Multiquantum triple-pulse spin-echo signals from quadrupole nuclei in magnetically ordered substances

We analyze theoretically the formation of NMR pulse responses from a quadrupole spin system in which the inhomogeneous broadening of a spectral line is due to both magnetic and electric quadrupole interactions. We derive formulas for the moments of formation of multiquantum echo signals in the case of three exciting pulses. For the first time we detected in experiments multiquantum spin-echo signals from copper nuclei in ferromagnetic copper sulfochromite in the cases of double-pulse and triple-pulse excitations. We find that there is good agreement between the calculated and experimentally observed moments of echo signal formation. Zh. éksp. Teor. Fiz. 115, 2106–2112 (June 1999)     

Transient NQR signals in the effective field of multipulse trains

This paper is a theoretical analysis of time-dependent nutation and echo signals in the effective field of multipulse trains in NQR. The results of experimental investigations of the same aspects were reported in earlier papers. The various features of dipole-dipole interactions in three-level quadrupole spin systems are discussed. It is shown that, in contrast to NMR, the dipole Hamiltonian in the interaction representation determined by the quadrupole Hamiltonian contains only three diagonal components of the dipole-dipole interaction tensor. On the other hand, the strong inhomogeneous broadening characteristic of NQR hinders exact measurement of these components by ordinary methods. The theoretical analysis suggests that the decay of the echo-signal envelope in the effective field of multipulse trains is determined solely by the dipole relaxation time, which serves as justification of a new experimental method used in measuring the characteristics of the dipole-dipole interaction tensor in spin systems with an inhomogeneously broadened spectrum. Zh. éksp. Teor. Fiz. 115, 1580–1592 (May 1999)     

Three-pulse spin echo signals from quadrupolar nuclei in magnetic materials

The time evolutions of the three-pulse spin echo signals from quadrupolar nuclei ⁶³Cu and ⁵³Cr in ferromagnetic CuCr₂S₄:Sb have been investigated at the temperature T=77 K. The experimental results were well explained by the developed theory of the time evolutions of the three-pulse echoes. The main assumption of this theory is the assumption that the temporal fluctuations in the electron magnetization lead to the fluctuations in the hyperfine and quadrupole interaction Hamiltonians.     

Multiple structure of two-pulse nuclear spin echo in cobalt films

The conditions for the formation of two-pulse echo signals from ⁵⁹Co nuclei in thin magnetic films at T=4.2 K are investigated. In the framework of the existing mechanisms, numerical simulation of the conditions for the formation of extra 3τ and 4τ echo signals (τ is the time delay between pulses) is carried out. It is shown that the multiple structure of the echo from ⁵⁹Co nuclei at T=4.2 K is due to a mechanism in which an additional hyperfine magnetic field proportional to nuclear magnetization is acting on the nuclear spin system.     

Nuclear magnetic relaxation in ferrimagnetic Y3Fe5−x SixO12 films

The effect of silicon impurities on the damping of spin-echo signals from the ⁵⁷Fe nuclei of tetrahedral Fe³⁺ ions in epitaxial yttrium-iron-garnet films was investigated. It was found that for silicon concentrations 0.015⩽x⩽0.037 the damping of the spin echo is a two-component process, which made it possible to separate nuclei into two types, differing by both the longitudinal and transverse magnetic relaxation times. For silicon concentrations 0.044⩽x⩽0.073 the decay of the echo can be described by one exponential and all nuclei in the sample have the same transverse relaxation times and the same longitudinal relaxation times. The experimental results are interpreted on the basis of the supposition that impurity “macromolecules” form around the Si⁴⁺ ions. The relaxation times of the iron nuclei in a “macromolecule” are much shorter than the relaxation times of iron nuclei belonging to the matrix ions. The radius of a “macromolecule” is estimated on the basis of percolation theory. Fiz. Tverd. Tela (St. Petersburg) 40, 1494–1497 (August 1998)     

Electron spin-echo envelope modulation at S-band. 3: Analysis of nuclear quadrupole interaction effects

In the present paper the nuclear modulation of electron spin echo signals at S-band is investigated in the case of interacting nuclei with a quadrupole moment high enough to cause nuclear quadrupole couplings not negligible with respect to the nuclear Zeeman and dipolar hyperfine couplings. Both the two-pulse and three-pulse electron spin echo envelope modulation (ESEEM) due to²⁷Al and¹⁴N are simulated at different values of the nuclear quadrupole coupling by numerical diagonalization of the nuclear Hamiltonians. The behavior of their amplitude and periods is discussed on the basis of the ratios between the strengths of the nuclear quadrupole interaction and the nuclear Zeeman and the dipolar hyperfine interactions. The interpretation of their trends in terms of the eigenfunctions and eigenvectors of the nuclear Hamiltonians is carried out by using analytical equations obtained by perturbation approaches. First order perturbation treatments for integer and half-integer nuclear spin quantum numbers are developed when the nuclear quadrupole coupling is the main interaction. A discussion on the limits of the interpretation based on the perturbation approach is also given by comparing the magnitude Fourier transform of the patterns calculated by exact diagonalization and analytical equations.     

Multiple nuclear spin echo in thin polycrystalline ferromagnetic films

The formation of multiple nuclear spin echo signals has been studied in thin ferromagnetic polycrystalline films of 3d-metals and their alloys with induced anisotropy at temperatures between 2.2 and 300 K using two-pulse and three-pulse excitation. A method is proposed for the experimental determination of the contributions made by different mechanisms to the formation of spin-echo signals in magnets with strongly inhomogeneous Zeeman and quadrupole interactions. It is shown that in ferromagnets with a high rf field gain at the nucleus, the frequency modulation mechanism has a substantial influence in observations of nuclear spin-echo signals at nuclei with a high magnetic moment, even at liquid-helium temperatures. Fiz. Tverd. Tela (St. Petersburg) 40, 1056–1061 (June 1998)     

Influence of molecular motions on NQR echoes

The influence of thermal molecular motions on spin echo decay in pure nuclear quadrupole resonance (NQR) is considered. Our calculations show that the Hahn echo decay is caused by dipole-dipole interaction of the nuclear spins and is strongly affected by molecular mobility that can lead to the shortening of the echo decay with increased temperature. Slow molecular motion yields an exponential τ₃ time dependence, while fast motion yields an exponential decay. The outlined theory allows us to explain an unusual shortening of the³⁵Cl NQR echo decay on heating in thiourea-C₂Cl₆ inclusion compound.     

Vector model of electron spin echo envelope modulation due to nuclear hyperfine and zeeman interactions

The transverse electron spin magnetization of a paramagnetic center with effective spinS=1/2 interacting with nonquadrupolar nuclei may be presented as a function of pairs of nuclei magnetization vectors which precess around the effective magnetic field directions. Each vector of the pair starts its precession perpendicular to both effective fields. The free induction decay (FID) signal is proportional to the scalar product of the vectors for nuclear spinI=1/2. The electron spin echo (ESE) signal can be described with two pairs of magnetization vectors. The ESE shape is not equal to two back-to-back FID signals except in the absence of ESE envelope modulation. A recursion relation is obtained which allows calculation of ESE signals for larger nuclear spins in the absence of nuclear quadrupole interaction. This relation can be used to calculate the time course of the ESE signal for arbitrary nuclear spins as a function of the nuclear magnetization vectors. While this formalism allows quantitative calculation of modulation from nuclei, it also provides a qualitative means of visualizing the modulation based on simple magnetization vectors.     

Analysis of correlation patterns in hyperfine sublevel correlation spectroscopy of<Emphasis Type="Italic">S</Emphasis>=1/2,<Emphasis Type="Italic">I</Emphasis>=3/2 systems

The properties of two-dimensional four-pulse electron spin echo envelope modulation spectra of nuclei with nuclear spinI=3/2 in disordered systems are discussed by means of calculated lithium hyperfine sublevel correlation spectra. Since a case of small coupling is treated, the multifrequency transition components appear only in the first quadrant of the two-dimensional spectra. The influence of the hyperfine and nuclear quadrupole interaction parameters on the cross peak ridges in the two-dimensional powder pattern is analyzed. Furthermore the possibility to determine the magnitude of the dipolar hyperfine and the nuclear quadrupole coupling from the cross peak line shapes is investigated. In this context the potential of those spectral features representing the so-called multiquantum transitions for the interpretation of the spectra is demonstrated.     

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (¹⁴N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T ₁ (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T ₂ (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.     

Sensitivity of nuclear-quadrupole double-resonance detection of half-integer spin nuclei

The sensitivity of the Slusher and Hahn’s nuclear quadrupole double resonance technique is calculated in general for an arbitrary nuclear spin S of the quadrupole nuclei and for an arbitrary asymmetry parameter η of the electric field gradient tensor. The nuclear spin S = 5/2 (¹⁷O, ²⁵Mg, …) is treated in details. The influence of the cross-relaxation rate between the quadrupole nuclei and the abundant spin system on the sensitivity of double resonance is discussed. The results of the theoretical analysis are applied in the analysis of the ¹H–¹⁷O nuclear quadrupole double resonance spectra in p-toluenesulfonamide and 2-nitrobenzoic acid. The 17O nuclear quadrupole resonance frequencies from a sulfonamide group are determined for the first time. The proton–oxygen cross-relaxation rates and the proton local frequency in zero external magnetic field are experimentally determined from the nuclear quadrupole double resonance spectra.     

Observation of a new coherent transient in NMR — Two-pulse nutational stimulated echo in the angular distribution of gamma-radiation from oriented nuclei

A new coherent transient in NMR, the two-pulse nutational stimulated echo is reported for the ferromagnetic system⁵⁰CoFe, observed by monitoring the nuclear spin dynamics as a function of the second pulse duration via anisotropic gamma quanta from thermally oriented radioactive nuclei,⁶⁰Co. The mechanism of echo formation under strong Larmor inhomogeneous broadening and the secondary but important role of inhomogeneity associated with the rf amplitude (Rabi freqeuncy) due to skin-effect are investigated via the method of concatenation of perturbation factors in the statistical tensor formalism. For those experiments performed on time scales short compared with irreversible relaxation the theoretical predictions and subsequent experimental time-domain signals are in excellent accord. Remarkable constancy of amplitude of the new gamma-detected two-pulse echo with increase of interpulse time interval is observed, the longitudinal relaxation being manifest in the off-echo signals. Comparisons are made with NMRON four-pulse stimulated off-echo decay (analogous with conventional NMR three pulse stimulated echo) which is also sensitive to longitudinal relaxation, and with three-pulse on-echo decay (analogous with conventional NMR two-pulse Hahn echo) which measures transverse relaxation.     

Polarization of quadrupolar nuclei

A method of obtaining high polarization and pure spin states of impurity nuclei with a moderately strong quadrupole interaction in solid diamagnetic hosts whose nuclei have spin 1/2, a large g factor (like ¹H and ¹⁹F), and a high degree of polarization is proposed. The method employs cross-relaxation transitions of the impurity nuclei with the host spins (with adiabatic variation of the external magnetic field) and simple radio-frequency pulses that invert the host nuclei or give rise to two-spin resonance of the host and impurity nuclei. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 539–543 (10 October 1998)     

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.     

Probing spatial correlations in the inhomogeneous glassy state of the cuprates by Cu NMR

We discuss the crossover of the form of the Cu Nuclear magnetic resonance (NMR) spin echo decay at the onset of Cu wipeout in lanthanum cuprates. Experimentally, the echo decay undergoes a crossover from Gaussian to exponential form below the temperature where the Cu NMR intensity drops. The wipeout and the change in behavior both arise because the nuclei experience spatially inhomogeneous spin fluctuations at low temperatures. We argue that regions where the spin fluctuations remain fast are localized on length scales of order 1-2 lattice spacings. The inhomogeneity is characterized by the local activation energy E_a(r); we estimate the functional form of E_a(r) for points where E_a>(r)∼0.     

Spectra of multiquantum echo signals from quadrupole nuclei with half-integral spin in magnetically ordered materials

The numerical simulation of two-pulse echo signals at times 2τ, 4τ, and 6τ for the I=5/2 spin and at time 2τ, 4τ, and 8τ for the I=7/2 spin (τ is the time interval between exciting pulses) is carried out. It is shown that a delay by 2τ in the moment of formation of the echo results in the disappearance of extreme quadrupole satellites in the NMR spectrum obtained by recording the frequency dependence of the echo amplitude. The echoes at the maximum possible time of formation (2I+1)τ are only observed at the frequency of the purely magnetic spectroscopic transition $ \pm \frac{1}{2} \rightleftarrows \mp \frac{1}{2}$ ; no such echoes are observed at the quadrupole satellite frequencies. The computations are compared with the experimental results obtained for the ⁵⁵Mn nuclei (spin I=5/2) in the perovskite GdCu₃Mn₄O₁₂ and the spinel Li_0.5Fe_2.5O₄: Mn.     

Contributions of Spin–Lattice Relaxation to the Echo Decay of Planar Cu in High-Temperature Superconductors

Measurement ofT_2G, the Gaussian component of the spin-echo envelope of planar Cu nuclei in high-temperature superconductors, gives important information about the real part of the Cu electron spin susceptibility. In the traditional picture of the planar Cu echo decay, the internuclear coupling is assumed to remain static with respect to spin–lattice relaxation and mutual exchange fluctuations. In some circumstances, however, this assumption breaks down. We calculate the internuclear corrections arising from spin–lattice relaxation to the conventional theory ofT_2Gand show thatT_2Gcan be easily corrected for these effects. We argue that mutual exchanges due to the perpendicular indirect couplings are suppressed in these materials. For YBa₂Cu₄O₈, we find a correction on the order of 10% inT_2Gand using the corrected values we find that the isotope ratio⁶³T_2G/⁶⁵T_2Gagrees with theory.     

Nuclear structure studies at Saha Institute of Nuclear Pysics using gamma detector arrays

In-beam gamma-ray spectroscopy, carried out at the Saha Institute of Nuclear Physics in the recent past, using heavy-ion projectiles from the pelletron accelerator centres in the country and multi-detector arrays have yielded significant data on the structure of a large number of nuclei spanning different mass regions. The experiments included the study of two-fold γγ-coincidence events for establishing decay schemes, directional correlation of oriented nuclei (DCO) for help in spin assignments and Doppler shift attenuation for lifetime information. The studies have led to the observation of rotational sequences of states in nuclei near closed shell in the mass A=110 region, vibrational spectra in nuclei with A ∼ 60, interplay between single-particle and collective modes of excitation in the doubly-odd bromine isotopes, decoupled bands with large quadrupole deformation in ⁷⁷Br, shape transition with rotational frequency within a band in ¹³⁵Pm and octupole collectivity in ¹⁵³Eu. Particle-rotor-model and cranked-shell-model calculations have been carried out to provide an understanding of the underlying nuclear structure.