Slow-motion line-shapes

The electron spin resonance line-shape of a tumbling radical is treated by a projection operator formalism that enables analytical expressions to be obtained. These are valid from the fast-motion limit to well into the slowmotion region so long as non-secular terms may be ignored.     

Spin dynamic simulations of solid effect DNP: the role of the relaxation superoperator

Relaxation plays a crucial role in the spin dynamics of dynamic nuclear polarisation. We review here two different strategies that have recently been used to incorporate relaxation in models to predict the spin dynamics of solid effect dynamic nuclear polarisation. A detailed explanation is provided on how the Lindblad–Kossakowski form of the master equation can be used to describe relaxation in a spin system. Fluctuations of the spin interactions with the environment as a cause of relaxation are discussed and it is demonstrated how the relaxation superoperator acting in Liouville space on the density operator can be derived in the Lindblad–Kossakowski form by averaging out non-secular terms in an appropriate interaction frame. Furthermore we provide a formalism for the derivation of the relaxation superoperator starting with a choice of a basis set in Hilbert space. We show that the differences in the prediction of the nuclear polarisation dynamics that are found for certain parameter choices arise from the use of different interaction frames in the two different strategies. In addition, we provide a summary of different relaxation mechanisms that need to be considered to obtain more realistic spin dynamic simulations of solid effect dynamic nuclear polarisation.     

Powder MAS NMR lineshapes of quadrupolar nuclei in the presence of second-order quadrupole interaction

We derive a complete analytical solution for the powder magic angle spinning (MAS) nuclear magnetic resonance (NMR) lineshape in the presence of second-order quadrupole interaction, considering a radiofrequency (rf) pulse of finite width, a finite MAS frequency, and a non-zero asymmetry parameter. I_x is calculated using two approaches. The first applies time-dependent perturbation theory in the presence of the rf pulse and stationary perturbation theory (SPT) in its absence. The second is based on the Magnus expansion of the density matrix in the interaction representation during the pulse and SPT in its absence. We solve the problem in the laboratory frame using the properties of the Fourier transform and spin operators. Diagonalisation is not required. Both approaches agree well with each other under all conditions and also with the transition probability approach for the central transition. The Magnus expansion exists at all times and the effect of the non-secular terms is negligible. We describe an analytical method of averaging I_x over the Euler angles and simulate the ¹¹B MAS NMR lineshapes for crystalline and vitreous B₂O₃. A critical analysis is given of all earlier calculations of the MAS NMR lineshape.     

CP/MAS of quadrupolar S = 3/2 nuclei.

The spin dynamics of Hartmann-Hahn cross-polarization from I = 1/2 to quadrupolar S = 3/2 nuclei is investigated. A density-matrix model applicable to cases where the quadrupole frequency vQ is much larger than the rf amplitude v1S of the S spins, predicts the time development of the spin state of an isolated I, S spin pair in static situations and in three distinct cases of magic-angle-spinning speed vR. These cases are characterized as slow, intermediate, and fast, depending on the magnitude of the parameter alpha = v1S2/vQvR relative to the intermediate value of 0.4. The model predictions are supported by numerical simulations. The polarization transfer from I to S is efficient in the limits of slow and fast sample spinning. When alpha < 1, the Hartmann-Hahn condition is shifted over once or twice vR. When the spinning rate is intermediate, poor spin-locking of the quadrupolar spins prevents the accumulation of a cross-polarization signal and, in addition, depletes the spin-locked I magnetization. Experimental CP/MAS data obtained in NaOH show that the concepts developed for isolated spin pairs are also applicable to cross-polarization in a strongly coupled multi-spin system.     

Quench dynamics in spin crossover induced by high pressure

In this paper we have analytically and numerically studied the dynamics of spin crossover induced by time-dependent pressure. We show that quasi static pressure, with a slow dependence on time, yields a spin crossover leading to transition from the high spin (HS) quantum system state to the low spin (LS) state. However, quench dynamics under shockwave load are more complicated. The final state of the system depends on the amplitude and pulse velocity, resulting in the mixture of the HS and LS states.     

Microwave-assisted switching of microscopic rings: correlation between nonlinear spin dynamics and critical microwave fields

We have studied the spin dynamics of microscopic permalloy rings at GHz frequencies. Increasing the irradiation power, we observe first nonlinear spin dynamics and second microwave-assisted switching (MAS). We explore the MAS phase diagram as a function of microwave power and frequency f and, in particular, extract the critical microwave field hc(f). Its frequency dependence reflects characteristic eigenfrequencies from both the linear and nonlinear spin-wave spectrum. By comparing hc(f) with the different susceptibilities, we gain insight into the microscopic processes which might be the basis of a predictive theory of MAS.     

Two dimensional XY type magnetism in intercalated graphite: an elastic and inelastic neutron scattering study

Stage-2 CoCl₂-GIC approximates a two-dimensional easy-plane (XY) ferromagnet on a triangular lattice. It has been found in prior work to order in two steps, with the intermediate phase showing long-ranged ferromagnetic correlations within the intercalate plane, but no correlations between neighboring planes. We have probed the wave vector and temperature dependence of the static and dynamic spin correlations in detail, including measurements of the critical scattering, the quasielastic scattering from vortex diffusion and the spin wave excitations with and without an external magnetic field. Some of the predictions for a Kosterlitz-Thouless type transition are met in this compound, at least qualitatively, including an apparent jump in the spin stiffness at the critical point and the existence of a diffusive central peak in the scattering function possibly originating from vortex autocorrelations. However, there are some inconsistencies between our observations and recent analytical studies as well as Monte Carlo-molecular dynamics simulations of the vortex dynamics that prevent unambigous assignment of the upper critical temperature as a vortex-binding transition.     

Theoretical and experimental assessment of single- and multiple-quantum cross-polarization in solid state NMR

Continuous wave cross-polarization (CP) NMR experiments with magic angle spinning (MAS) are reviewed for the case of isolated spin pairs I-S, with spin quantum numbers I = ½ and S ½ (1/2, 3/2, …). For two spin-1/2 nuclei, the Hartmann-Hahn matching conditions are examined at various sample rotation rates ν_R, especially with regard to off-resonance behaviour. In addition to signal enhancement, the CPMAS experiment can be used for the selective determination of inter-nuclear distances between spin-1/2 nuclei. Theoretical examination of the CP transfers to single-quantum (1Q-CPMAS) and multiple-quantum (MQ-CPMAS) levels of quadrupolar nuclei is presented. Simple analytical formulae describing the Hartmann-Hahn matching under various experimental conditions are verified using computer simulations of the spin density matrix under MAS, and the experimental data. The strategies for the most efficient acquisition of 1Q-CPMAS and MQ-CPMAS spectra are extensively discussed.     

An ensemble of paired spin(-1/2) nuclei in a rotating solid: Polarization evolution and NMR spectrum in a wobbling frame

The evolution of the magnetic polarization of an ensemble of paired spin(-1/2) nuclei in an MAS NMR (nuclear magnetic resonance) experiment and the induced spectrum are described theoretically by means of a Liouville-von Neumann equation representation in a wobbling rotating frame in combination with the averaged Hamiltonian theory. In this method, the effect of a high-intensity external static magnetic field and the effects of the leftover interaction components of the Hamiltonian that commute with the approximate Hamiltonian are taken into account simultaneously and equivalently. This method reproduces details that really exist in the recorded spectra, caused by secular terms in the Hamiltonian, which might otherwise be smoothed out owing to the approximate treatment of the effects of the secular terms. Complete analytical expressions, which describe the whole NMR spectrum including the rotational sideband sets, and which consider all the relevant intermolecular interactions, are obtained.     

Dynamical and static spin conductivities in the Heisenberg model on honeycomb lattice: The effects of magnetic long range ordering

We have studied both dynamical and static spin conductivities of Heisenberg antiferromagnet on honeycomb lattice in the presence of a magnetic long range ordering. The effects of spatial anisotropy as weak Dzyaloshinskii–Moriya interaction and next nearest neighbor exchange coupling on the behaviors of conductivities are discussed. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. Using Holstein–Primakoff bosonic transformations, the behaviors of spin transport properties have been studied by means of excitation spectrum of mapped bosonic gas. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various Dzyaloshinskii–Moriya interaction strengths. Furthermore we have studied the frequency dependence of dynamical spin conductivity for various Dzyaloshinskii–Moriya interaction strengths and different next nearest neighbor coupling constants. We find that the height of peak in the temperature dependence of static spin conductivity increases upon increasing the anisotropy parameter. The static spin conductivity is found to be monotonically increasing with anisotropy parameter due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different next nearest neighbor coupling constants.     

Analytic perturbation functions for static interactions in perturbed angular correlations of ®rays

Analytic expressions are presented for powder and single crystal perturbation functions in ®–®-angular correlations for static interactions. Magnetic dipole interactions for arbitrary spin as well as non-axially symmetric electric quadrupole interactions up to spin 5/2 are treated. Symmetry properties of all matrices involved are discussed, as well as their consequences for the perturbation functions. A new complementarity rule for powder perturbation functions is presented.     

Application of the Floquet theory to multiple quantum NMR of dipolar-coupled multi-spin systems under magic angle spinning

A new analytical Liouville-space representation of the time-propagator under magic angle spinning (MAS) is introduced using the formalized quantum Floquet theory. This approach has the advantage that it is applicable to the analysis of any type of NMR experiment where MAS is combined with multiple-pulse excitation. General relationships describing the spectral parameters in multiple-quantum (MQ) MAS spectra are derived in this representation. Their use is illustrated with an application to double-quantum (DQ) NMR spectra of dipolar-coupled multi-spin systems. Corresponding to the separation of the MAS time-propagator into a rotor modulated and a dephasing component, two distinct mechanisms for DQ excitation are identified. One of them exploits the rotor-modulated component to excite DQ coherences through dipolar-recoupling techniques, which are familiar for spin pairs. Analytical expressions of the integral intensities and linewidths in the resulting DQ sideband pattern are derived in the form of power series expansions of the inverse rotor frequency, of which coefficients depend on structural parameters. In a multi-spin system they can most reliably be extracted in the fast spinning regime. The other mechanism exploits the dephasing component, which is characteristic to multi-spin systems only. This is shown to give rise to DQ coherences by free evolution at full rotor periods. The possibility to exploit it for selective excitation of higher order MQ coherences is discussed. In either case, the dephasing component also leads to residual broadening. The main results of the theoretical developments are demonstrated experimentally on adamantane.     

固体核磁共振魔角旋转条件下的定量交叉极化技术(英文)

交叉极化与魔角旋转结合（CP/MAS）的方法已经成为增强固体核磁共振（NMR）检测灵敏度最重要的技术之一.CP/MAS技术的应用大大提高了固体NMR谱图的采集效率.然而,I-S偶极耦合作用、旋转坐标系下的自旋-晶格弛豫、分子运动,以及样品中丰核的分布情况等因素,通常会导致CP/MAS谱图失去定量作用.近年来,多个研究组通过改进或者设计新型固体NMR脉冲序列,获得了基于CP的可用于定量分析的固体NMR谱图.本综述首先简要介绍了CP及CP动力学,随后介绍了一系列基于CP的定量固体NMR信号增强技术,具体包括ramped-amplitude CP（RAMP-CP）、multiple-contact CP、quantification of CP（QCP）、Lee-Goldburg frequency modulated CP（LG-FMCP）和quantitative CP（QUCP）.     

CP MAS Kinetics Study of Ionic Liquids Confined in Mesoporous Silica: Convergence of Non-Classical and Classical Spin Coupling Models

The high data point density measurements of ¹H→¹¹B cross-polarization (CP) kinetics upon magic-angle spinning (MAS) of [bmim][BF₄] confined in mesoporous SBA-15 and MCM-41 were carried out. The complex shaped ¹¹B CP MAS signals were observed in both silica and decomposed into two Lorentz components. This points towards the possibility of bimodal distribution of [bmim][BF₄] in the studied confinements. The convergence of classical and non-classical spin coupling models was deduced processing CP kinetic curves. A good fit of the theoretical curves to the experimental data was achieved using both models without any non-random deviations between theory and experiment to appear. The convergence of spin coupling models was discussed in terms of relatively high mobility of BF₄ ^? anion respect to the cation and the dynamics of anions in pores. These factors delete the borders between spin clusters. The spin diffusion along the pore surfaces in MCM-41 is more than twice faster than in SBA-15.     

Microheterogeneity in phenyl group modified inorganic/organic hybrid gels after aerosol drying or slow solvent evaporation

Sol-gel systems were prepared by co-hydrolysis and co-condensation of tetraethoxysilane (TEOS) and phenyltriethoxysilane (PhTES). The sols were transferred into silica gels by Evaporation Induced Self-Assembly (EISA) or Aerosol Assisted Self-Assembly (AASA) using a laboratory spray-dryer. The structural properties such as porosity and homogeneity/microheterogeneity of these different systems are compared by N(2) sorption measurements, thermal analysis (TG, DTG and DTA), (29)Si MAS NMR and (29)Si{(1)H} CP MAS NMR. The cross polarization of the AASA gels can be described with the conventional I-S dynamics of a homogeneous proton spin bath. The EISA gels are heterogeneous, and the I-I(*)-S model, or a bimodal I-S model, was employed for the simulation of CP dynamics. Microheterogeneities are observed by (1)H-(29)Si cross polarization on an EISA sample, whereas rapid drying (AASA) transfers the corresponding sol into homogeneous xerogels. The EISA gels are microporous after calcination at 923 K, and the AASA gels are dense.     

Sensitivity enhancement of the central-transition signal of half-integer spin quadrupolar nuclei in solid-state NMR: features of multiple fast amplitude-modulated pulse transfer

Sensitivity enhancement of solid-state NMR spectrum of half-integer spin quadrupolar nuclei under both magic-angle spinning (MAS) and static cases has been demonstrated by transferring polarisation associated with satellite transitions to the central m=-1/2-->1/2 transition with suitably modulated radio-frequency pulse schemes. It has been shown that after the application of such enhancement schemes, there still remains polarisation in the satellite transitions that can be transferred to the central transition. This polarisation is available without having to wait for the spin system to return to thermal equilibrium. We demonstrate here the additional sensitivity enhancement obtained by making use of this remaining polarisation with fast amplitude-modulated (FAM) pulse schemes under both MAS and static conditions on a spin-3/2 and a spin-5/2 system. Considerable signal enhancement is obtained with the application of the multiple FAM sequence, denoted as m-FAM. We also report here some of the salient features of these multiple FAM sequences with respect to the nutation frequency of the pulses and the spinning frequency.     

Phase Coherence and Spin Squeezing in One-Axis Twisting Model with Decay

We investigate phase coherence and spin squeezing of a collective spin governed by one-axis twisting Hamiltonian with decay. Here we are interested in the dependence of phase coherence and spin squeezing parameter on the decay. The analytical expressions of phase coherence and spin squeezing parameter are obtained. The stronger decay can induce a stronger spin squeezing, and the squeezing can maintain a longer time interval. Moreover, more squeezing can be achieved by increasing the number of particles.     

固体中13C CP/MAS谱编辑一些改进

本文将基本的谱编辑脉冲序列与消旋转边带的TOSS脉冲序列联用,可以实现强磁场下¹³C CP/MAS谱编辑.通常,固体中非质子化碳与甲基碳的自旋晶格弛豫时间差别很大,此差别可作为谱编辑过程中区分它们的一条附加判据.对具有复杂分子结构的体系,此判据的作用尤其重要.文中的实例将表明:一个完整的¹³C CP/MAS谱编辑一般可通过SCPTOSS谱(短接触时间交叉极化谱);SCPPITOSS (短接触时间交叉极化极化反转)谱,LCPDTOSS (长接触时间交叉极化及去极化)谱及部分弛豫的LCPDTOSS谱适当组合而得到.     

Nonlinear oscillations of magnetization for ferromagnetic particles in the vortex state and their ordered arrays

The dynamics of magnetization oscillations with a considerable amplitude and a radial symmetry in small ferromagnetic particles in the form of a thin disk with a magnetic vortex has been investigated. The collective variables that describe radially symmetric oscillations of the magnetization dynamics for particles in the vortex state are introduced, and the dependence of the particle energy is studied as a function of these variables. The analytical expressions describing the frequency of magnetization oscillations with a radial symmetry, including nonlinear oscillations, are derived using the collective variables. It is shown that the presence of a magnetic field oriented perpendicular to the particle plane reduces the oscillation frequency and can lead to hybridization of this mode with other modes of spin oscillations, including the mode of translational oscillations of the vortex core. The soliton solutions describing the propagation of collective oscillations along the chain of magnetic particles are found.