Electron spin-echo experiments in photo-excited triplet states in an external magnetic field

Electron spin-echo experiments in the photo-excited triplet states of quinoxaline-d₆ and naphthalene-d₈ at 1·2 K in an external magnetic field are presented. These include two-pulse Hahn echoes, three-pulse stimulated echoes and Carr-Purcell pulse-echo trains. The decay of the Hahn and stimulated echoes as a function of pulse interval yields measures of the spin relaxation times. Furthermore, the Hahn echo is used to obtain E.P.R. line shapes and the dynamics of the triplet sublevel populations. The angular dependence of the Hahn echo is also investigated. The Hahn echo decay time and decay modulation suggest the kind of role played by nuclear spins in the loss of electron spin phase coherence. Some promising characteristics of the pulse method are discussed.     

Observation of coherent oscillations in a single electron spin

Rabi nutations and Hahn echo modulation of a single electron spin in a single defect center have been observed. The coherent evolution of the spin quantum state is followed via optical detection of the spin state. Coherence times up to several microseconds at room temperature have been measured. Optical excitation of the spin states leads to decoherence. Quantum beats between electron spin transitions in a single spin Hahn echo experiment are observed. A closer analysis reveals that beats also result from the hyperfine coupling of the electron spin to a single 14N nuclear spin. The results are analyzed in terms of a density matrix approach of an electron spin interacting with two oscillating fields.     

Characterization of ZnO and Zn0.95Co0.05O prepared by sol-gel method using PAC spectroscopy

We report on the first NMR study of ⁷³Ge nuclear spin decoherence in germanium single crystals with different abundance of the ⁷³Ge isotope. Hahn echo decays are well fit by a superposition of two exponentials. The deviation from the single exponential is more pronounced in the more spin-diluted sample, causing long-lived echoes. We show that the decay of these echoes becomes slower with the reduction of ⁷³Ge abundance and is therefore caused by dipole–dipole interaction, reflecting the fundamental decoherence process in the spin system. The fast decay at the beginning of the relaxation process is shown to be mainly caused by the quadrupole interaction. Our experimental findings are supported by the calculations of Hahn echo decays in the germanium crystals under study. Quite good agreement between the theory and experiment is demonstrated.     

Homonuclear vanadium-51 dipolar couplings in inorganic solids obtained via hahn spin echo decay NMR spectroscopy

Dipolar dephasing of the magnetization following a Hahn spin echo pulse sequence potentially provides a quantitative means for determining the dipolar second moment in solids. In this work, the possibility of employing Hahn spin echo decay spectroscopy to obtain quantitative ⁵¹V–⁵¹V dipolar second moments is explored. Theoretical spin echo response curves are compared to experimental ones for a collection of crystalline vanadium-containing compounds. This work suggests that ⁵¹V dipolar second moments can be obtained by selectively exciting the central m = 1/2 → −1/2 by a Hahn echo sequence for vanadate compounds with line broadening no greater than approximately 220 ppm. For vanadates with greater broadening of the central transition due to chemical shift, second-order quadrupolar, and dipolar interactions, off-resonance effects lead to an oscillatory time dependence of the spin echo. Experimentally determined second moments of the normalized echo decay intensities lie within 10–33% of the calculated values if the second moments are extrapolated to zero evolution time due to the time scale dependence of spin exchange among neighboring vanadium nuclei. Alternatively, the second moments can be obtained to within 10–25% of the calculated values if the broadening of the central transition due to chemical shift and second-order quadrupolar effects can be estimated.     

Long-lived NMR echoes in solids

A new type of long-lived NMR echo in solids with homogeneously broadened dipolar spectra is discussed. The echo can be generated by a simple two-pulse Hahn sequence in solid samples, where dipolar-coupled nuclei have different chemical shifts. We present general considerations and simple theoretical models which explain some features of this phenomenon.     

Phosphorus-31 solid-state nmr in high-field gradients: prospects for imaging bone using the long echo-train summation technique (LETS)

Stray-field techniques are reported for 31P studies of solids for a variety of compounds including bone, bone meal and calcium hydroxyapatite. Long Hahn echo trains produced by the application of many pulses were used as in the long echo-train summation technique. Double-resonance enhancements of 31P by use of both direct and indirect experiments were attempted on a sample of NH4PF6:31P[19F] double resonance produced, at most, a 26% increase in the initial level of the 31P echo signal.     

Unilateral NMR study of a XVI century wall painted

Wall paintings in the XVI century Serra Chapel in the "Chiesa di Nostra Signora del Sacro Cuore" Rome, have been studied using unilateral NMR. In order to map the distribution of moisture content in the wall painted, a large number of Hahn echo measurements, covering large areas of the wall painting were performed. Because the intensity of the Hahn echo is proportional to the amount of moisture in the area under study, the experimental data were transformed into 2D gradient colour maps which allowed an easy visualization of the moisture content of the wall. The state of conservation of the wall painting was monitored using T2 measurements specially with regards to outcropping salt.     

Influence of High Orientational Order on the Shape of the Echo Response from a Hahn Pulse Sequence

The amplitude modulations in the simulations of the Hahn echo responses from cholestane spin labels in samples characterized by a high degree of orientational order are shown to arise from the use of “soft” pulses. Soft pulses have a limited spectral range and cover only a small portion of the CW-ESR spectra, so that not all the spins are on-resonance. The magnetization vectors of the off-resonance spins only partially tilted away from the laboratoryzaxis, the direction of the applied static magnetic field. They thus contribute oscillating components to the magnetization in thexyplane. The contribution from the off-resonance spins to the Hahn echo formation is significant in highly oriented samples, but cancels out in samples exhibiting a small degree of order. Experimental echo responses obtained from CSL molecules embedded in rigid matrices of eggPC bilayers and the liquid crystalline materials ZLI and MBBA confirm the theoretical predictions.     

三种测量橡胶交联密度的核磁共振方法比较

核磁共振（NMR）技术已经成为测量橡胶交联密度的一种常用技术手段．该文探讨了用于测量橡胶交联密度的三种NMR方法：¹H双量子（DQ）NMR、¹H Hahn回波和¹H CPMG回波,讨论了这些方法测量值差异的来源．在此基础上进一步研究了¹H CPMG回波方法中回波时间对测量值的影响,探讨了改善¹H CPMG回波方法的方案．     

Lattice QCD calculations for the physical equation of state

In this report we consider the numerical simulations at finite temperature using lattice QCD data for the computation of the thermodynamical quantities including the pressure, energy density and the entropy density. These physical quantities can be related to the equation of state for quarks and gluons. We shall apply the lattice data to the evaluation of the specific structure of the gluon and quark condensates at finite temperature in relation to the deconfinement and chiral phase transitions. Finally we mention the quantum nature of the phases at lower temperatures.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

Decoherence in a two-level system coupled to a fermion environment with phase transitions

The decoherence process characterized by Loschmidt echo (LE) in a two-level system dephasingly coupled to a fermion environment with phase transitions is studied in this Letter. The results show that the LE of the two-level system may act as a witness of the environment's phase transitions, which is similar to the relation between quantum phase transitions and the LE.     

Concentration and temperature dependence of diluent dynamics studied by line shape experiments on a phosphate ester in polycarbonate

³¹P Hahn spin echo line shape and proton line shape experiments are reported on bisphenol A polycarbonate (BPAPC)-tris(2-ethylhexyl)phosphate (TOP) systems to study the concentration and temperature dependence of the local dynamics. In an earlier ³¹P line shape study a lattice model was presented as a framework to interpret the plasticization and antiplasticization behavior of the diluent based on a fractional population given by the type of nearest neighbor contacts in the mixed polymer-diluent glass. In this study, ³¹P spin echo line shapes of BPAPC, with 5%, 10% and 15% TOP, which monitor the diluent dynamics, at different temperatures and echo delay times are simulated in terms of fast- and slow-moving components, and the resulting fractional populations are compared with that predicted by the lattice model. Comparisons with the lattice model calculations are also made in the simulation of the ¹H line shapes on BPAPC with 5% and 10% TOP, which probes both the polymer and diluent dynamics, and on BPAPC with 5% and 10% perdeuterated trioctylphosphate (DTOP), which detects only the polymer motion. Fairly good line shape simulations and agreement between the lattice model and the fitting results at low diluent concentrations are obtained in all cases. Restricted cone motion best describes the slow-moving component in the ³¹P line shape fittings. For the fast component, rotational Brownian diffusion with a distribution of correlation times corresponding to a stretched exponential function is used. An activation energy E_a of 56 kJ/mol and an exponent of 0.7 for the fractional exponential correlation function are obtained and used to calculate the mechanical loss peak which was compared with the experimental loss data. The plateau character of the fractional population as a function of temperature can also be interpreted and understood in terms of the lattice model.     

Anomalous pulse angle dependence of the single and double quantum echoes in a photoinduced spin-correlated coupled radical pair

In this work the response of a spin-correlated coupled radical pair to the sequence flash-t-P _ζ-τ-P _2ζ-T is investigated. For the theoretical analysis, the density operator formalism is used. Analytical expressions are derived for the electron spin single (SQ ESE) and double-quantum echoes (DQ ESE) as a function of pulse flip angle and singlet-triplet mixing angle. To illustrate the theoretical results, computer simulations are presented. In the limit of weak coupling, the “out-of-phase” SQ ESE is shown to be of a pure two-spin order having the maximal amplitude for the flip angle of 65.9°. The echo following the Hahn sequence vanishes in the same limit. This confirms the theoretical result already presented in the literature. However, the more general analysis shows that outside the weak coupling approximation the Hahn echo is of purely one-spin order, whereas the echo following the flash-t-P _ζ-τ-P _2ζ-t sequence has its maximal amplitude for the flip angle of 75° and the singlet-triplet mixing angle of 27°. The “in-phase” single- and double-quantum echoes are shown to vanish due to averaging out, within the electron spin resonance spectrometer deadtime, of contributions modulated with the sum and difference of the zero-quantum beat frequency and the frequency due to the spin-spin interaction within the pair. The calculated out-of-phase DQ ESE signal is inverted with respect to the out-of-phase SQ ESE and has only the half of its amplitude. The DQ ESE vanishes for the Hahn sequence. The echo has maximal amplitude in the weak-coupling limit for the flip angle of 65.9°. In contradiction to the analytical result previously published, the out-of-phase DQ ESE does not vanish for long τ and large zero-quantum-beat frequency.     

F/Si distance determination in fluoride-containing octadecasil by Hartmann–Hahn cross-polarization under fast magic-angle spinning

¹⁹F/²⁹Si Hartmann–Hahn continuous wave cross-polarization (CP) has been applied under fast magic-angle spinning (MAS) to a powder sample of octadecasil. Strong oscillations occur during CP on a sideband matching condition between the isolated ²⁹Si–¹⁹F spin pairs formed by the silicons in the D4R units and the fluoride anions. The magnitude of the dipolar coupling constant was deduced directly from the line-splitting between the intense singularities of the Pake-like patterns obtained by Fourier transformation of the oscillatory polarization transfer. The corresponding Si–F internuclear distance, r=2.62±0.05 Å, is found to be in very good agreement with the X-ray crystal structure and the value of 2.69±0.04 Å recently reported from rotational echo double resonance (REDOR) and transferred echo double resonance (TEDOR) nuclear magnetic resonance (NMR) experiments. Furthermore, the CP technique is still reliable under fast MAS where both REDOR and TEDOR sequences suffer from severe artefacts due to finite pulse lengths. In octadecasil, a spinning frequency of 14 kHz is shown to be necessary for an effective suppression of ¹⁹F–¹⁹F spin diffusion. The influences of experimental missettings and radiofrequency (RF) field inhomogeneity are taken into account.     

Photon echo area theorem for optically dense media

The McCall–Hahn area theorem for a photon echo in an optically dense medium is generalized in light of an absorption line consisting of several spectrally unresolved optical transitions and characterized by symmetrical form. Certain theoretical results are compared to experimental data obtained for a photon echo in a Tm³⁺:Y₃Al₅O₁₂ crystal.     

Determination of quadrupole parameters with a composite pulse for spurious signal suppression

Spurious signals such as the piezoelectric signal from a ferroelectric crystal or the ringing signal from the NMR probe head tuned for low gyromagnetic ratio nuclei are often observed in pulsed NMR. Both signals are cancelled using the Hahn echo sequence with appropriate phase cyclings. The present paper applies a composite-pulse sequence to cancel the ringing signal. The main advantage of this sequence over the Hahn echo sequence is in the simplicity of optimizing the line intensity: the optimization of only one pulse duration for this sequence but of two pulse durations and the interpulse delay for the Hahn echo sequence. We are interested in half-integer quadrupole spins (I = 3/2, 5/2, 7/2, and 9/2), which means that we must consider the first-order quadrupole interaction during the pulses. For simplicity, we deal mainly with spin I = 3/2 nuclei. Since the central-line intensity depends on the ratio of the quadrupole coupling constant (QCC) to the amplitude of the RF pulse, we can determine the QCC from a featureless lineshape by fitting the variation of the experimental central-line intensity for increasing pulse duration with theoretical results. Contrary to the one-pulse sequence where the central-line intensity is proportional to the pulse duration if the latter is short, there is no such condition with the composite-pulse sequence. In other words, this sequence does not allow us to quantify the relative spin populations in powders. The size of the sample must be much smaller than that of the RF coil in order for the RF magnetic field to become homogeneous for the sample. We used (87)Rb (I = 3/2) in an aqueous solution of RbCl and in RbNb2O5F powder, (131)Xe (I = 3/2) of xenon gas physisorbed in Na-Y zeolite, and (23)Na (I = 3/2) in two well-known powders (NaNO3 and NaNO2) to support our theoretical result.     

Collapse and Revival of the Electron Spin Echo of Impurity Yb3+ Ions on Hidden Frequency Combs of Hyperfine Interactions in a Y2SiO5 Single Crystal

JETP Letters - The collapse and revival of Hahn electron spin echo signals excited on electron–nuclear spin levels of an impurity 173Yb3+ ion in yttrium orthosilicate Y2SiO5 have been...