Analysis of Spin Diffusion and Cross Correlation on the Net Nuclear Overhauser Effect in NMR

The effect of dipole–dipole cross correlations on the net nuclear Overhauser effect (NOE) has been analyzed here for realistic systems by extending the three-spin calculations to four and five spins in order to account for additional cross correlations and spin diffusion. These have been compared with the addition of leakage terms to the three-spin system. The additional spins enhance cross-correlation effects on one hand but on the other act as supplementary relaxation pathways for the magnetization to diffuse. This analysis shows that for a linear array of spins in the long-correlation limit, dipole–dipole cross correlations increase net NOE, while spin diffusion decreases it, and that the cumulative effect is a reduced effect of cross correlations. In other geometries and correlation limits, the effect of cross correlations on net NOE is generally small.     

Transverse magnetization transfer under planar mixing conditions in spin systems consisting of three coupled spins 1/2

Polarization transfer under planar mixing conditions is a widely used tool in modern NMR-experiments. In the case of two coupled spins 1/2 or a chain of three or more spins 1/2 with only nearest neighbor couplings, it is only possible to transfer a single magnetization component (longitudinal magnetization in the principle axis system of the planar coupling tensors). However, if all couplings in a three-spin system are non-zero, it turns out that all magnetization components can be efficiently transferred even under strictly planar mixing conditions. In this article a detailed theoretical analysis is presented based on analytical transverse coherence transfer functions and on the underlying commutator algebra. In addition, transverse magnetization transfer is demonstrated experimentally. The results show that in highly coupled spin systems, as for example in the case of partially aligned samples with many residual dipolar couplings, special care has to be taken to avoid phase distortions if planar mixing steps are used.     

Off-angle correlation spectroscopy applied to spin-1/2 and quadrupolar nuclei

A two-dimensional correlation experiment is described, in which homonuclear dipolar couplings are used to realize through-space magnetization exchange on spin-1/2 (³¹P) and on quadrupolar nuclei (²³Na and ¹¹B). In the detection period, Magic Angle Spinning is applied to enhance resolution, and the dipole couplings are re-introduced in the mixing period by spinning off the Magic Angle. The dependency of the exchange rates on the mixing time and the spinning angle is investigated. The influence of strong spin-locking during mixing is discussed, and shown in the spin-1/2 case to remove the dependence on chemical shift offset effects. For quadrupolar spins, the experiment yields information on the relative tensor orientations of the coupled quadrupoles. Applications to crystalline sodium aluminum diphosphate, sodium sulphite, and potassium borate glasses are shown.     

J-ONLY-TOCSY: efficient suppression of RDC-induced transfer in homonuclear TOCSY experiments using JESTER-1-derived multiple pulse sequences

The main purpose of homonuclear Hartmann-Hahn or TOCSY experiments is the assignment of spin systems based on efficient coherence transfer via scalar couplings. In partially aligned samples, however, magnetization is also transferred via residual dipolar couplings (RDCs) and therefore through space correlations can be observed in COSY and TOCSY experiments that make the unambiguous assignment of covalently bound spins impossible. In this article, we show that the JESTER-1 multiple pulse sequence, originally designed for broadband heteronuclear isotropic Hartmann-Hahn transfer, efficiently suppresses the homonuclear dipolar coupling Hamiltonian. This suppression can be enhanced even further by variation of the supercycling scheme. The application of the resulting element in homonuclear TOCSY periods results in coherence transfer via J-couplings only. As a consequence, the assignment of scalar coupled spin systems is also possible in partially aligned samples. The bandwidth of coherence transfer for the JESTER-1-derived sequences is comparable to existing TOCSY multiple pulse sequences. Results are demonstrated in theory and experiment.     

A simulation algorithm based on Bloch equations and product operator matrix: application to dipolar and scalar couplings

A product operator matrix is proposed to describe scalar couplings in liquid NMR. Combination of the product operator matrix and non-linear Bloch equations is employed to describe effects of chemical shift, translational diffusion, dipolar field, radiation damping, and relaxation in multiple spin systems with both scalar and dipolar couplings. A new simulation algorithm based on this approach is used to simulate NMR signals from dipolar field effects in the presence of scalar couplings. Several typical coupled spin systems with both intra-molecular scalar couplings and inter-molecular dipolar couplings are simulated. Monte Carlo methods are incorporated into simulations as well to analyze diffusion process in these complicated spin systems. The simulated results of diffusion and relaxation parameters and 2D NMR spectra are coincident with the experimental measurements, and agree with theoretical predictions as well. The simulation algorithm presented herein therefore provides a convenient means for designing pulse sequences and quantifying experimental results in complex coupled spin systems.     

Determining the relative sign and size of scalar and residual dipolar couplings in homonuclear two-spin systems

Based on the sign and amplitude of TOCSY transfer functions, it is possible to determine the relative sign and size of scalar and residual dipolar couplings in homonuclear spin systems consisting of two spins 1/2. The efficiency of different mixing sequences and different transfer functions is examined both theoretically and experimentally.     

Finite-temperature transitions in dipolar spin ice in a large magnetic field

We use Monte Carlo simulations to identify the mechanism that allows for phase transitions in dipolar spin ice to occur and survive for an applied magnetic field H much larger in strength than that of the spin-spin interactions. In the most generic and highest symmetry case, the spins on one out of four sublattices of the pyrochlore decouple from the total local exchange+dipolar+applied field. In the special case where H is aligned perfectly along the [110] crystallographic direction, spin chains perpendicular to H show a transition to q=X long-range order, which proceeds via a one- to three-dimensional crossover. We propose that these transitions are relevant to the origin of specific heat features observed in powder samples of the Dy2Ti2O7 spin ice material for H above 1 Tesla.     

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

Through the Jordan-Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called ``spin waves', which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.     

Rotational-resonance distance measurements in multi-spin systems

It is demonstrated that internuclear distances can be evaluated from rotational-resonance (RR) experiments in uniformly (13)C-labelled compounds. The errors in the obtained distances are less than 10% without the need to know any parameters of the spin system except the isotropic chemical shifts of all spins. We describe the multi-spin system with a simple fictitious spin-1/2 model. The influence of the couplings to the passive spins (J and dipolar coupling) is described by an empirical constant offset from the rotational-resonance condition. Using simulated data for a three-spin system, we show that the two-spin model describes the rotational-resonance transfer curves well as long as none of the passive spins is close to a rotational-resonance condition with one of the active spins. The usability of the two-spin model is demonstrated experimentally using a sample of acetylcholine perchlorate with labelling schemes of various levels of complexity. Doubly-, triply-, and fully labelled compounds lead to strongly varying RR polarization-transfer curves but the evaluated distances using the two-spin model are identical within the expected error limits and coincide with the distance from the X-ray structure. Rotational-resonance distance measurements in fully labelled compounds allow, in particular, the measurement of weak couplings in the presence of strong couplings.     

Dirac neutrino masses from generalized supersymmetry breaking

We demonstrate that Dirac neutrino masses in the experimentally preferred range are generated within supersymmetric gauge extensions of the standard model with a generalized supersymmetry breaking sector. If the superpotential neutrino Yukawa terms are forbidden by the gauge symmetry [such as a U(1)'], sub-eV scale effective Dirac mass terms can arise at tree level from hard supersymmetry breaking Yukawa couplings, or at one loop due to nonanalytic soft supersymmetry breaking trilinear scalar couplings. The radiative neutrino magnetic and electric dipole moments vanish at one-loop order.     

Geometry of multiple-spin systems as reflected in 13C-{1H} dipolar spectra measured at Lee-Goldburg cross-polarization

Theoretical calculation and analysis of (13)C-{(1)H} dipolar spectra of small-size spin clusters is presented. Dipolar spectra simulated using the time-independent average Hamiltonian are compared with the dipolar profiles obtained by 2D and 3D (1)H-(13)C correlation experiments employing Lee-Goldburg off-resonance cross-polarization (LG-CP). It is demonstrated that the structural parameters such as interatomic distances as well as mutual orientation of internuclear vectors can be derived from the dipolar profiles of simple spin clusters. Simplified analysis of the dipolar spectra based on isolated-like spin-pair approach can be used only if interacting spin cluster is reduced to the three-spin system in which the angle between both internuclear vectors ranges from 45 degrees to 135 degrees . For other local arrangements of spin systems the produced dipolar spectra must be analyzed with high caution. Contributions of all interacting spins to dipolar evolution of (13)C magnetization are mutually mixed and cannot be easily separated. However, simplification of the dipolar spectra is achieved by selective excitation. Enhanced selectivity of LG-CP transfer due to the initial (1)H chemical-shift-evolution period makes it possible to construct the dipolar spectra from (1)H-(13)C cross-peak intensities for every detected (1)H-(13)C spin-pair. Consequently, isolated-like spin pair evolution of the detected (1)H-(13)C coherence dominates to the resulting dipolar profile, while the influence of other interacting spins is suppressed. However, this suppression is not quite complete and analysis of the selective dipolar spectra based on isolated-like spin-pair approach cannot be used generally. Especially evolution of long-range (1)H-(13)C coherence is still significantly affected by spin states of other coupled hydrogen atoms.     

Field-dependent nuclear relaxation of spins 1/2 induced by dipole-dipole couplings to quadrupole spins: LaF3 crystals as an example

A general theory of spin-lattice nuclear relaxation of spins I=1/2 caused by dipole-dipole couplings to quadrupole spins S1, characterized by a non-zero averaged (static) quadrupole coupling, is presented. In multispin systems containing quadrupolar and dipolar nuclei, transitions of spins 1/2 leading to their relaxation are associated through dipole-dipole couplings with certain transitions of quadrupole spins. The averaged quadrupole coupling attributes to the energy level structure of the quadrupole spin and influences in this manner relaxation processes of the spin 1/2. Typically, quadrupole spins exhibit also a complex multiexponential relaxation sensed by the dipolar spin as an additional modulation of the mutual dipole-dipole coupling. The proposed model includes both effects and is valid for an arbitrary magnetic field and an arbitrary quadrupole spin quantum number. The theory is applied to interpret fluorine relaxation profiles in LaF3 ionic crystals. The obtained results are compared with predictions of the 'classical' Solomon relaxation theory.     

Comment on “Geometry effect on the magnetic ordering of geometrically frustrated rectangular and triangular magnets” [Phys. Lett. A 375 (13) (2011) 1548]

In a recent letter Li et al. [Phys. Lett. A 375 (2011) 1548] have investigated some geometric effects on the ordering of artificial spin ice materials. They have argued that the system ground-state undergoes a transition when the lattice spacing in one direction is sufficiently larger than in the other. Their results were obtained by evaluating the dipolar interactions using a restrict set of spin pairs. In this comment we show that by taking into account all the dipolar interactions among the spins no ground-state transition is observed.     

Multiple quantum spin counting techniques with quadrupolar nuclei

Phase incremented and continuous irradiation multiple spin correlation methods are applied to spin [Formula: see text] nuclei with small quadrupole couplings such as (7)Li in LiCl and are shown to successfully produce a coherently coupled dipolar spin network. Application to the analogous Na salt shows successful spin correlation evolving at a slower rate due to the weaker homonuclear dipolar coupling strength between Na nuclei. The results are analysed using a statistical approach. Spin counting is non-trivial as not only multiple quantum coherences between spins are generated but also within the quadrupolar spin levels. Na(2)C(2)O(4) is investigated as a material with non-negligible quadrupole coupling and it is in this limit that the spin correlation techniques are found to break down.     

Methylene spectral editing in solid-state 13C NMR by three-spin coherence selection

A robust new solid-state nuclear magnetic resonance (NMR) method for selecting CH2 signals in magic-angle spinning (MAS) 13C NMR spectra is presented. Heteronuclear dipolar evolution for a duration of 0.043 ms, under MREV-8 homonuclear proton decoupling, converts 13C magnetization of CH2 groups into two- and three-spin coherences. The CH2 selection in the SIJ (C H H) spin system is based on the three-spin coherence S(x)I(z)J(z), which is distinguished from 13C magnetization (S(x)) by a 1H 0 degrees/90 degrees pulse consisting of two 45 degrees pulses. The two-spin coherences of the type S(y)I(z) are removed by a 13C 90 degrees x-pulse. The three-spin coherence is reconverted into magnetization during the remainder of the rotation period, still under MREV-8 decoupling. The required elimination of 13C chemical-shift precession is achieved by a prefocusing 180 degrees pulse bracketed by two rotation periods. The selection of the desired three-spin coherence has an efficiency of 13% theoretically and of 8% experimentally relative to the standard CP/MAS spectrum. However, long-range couplings also produce some three-spin coherences of methine (CH) carbons. Therefore, the length of the 13C pulse flipping the two-spin coherences is increased by 12% to slightly invert the CH signals arising from two-spin coherences and thus cancel the signal from long-range three-spin coherences. The signal intensity in this cleaner spectrum is 6% relative to the regular CP/TOSS spectrum. The only residual signal is from methyl groups, which are suppressed at least sixfold relative to the CH2 peaks. The experiment is demonstrated on cholesteryl acetate and applied to two humic acids.     

Quantum competitions between the effects of the interlayer exchange couplings and the magnetically structural symmetry in a four-layer ferrimagnetic superlattice

The magnon energy spectra, the sublayer magnetization and the quantum fluctuations in a ferrimagnetic superlattice consisting of four different magnetic sublayers are studied by employing the linear spin-wave approach and Green's function technique. The effects of the interlayer exchange couplings and the spin quantum numbers on the sublayer magnetization and the quantum fluctuations of the systems are discussed for three different spin configurations. The roles of quantum competitions among the interlayer exchange couplings and the symmetry of the different spin configurations have been understood. The magnetizations of some sublayers increase monotonously, while those of others can exhibit their maximum, and the quantum fluctuations of the whole superlattice system can show a minimum when one of the antiferromagnetic interlayer exchange couplings increases. This is due to the quantum competition/transmission of effects of the interlayer exchange couplings. When the spin quantum number of sublayers varies, the system goes through from a quantum region of small spin numbers to a classical region of large spin numbers. The quantum fluctuations of the system exhibit a maximum as a function of the spin quantum number of a sublayer, which is related with higher symmetry of the system. It belongs to the type III Shubnikov group of magnetic groups. This magnetically structural symmetry consists of not only the symmetry of space group, but also the symmetry of the direction and strength of spins.     

NMR relaxation in multipolar AX systems under spin locking conditions

A relaxation matrix has been calculated for a multipolar AX spin system under the on-resonance spin-locking condition. Auto- and cross-correlation terms between dipolar, quadrupolar, and CSA interactions are considered. It is shown that the spin-lock leads to many relaxation pathways being blocked, resulting in a considerably simplified relaxation network. The presence of spectral densities at zero frequency, associated with locked nuclei, allows efficient relaxation also in the absence of fast molecular motions.     

Kagomé ice state in the dipolar spin ice Dy2Ti2O7

We have investigated the kagomé ice behavior of the dipolar spin-ice compound Dy2Ti2O7 in a magnetic field along a [111] direction using neutron scattering and Monte Carlo simulations. The spin correlations show that the kagomé ice behavior predicted for the nearest-neighbor interacting model, where the field induces dimensional reduction and spins are frustrated in each two-dimensional kagomé lattice, occurs in the dipole interacting system. The spins freeze at low temperatures within the macroscopically degenerate ground states of the nearest-neighbor model.     

Theoretical Study of Dipolar Relaxation of Coupled Nuclear Spins at Variable Magnetic Field

A theoretical study was made of magnetic field-dependent dipolar relaxation in two- and three-spin systems. The results for the nuclear magnetic relaxation dispersion (NMRD) curves were compared with those for the simpler model of fluctuating local fields. For both models it was found that at low fields spins tend to relax with a common T ₁-relaxation time. Sharp features in the NMRD curves coming from nuclear spin level anti-crossings are also predicted by both models. However, the simple model fails to describe the behavior of so-called long-lived spin states (LLS). We have studied the LLS as function of magnetic field and molecular geometry and simulated experimental results for the LLS in histidine amino acid obtained at the laboratory of Prof. H.-M. Vieth (Free University Berlin, Germany). In addition, we described polarization transfer in a three-spin system where two spins are protons, which are initially hyperpolarized by para-hydrogen induced polarization (PHIP), while the third spin is a spin ½ hetero-nucleus, which acquires polarization in the course of cross-relaxation.