are presented as well as a detailed analysis of experimental results.

Some aspects of quasi-steady state of nitrogen-14 quadrupolar spin-system

The behaviour of nuclear quadrupole resonance (NQR) signal was studied after applying one or more additional RF pulses to the spin-system which was previously prepared to be in the quasi-steady state. The experiments revealed some peculiarities in the behaviour of the signals which are important for the understanding of the dynamic properties of the quadrupolar spin-system. The experimental results are presented for polycrystalline NaNO 2.

Rotary echoes in nitrogen-14 quadrupolar spin-system

This is a study of the influence of the multi-pulse sequences consisting of one or more blocks of short-repetition phase alternated pulses on nitrogen-14 NQR spin-system. It was shown that these sequences permit detecting rotary echo signals in the effective field of the pulse sequence. Multiple rotary echoes were detected and analysed. The obtained results add to the understanding of dynamic properties of quadrupolar spin-system. Experimental results for polycrystalline NaNO 2 are presented.