Nonsecular contribution to the decay of spin-echo signals of quadrupolar nuclei in magnetically ordered materials

We analyze the influence of fluctuations of the nonsecular part of the spin Hamiltonian on the decay of ordinary and multiquantum signals of the two-pulse spin echo in a quadrupole spin system with an inhomogeneously broadened spectral line. Expressions are obtained for the rate of decay of an echo in the case of selective excitation of a signal from quadrupole nuclei with arbitrary spin. These expressions are then used to analyze the experimentally observed ordinary and multiquantum echo signals from quadrupole nuclei with spin I=3/2 (⁵³Cr, ⁶³Cu, and ⁶⁵Cu) in ferromagnetic chromium chalcogenide spinels. Zh. éksp. Teor. Fiz. 116, 204–216 (July 1999)     

Role of U(3(A−1)) multiquantum excited states in calculating spectroscopic quantities for 4 8 Be

A set of equations for deriving the SU(3)-irreducible density matrix for U(3(A?1)) multiquantum excited states involved is given. For the ₄ ⁸ Be nucleus, the binding energies, radii, spectra, electric quadrupole moments, and probabilities B(E2) of electric quadrupole transitions are computed in the multiquantum approximation of the unitary scheme. The values obtained for the above spectroscopic quantities are investigated versus the number of basis functions involved.     

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)     

Electric quadrupole moments of light nuclei and transition probabilities for them in the multiquantum approximation of the orthogonal scheme

A method for calculating electric quadrupole moments of light nuclei and probabilities of electric quadrupole transitions in them in the multiquantum approximation of the orthogonal scheme is proposed. Specific calculations of these quantities are performed for the ₄ ⁸ Be nucleus with allowance for all U(3(A ? 1)) states characterized by the λ = [44] Young diagram, the quantum numbers K _min and K _min + 2 of the O(3A ? 1)) group, and the number E = K + 2N (N = 0, 1, …, 9) of oscillator quanta. It is shown that an extension of the basis from the E = K _min to the E = K _min + 2 approximation leads to an increase of 15 to 45% in the electric quadrupole moments and to an increase in the transition probabilities B(E2) by a factor of 1.6 to 2.8. The inclusion of E = K + 2N (N = 0, 1, …), states involving multiquantum excitations (ρ excitations) increases additionally the results by 10 to 30%. The results of these calculations are compared with their counterparts obtained in the multiquantum approximation of the unitary scheme.     

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.     

Determination of T1-spin-lattice relaxation time in a two-level system by continuous wave multiquantum electron paramagnetic resonance spectroscopy in a presence of tetrachromatic microwave irradiation

Applicability of continuous wave multiquantum EPR methods to study relaxation times at X-band is examined. Multiquantum transitions excited in a two-level system by tetrachromatic irradiation are used for these studies. The Bloch equation model is applied to simulate lineshapes of the three quantum transitions as a function of frequency difference between exciting fields. The dependence of multiquantum transition signals on relaxation times and microwave amplitude is shown. On this basis a method of deducing relaxation times from these signals is formulated. The case of a homogeneously and inhomogeneously broadened resonance line is considered. Two experimental methods are used to verify the proposed hypothesis: the X-band continuous wave multiquantum EPR with four frequencies microwave field and saturation recovery EPR. The values of T₁ obtained from CW MQ EPR and SR EPR are compared.     

Nuclear spin echo in magnetics with inhomogeneous hyperfine and quadrupole interaction

Additional spin-ocho signale from quadrupole nuclei with I=7/2 (Co⁵⁹ nuclei in Co and Fe−Co thin films) were investigated. It has been shown, that the time dependence of the additional ocho signals, arising at the time moments 2nς reflect quadrupole interaction inhomogenety.     

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.     

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)     

An ab initio analysis of electronic states associated with a silicon vacancy in cubic symmetry

The electronic orbitals localized in the vicinity of a vacancy in a silicon crystal are calculated by an ab initio method based on the density functional theory and analyzed in association with the elastic softening observed by the recent ultrasonic experiments, especially focused on an estimate of the electric quadrupole moments. The localized orbitals due to the existence of a vacancy show largely extended properties and the quadrupole moments calculated from the orbitals indicate the strong dependence on cell sizes up to 511 atoms in the basic cell. Asymptotic values of the quadrupole moments in the limit of large size are obtained by an extrapolating method. It is shown that the quadrupole moments are enhanced due to the extension of the orbitals and the ratio of the quadrupole moments of Γ₅ and Γ₃ symmetries agrees well with the value deduced from the experimental results.     

Nuclear quadrupole resonance echoes from hexamethylenetetramine

We investigated the echo phenomenon of nuclear quadrupole resonance (NQR) from hexamethylenetetramine (HMT). We detected the pure NQR echo signal of HMT with a short pulse interval. The intensity of the echo signal increased as the pulse interval time was decreased. We observed that a clean echo signal was generated even when the pulse interval was shorter than the decay time constant T₂^*. Since the short interval time gives a strong echo, our result insists that shorter interval time is preferred for the NQR detection.     

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 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.     

Static and dynamic quadrupole moments of high-spin isomers in the Pb-region

Quadrupole moments of high-spin isomers in the Pb-region are studied by using core polarization charges induced by the coupling of single-particle states to giant resonances. We found that the core polarization charges are enough to reproduce the observed quadrupole moments of the isotones with neutron number N=126 quantitatively without any intrinsic deformation. The mass number dependence of the quadrupole moments in the Rn-isotopes is also discussed by taking into account the configuration mixing involving the neutron excited first 2⁺ state.     

Novel isotope effects observed in polarization echo experiments in glasses

In recent years unexpected magnetic field effects have been observed in dielectric measurements on insulating glasses at very low temperatures. Polarization echo experiments have indicated that atomic tunneling systems are responsible for these effects and that the nuclear properties of the tunneling particles are of importance. Subsequently, it was suggested that the magnetic field effects are caused by tunneling systems carrying a nuclear quadrupole moment. Now we have studied the isotope effect in echo experiments on fully deuterated and ordinary glycerol clearly showing the crucial role of the nuclear quadrupole moments for the magnetic field effects. In addition, we have observed a new effect in the decay of spontaneous echoes in zero magnetic field for the deuterated samples which can be explained in terms of a quantum beating involving the quadrupole levels.     

Determination of the spectroscopic quadrupole moments of 33 75 As and 29 63 Cu

The HFS-splitting of the 2s-2p and 3d-2p transitions of muonic arsenic and 3d-2p transitions of copper have been measured with high resolution Ge-semiconductor detectors to determine the nuclear quadrupole moments. A coincidence measurement was performed to separate the 2s-2p transition from the background. The nuclear spectroscopic quadrupole moments were found to be:Q _spec=0.314(6) b for ₃₃ ⁷⁵ AsQ _spec=0.220(15) b for ₂₉ ⁶³ Cu. In addition, generalized Barrett moments were determined in a model-independent analysis of muonic transition energies.     

Primary acoustic echo during excitation of a paramagnetic crystal by picosecond elastic video pulses

The primary acoustic echo formed during excitation of a paramagnetic crystal with effective spin S=1 by two transverse picosecond elastic video pulses is investigated theoretically. Both exciting video pulses are applied perpendicular to the external magnetic field. It is shown that the primary acoustic echo in the general case consists of six longitudinal and transverse signals at the frequencies of the transitions within a Zeeman triplet. The optimal parameters of the exciting video pulses for the appearance of different echo signals are determined. Fiz. Tverd. Tela (St. Petersburg) 41, 623–628 (April 1999)     

Phase errors in FSE signals due to low frequency electromagnetic interference

ObjectiveTo quantitatively evaluate induced phase errors in fast spin echo (FSE) signals due to low frequency electromagnetic inference (EMI).MethodsSpecific form of Bloch equation is numerically solved in time domain for two different FSE pulse sequences (ETL = 8) with two different bandwidths. A single spin is modeled at x = 10 cm, EMI frequencies are simulated from 1 to 1000 Hz and phase errors at different echo times are calculated.ResultsPhase errors in the received echo signals induced by EMI are significantly higher at low frequencies (< 200 Hz) than at high frequencies and the phase errors at low frequencies can be effectively reduced by using high receiving bandwidth.ConclusionPulse sequence bandwidth can be used to control the phase errors in the FSE signals due to low frequency EMI.     

Influence of relaxation processes on amplitude and shape of echo signals

A theory of signal-processing analog devices that use the phenomenon of spin, light, or nuclear quadrupole echo is considered with allowance for noise immunity. Main equations describing these phenomena are solved by multiplicative integration. Such an approach makes it possible to calculate echo signals of arbitrary amplitude and structure in a general form.