6Li NMR in lithium borate glasses

In anticipation of using fluctuations in the nuclear dipolar and quadrupolar interaction as a probe of lithium ion motion in lithium borate glasses, the static values of these interactions were measured using a variety of echo techniques. The static quadrupolar echo spectrum of ⁷Li and a calculation of the dipolar interaction in crystalline Li₂B₄O₇ (same chemical composition as the glass under study) were used to estimate the strength of the two interactions. These indicate that the dipolar and quadrupolar interactions for ⁶Li will be of similar size and the dipolar interaction will be dominated by the unlike spin interaction between the ⁶Li and the ¹⁰B, ¹¹B spins. An appropriate theoretical model is proposed and explicit expressions for the echo amplitude are calculated in terms of the dipolar and quadrupolar second moments. This single spin model takes into account the quadrupolar interaction but treats the dipolar interaction as an effective magnetic field. Experimental results are presented which show the essential validity of the model and measurements lead to reasonable values for the dipolar and quadrupolar second moments. The relative merits of the various echo techniques are discussed.     

Li NMR in lithium borate glasses

In anticipation of using fluctuations in the nuclear dipolar and quadrupolar interaction as a probe of lithium ion motion in lithium borate glasses, the static values of these interactions were measured using a variety of echo techniques. The static quadrupolar echo spectrum of ⁷Li and a calculation of the dipolar interaction in crystalline Li₂B₄O₇ (same chemical composition as the glass under study) were used to estimate the strength of the two interactions. These indicate that the dipolar and quadrupolar interactions for ⁶Li will be of similar size and the dipolar interaction will be dominated by the unlike spin interaction between the ⁶Li and the ¹⁰B, ¹¹B spins. An appropriate theoretical model is proposed and explicit expressions for the echo amplitude are calculated in terms of the dipolar and quadrupolar second moments. This single spin model takes into account the quadrupolar interaction but treats the dipolar interaction as an effective magnetic field. Experimental results are presented which show the essential validity of the model and measurements lead to reasonable values for the dipolar and quadrupolar second moments. The relative merits of the various echo techniques are discussed.     

Weak magnetic field behavior of photon echo in a LuLiF4:Er3+ crystal

We report the first observation and study of the photon echo in Er³⁺:LuLiF₄. The energy transition is ⁴ I _15/2 → ⁴ F _9/2 (λ = 6536 Å). The density of ErF₃ is 0.025 wt %. The operation temperature is 1.9 K. Measurements were made at low (up to 1200 Oe) and even zero external magnetic fields. We studied the behavior of the photon echo intensity vs. the magnetic field magnitude and direction about the crystal axis C and vs. the laser pulse separation t ₁₂ and observed an exponential growth and then, after a certain plateau, an exponential decrease in the photon echo intensity as a function of magnetic field upon increasing the magnetic field from zero. The parameters describing the exponential growth and decrease are independent of the direction of magnetic field. The value of the magnetic field (～20–200 Oe) at which the echo intensity is maximal and the value of the maximum itself decrease with increasing pulse separation t ₁₂ and the angle Θ between the magnetic field and crystal axis. The echo intensity decreases exponentially with increasing Θ. The parameter describing the exponential decrease is independent of the magnitude of the field. The echo intensity as a function of pulse separation shows exponential decay. The phase relaxation time depends on the magnitude and direction of the magnetic field. T ₂ is equal to 202 ± 16 ns at zero magnetic field. A phenomenological formula is suggested, which qualitatively presents the mentioned dependences, and the polarization properties of the backward photon echo in this crystal are studied. Because the ion of trivalent erbium is an optimum data carrier, the above results show that fine control of the multichannel transfer of processed optical information may be achieved by weak magnetic fields.     

Modulation of the shape of the photon echo pulse by a pulsed magnetic field: Zeeman splitting in LuLiF4:Er3+ and YLiF4:Er3+

A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF₄:Er³⁺ and YLiF₄:Er³⁺. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment ?? and makes it possible to determine the difference of the g factors of the ground and excited ⁴ F _9/2(I) states of the Er³⁺ ion in the LuLiF₄ the YLiF₄ matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.     

Conventional and collision photon echo in ytterbium vapor

The polarization properties of the photon echo generated by two linearly polarized pulses of resonant radiation at the (6s6p)³ P ₁ ? (6s ²)¹ S ₀ transition of ¹⁷⁴Yb are investigated. A complicated polarization behavior of the photon echo versus an angle between the polarization vectors of the excitation pulses is revealed in a mixture of ytterbium vapor with inert gas. For the angles ranging from 0° to 75°, a conventional echo with its linear polarization coinciding with the second excitation pulse dominates and the echo amplitude decreases with an increasing angle. For the angles ranging from 75° to 89°, the photon echo is elliptically polarized. Finally, for an angle of 90°, the conventional echo disappears and the collision echo becomes linearly polarized along the first excitation pulse.     

Self-induced three-level echo

A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the ³ P ₀-³ H ₆ transition in impurity praseodymium ions in the LaF₃ matrix upon ultrashort coherent excitation of the adjacent optically allowed ³ H ₄-³ P ₀ transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the ³ P ₀-³ H ₆ generation transition and completely eliminates polarization at the ³ H ₄-³ P ₀ excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden ³ H ₆-³ H ₄ transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.     

Natural orbitals,diatomic molecules and ERD

The effects of molecular motions on spin-echo signals (2n + 1)90°_y—τ—90°_x:—Acq(t) in nuclear spin systems with dipolar interactions have been investigated. It was found that in the case of a rigid lattice (M₂τ² _c: >> 1) and a motionally narrowed NMR line (M₂τ² _c,<< 1) a maximum of echo signals is observed at t_e = 2τ + t₂—t₁/2, where t₁ and t₂ are the widths of the RF pulses. It also was found that in the slow motion region (M₂τ² _c ? 1) an amplitude of the dipolar echo signal is reduced and the maximum of the echo signal is shifted to the end of the second pulse. The theory developed is confirmed by the experimental results obtained for C₆H₆.     

Square-roots,internal symmetries,and fermion field quantization

It is observed that the complex square-root of the hermitian matrix σ^μ p _μ associated with a physical four-momentum admits Lorentz-independent unitary transformations that may be related to the internal symmetries of hadrons. An operator-valued square-root of the Hilbert space inner product in relativistic one-electron theory brings in fermion field quantization conditions as a direct concomitant of its linearity and hermicity properties.     

Measurement of Small One-Bond Proton–Carbon Residual Dipolar Coupling Constants in Partially Oriented C Natural Abundance Oligosaccharide Samples: Analysis of Heteronuclear JCH-Modulated Spectra with the BIRD Inversion Pulse

Two 2D J-modulated HSQC-based experiments were designed for precise determination of small residual dipolar one-bond carbon–proton coupling constants in ¹³C natural abundance carbohydrates. Crucial to the precision of a few hundredths of Hz achieved by these methods was the use of long modulation intervals and BIRD pulses, which acted as semiselective inversion pulses. The BIRD pulses eliminated effective evolution of all but ¹J_CH couplings, resulting in signal modulation that can be described by simple modulation functions. A thorough analysis of such modulation functions for a typical four-spin carbohydrate spin system was performed for both experiments. The results showed that the evolution of the ¹H–¹H and long-range ¹H–¹³C couplings during the BIRD pulses did not necessitate the introduction of more complicated modulation functions. The effects of pulse imperfections were also inspected. While weakly coupled spin systems can be analyzed by simple fitting of cross peak intensities, in strongly coupled spin systems the evolution of the density matrix needs to be considered in order to analyse data accurately. However, if strong coupling effects are modest the errors in coupling constants determined by the “weak coupling” analysis are of similar magnitudes in oriented and isotropic samples and are partially cancelled during dipolar coupling calculation. Simple criteria have been established as to when the strong coupling treatment needs to be invoked.     

Spin-Label EPR for Determining Polarity and Proticity in Biomolecular Assemblies: Transmembrane Profiles

Hyperfine couplings and g-values of nitroxyl spin labels are sensitive to polarity and hydrogen bonding in the environment probed. The dependences of these electronic paramagnetic resonance (EPR) properties on environmental dielectric permittivity and proticity are reviewed. Calibrations are given, in terms of the Block–Walker reaction field and local proton donor concentration, for the nitroxides that are commonly used in spin labeling of lipids and proteins. Applications to studies of the transverse polarity profiles in lipid bilayers, which constitute the permeability barrier of biological membranes, are reviewed. Emphasis is given to parallels with the permeation profiles of oxygen and nitric oxide that are determined from spin-label relaxation enhancements by using nonlinear continuous-wave EPR and saturation recovery EPR, and with permeation profiles of D₂O that are determined by using ²H electron spin echo envelope modulation spectroscopy.     

N.M.R. dipolar echoes in solids containing spin-1/2 pairs

The proton echo responses to resonant 90°-τ-β_90° (XY) and 90-τ-β_0° (XX) pulse sequences in powdered crystalline hydrates are reported. The echo produced by the XY sequence consists of two components: one is proportional to sin² β and the other to sin² β cos² β; the former component decays much faster than the latter on increasing the pulse spacing τ. In contrast, the XX sequence produces a single component echo of the form - sin² β cosβ. The maximum echo amplitudes for the sequences 90°-τ-90°_90° and 90°-τ-54°44′_0° exhibit a gaussian dependence on τ² over at least 95 per cent of their decays. The decay constant for the 90-τ-90°_90° echo corresponds to M ₂(inter) = 5/6 M ₂ ^vv(inter), where M ₂ ^vv(inter) is the interpair second moment calculated by the van Vleck procedure. These observations can be explained in terms of a simple model consisting of a planar arrangement of two spin-1/2 pairs provided the interpair dipolar hamiltonian is truncated so that [?^o _a(intra) + ?^{o, t} _d(inter), ?_z] = 0 and [?^o _a(intra), ?^{o, t} _d(inter)] = 0.

The model predicts the echo behaviour only if the spin-1 character of the eigenfunctions of ?^o _d(intra) + ?_z is preserved in the presence of the interpair interactions. It is shown that the XX echo and the sin² β cos² β components of the XY sequence originate solely in the interpair interactions and contain no contributions from the intrapair interactions. The decay of the maximum echo amplitude with increasing τ is caused by the incomplete refocusing of the interpair interactions by the XX and XY sequences; the correct decay is only determined provided the interpair dipolar hamiltonian is correctly truncated. The model also accounts for the proton echo behaviour in solid hydrogen reported by Metzger and Gaines.

Interestingly, the N.M.R. behaviour observed for these spin-1/2 pair systems is largely determined by the eigenfunctions of the spin Hamiltonian with M_z = 0.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

Photon echo generated at the transition 0–1 in ytterbium vapor

Photon echo generated at the inter-combination transition (6s ²) ¹ S ₀ ? (6s6p) ³ P ₁ of ¹⁷⁴Yb was investigated for pure ytterbium vapor and for its mixtures with atomic buffers. In pure ytterbium vapor, the polarization of photon echoes at this 0?C1 transition coincides with the polarization of the second exciting pulse for all combinations of linear and circular polarizations of exciting radiation pulses. Photon echo does not appear either for linear orthogonal or for opposite circular polarizations of exciting pulses in pure ytterbium. In mixtures of ytterbium with atomic buffers (Kr, Xe), collision induced photon echo arises only for exciting pulses of linear orthogonal polarizations, its power is essentially less than that of the ordinary echo generated by pulses with parallel polarizations in the same mixture. Polarization of collision induced echo is linear, and it coincides with polarization of the first exciting pulse. Experimental results agree with calculations, and they confirm that the collision induced photon echo at this transition arises exclusively due to anisotropy of depolarizing collisions.     

Photon echo in the presence of a magnetic field: New prospects for data accumulation and processing

The possibility for echo signal switching-off and the switching of echo polarization between the ±45° positions is demonstrated for the photon echo (PE) and stimulated photon echo (SPE) generated in Yb vapor at the (6s6p)³ P ₁ ? (6s ²)¹ S ₀ transition by two pulses of the resonant linearly polarized radiation at appropriate experimental parameters in the weak magnetic field limit. The experimental data are in qualitative agreement with the theoretical analysis and the calculations made for the 1 ? 0 transition. The strong magnetic field limit leads to unpolarized PE and SPE signals generated by linearly polarized radiation pulses. The possibility of the generation of a long-lived echo in ytterbium vapor due to the magnetic field induced mixing of the upper working level with the metastable level is discussed. The results can be employed for the optical data storage and processing.     

Quasiquadrupolar echoes in solids containing spins-12 triads undergoing hindered reorientation

The spin echo responses to resonant 90⁰-τ-β_φ⁰ rf pulse sequences in solids containing spin-$\text{1}\text{2}$ triads undergoing hindered rotations, are shown to be predicted by a model of dipolar coupled quasiparticles of spin-$\text{3}\text{2}$.     

Excitation conditions for quantitative determination of quadrupolar spins with one pulse or spin-echo sequences in solid-state NMR

One of the major problems concerning quadrupolar spins in solid-state NMR is their quantification. If the optimal excitation conditions with one radio-frequency pulse are widespread known now, this is not the case with the spin-echo sequences. This paper reports some theoretical predictions and their limitations concerning quantification with the echo obtained with spin-echo resonances. To realize that, first, the relative line intensity of a transition (m+1,m) is defined in order to allow the comparison of results, from different authors. Then results concerning one pulse excitation on a spinI=3/2 are summarized. The condition of short pulse excitation is generalized to higher spins using the Pauli matrices applied to the two extreme cases: hard pulse or non selective excitation, and selective excitation. Finally the same procedure has been followed for the spin-echo sequence involving twox-pulses. It was shown that the optimum conditions are: both the pulse length must be sufficiently short, and the interpulse delay should be taken as short as the duration of the FID provided the phase of the second pulse alternates without changing the receiver phase. In these conditions, the relative echo amplitude depends linearly on the first pulse length and quadratically on the second. The limitations are: the homonuclear magnetic dipolar interaction must be much smaller than the heteronuclear case which must be itself much smaller than the amplitude of the pulse. Furthermore, quantification with the echo requires the determination of the spin-spin relaxation time as well.     

Temperature evolution of spin-transfer switching in nonlocal spin valves with dipolar coupling

The spin-transfer effect has been achieved in nanoscale metallic nonlocal spin valves. A magnetic domain (∼70×150 nm²) in an extended wire can be switched by a pure spin current between 4.5 and 200 K. The dipolar coupling between the magnetic spin injector (F₁) and spin detector (F₂), the surface anisotropy of the thin F₂ layer, and the thermal instability of F₂ generates complex switching characteristics. Analysis of the results allows for detailed understanding of magnetic configurations during the current-sweep and the field-sweep measurements. The critical current (I_c) for spin-transfer switching gradually decreases as the temperature increases. The I_c⁺ for the transition from parallel (P) state to antiparallel (AP) state decreases faster than the I_c^‐ for the transition from AP to P due to the dipolar coupling. Above 200 K, the dipolar coupling and the thermal instability prevents a stable P state in the absence of an external field.     

MRICOM–MRI COntrast Modelling using 2D T1–T2 correlation spectra and relaxation signatures

Image contrast is calculated by inputting experimental 2D T₁–T₂ relaxation spectra into the ODIN software interface. The method involves characterising a magnetic resonance imaging pulse sequence with a “relaxation signature” which describes the sensitivity of the sequence to relaxation and is independent of sample parameters. Maximising (or minimising) the overlap between the experimental 2D T₁–T₂ relaxation spectra and the relaxation signature can then be used to maximise image contrast. The concept is illustrated using relaxation signatures for the echo planar imaging and Turbo spin-echo imaging sequences, together with in-vitro 2D T₁–T₂ spectra for liver and cartilage.     

de Haas van Alphen (dHvA) effect in two-dimensional (2D) conductors: susceptibility oscillations

A new scheme for analyzing the de Haas van Alphen (dHvA) effect in nearly two dimensional (2D) metals (i.e. with nearly cylindrical Fermi surface) is presented. The envelope of the magnetic susceptibility oscillations is calculated in the entire range of magnetic fields and temperatures. The resulting envelope function is found to be proportional to a universal function of the dimensionless parameter Q=hω_c/k _B T. The upper (i.e. paramagnetic) branch of the susceptibility envelope has a maximum at a certain Q = 5.45. This universal value may be useful for determining the effective cyclotron mass and the Fermi energy of nearly 2D metals. A simple relation between magnetization oscillations amplitude and calculated susceptibility amplitudes is derived. The corresponding limiting formulae for the magnetization oscillations envelope are found to match smoothly around the value X = 2π²/Q?2 of the Lifshitz-Kosevich (LK) smearing parameter. The influence of Fermi surface sheets with open orbits on magneto-quantum oscillations is considered. Triangle-like rather than saw-tooth-like oscillations at ultralow temperatures are obtained and substantially diminished magnetization and susceptibility amplitudes are calculated. This suggests the possibility of estimating the band structure parameters of Fermi surface sheets from magneto-quantum oscillations measurements.     

Theoretical and experimental study of quadrupolar echoes for half-integer spins in static solid-state NMR

Numerical simulations of powder spectra produced by a two-pulse sequence applied to a quadrupolar nuclei system of half-integer spin number make it possible to propose simple experimental instructions to record static echo spectra with minimum lineshape distortion. Calculations take into account quadrupolar (first and second orders), shielding, scalar and inhomogeneous dipolar interactions as well as the radiofrequency pulse specifications (strength, duration, phase). The suggested instructions have been checked experimentally in different cases: for a large spin number system with Li⁹³NbO₃, when two interactions are present with a ^63/65Cu complex, and in the two-site system of ⁸⁷Rb₂SO₄.