Determination of the asymmetry parameter of EFG tensor from moments of NQR nutation spectra in powders

A novel approach to determination of the asymmetry parameter of the EFG tensor from zero-field nutation NQR spectra of the spinI = 3/2 nuclei in powder samples is reported. The proposed theoretical treatment uses lineshape analysis of the nutation NQR spectra by the method of line moments. The analytical formulas for the lineshape of the powder nutation spectrum are given. It is shown that the asymmetry parameter can be determined from the second moment 〈ω²〉 and the frequency of only one singularity ω₂ of the nutation spectrum. It is also shown that the asymmetry parameter can be determined from the second and fourth spectrum moments alone. The method is successfully demonstrated for the simulated nutation NQR spectra of the spinI = 3/2 nuclei in powder samples.     

Influence of relaxation on the two-dimensional nutational nuclear-quadrupole-resonance spectra

The influence of relaxation and frequency detuning on the nutational frequency and the damping factor of a nutational interference pattern is analyzed. It is established that relaxation leads to decrease in nutational frequency, while detuning increases the nutation frequency. A relation is obtained between the relaxation times and the frequency detuning at which the influence of both factors cancels out. Conditions such that singularities of the nutational nuclear-quadrupole-resonance (NQR) spectrum (I=3/2) may be resolved are determined, and a formula for the asymmetry parameter ν is obtained, taking account of relaxation. Having determined the region of existence of nutation and established the conditions under which the singularities of the NQR spectrum of the powder (I=3/2) may be resolved, the asymmetry parameter may be reliably determined from the experimental nutational spectrum of the powder. Experimental nutational³⁵Cl NQR spectra are given for TiCl₄ and 2,4,6-trichloro-1,3,5-triazine. Kaliningrad State University, Baltiisk State Academy of the Russian Federation, Kaliningrad. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 41, No. 12, pp 66–71, December, 1998.     

Application of Nutations to Studying the Exchange Processes by the Method of Nuclear Quadrupole Resonance Spectroscopy

A method of direct determining the discontinuous rotational reorientation angles from NQR exchange spectra based on recording of two-dimensional nutations of magnetization after the mixing period is suggested. The possible modification of the Jeener pulse sequence with independently varying duration of pulses for obtaining a 2D exchange nutation spectrum is described. Shapes of singularities in the 2D nutation spectrum of CCl₂- and CCl₃-group reorientations, which depend on the angle _S between C–Cl bonds and on the asymmetry parameter for nonequivalent positions of nuclei participating in the exchange are examined. The 2D exchange NQR nutation spectra of ³⁵Cl in powders prepared from C₂Cl₄ and C₂Cl₆ molecular crystals are modeled. The advantages and capabilities of the method are discussed.     

Determination of Reorientation Angles from Two-Dimensional Exchange Spectra of Powders in Radiospectroscopy

A method for transforming a 2D exchange spectrum into an orientation representation is proposed which is based on finding the reorientation probability as a function of angles. A procedure of evaluation and analysis of two-dimensional magnetic spectra of powders is described and a method for finding the asymmetry parameter from 2D exchange spectra is proposed. The capabilities of the method are illustrated for a model ³⁵Cl 2D nutation exchange NQR spectrum of chloral hydrate CCl₃CH(OH)₂ and an experimental ¹³C 2D exchange NMR spectrum of dimethylsulphone CH₃–SO₂–CH₃. The asymmetry parameter of the chemical shift tensor for this compound is determined.     

Angle-selective measurements of spin soliton in ladder polydiacetylene by pulsed 94 GHz EPR

Angle-selection experiments of a spin soliton in randomly oriented ladder polydiacetylene were carried out by pulsed electron paramagnetic resonance (EPR) at W-band. EPR measurement using 94 GHz microwaves increased the difference in the resonance field due tog anisotropy of the spin soliton to allow the orientation dependence of transient nutation, electron nuclear double resonance (ENDOR) and spin relaxations to be investigated. The shape of theg anisotropy-resolved nutation spectrum was discussed on the basis of the EPR transition moments and the differences between spin relaxation times. Reliable assignments of hyperfine couplings to the β protons (H_β) of the alkyl side chains were achieved with the support of W-band ENDOR measurements. No significant orientational dependence in theT ₁ andT ₂ processes was found in terms of isotropy of the H_β-hyperfine interaction.     

Magnetic properties of high-T c superconductors from NQR and NMR measurements

NMR and NQR spectra and spin-lattice relaxation measurements carried out in LASCO and YBCO-type crystals are presented and analyzed in order to derive insights on the correlations and spin-dynamics of the Cu²⁺ ions and on the microscopic mechanisms of high-T _c superconductivity. As an illustrative example on how the magnetic correlation length and spin dynamics properties can be extracted from the relaxation rateW, the³⁵Cl NMR data in the two-dimensional Heisenberg system Sr₂CuCl₂O₂, around the paramagnetic-antiferromagnetic (PA-AF) transition are first considered. Then the¹³⁹La NQR relaxation measurements in La_2?xSr_xCuO₄ are briefly reviewed and it is shown how a simple picture of localized Cu²⁺ magnetic moments, whose spin fluctuation times are controlled by the charge defects induced by the doping, leads in a direct way to quantitative estimates for the progressive shift, on cooling, of the spectral density of the low-frequency spin excitations towards the high frequency range. This phenomenon can be described in terms of effective spin at the Cu²⁺ ions, and its similarities with the analogous effect of progressive delocalization in Heavy Fermions systems are pointed out. Thus, the superconducting transition appears to occur in an unconventional Fermi liquid with AF correlations among itinerant pseudoparticles, possibly involving a mechanism not directly related to the magnetic correlated dynamics. In fact, a universal behavior of the relaxation rates as a function of temperature is observed, regardless of the transition temperatureT _c. The independence ofT _c from the low frequency static and dynamical spin properties is also indicated by⁸⁹Y Knight shifts and from⁶³Cu relaxation rates in systems like YBa₂Cu₄O₈ (Y124), whereT _c can be changed by atomic substitutions and by controlling the oxygen stoichiometry. The effect of an external magnetic field on the correlated spin dynamics of the AF Fermi liquid is investigated and from a comparison of Cu NQR relaxation and NMR relaxation in oriented powder of YBCO and LASCO it is shown that the external field has the small but unambiguous effect of depressing the relaxation rates aboveT _c, besides strongly enhancing them in the superconducting phase. A maximum in the ratio \({{W\left( {NQR} \right)} \mathord{\left/ {\vphantom {{W\left( {NQR} \right)} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}} \right. \kern-0em} {W\left( {\vec H\left\| {\vec c} \right.} \right)}}\) is thus observed around 80 K, either in LASCO or in YBCO, again indicating that the transition could be driven by a mechanism not directly involving the spin dynamic properties. To study the role of the fluxions belowT _c ⁸⁹Y NMR shifts and spectra in oriented powders of YBCO are analyzed. Information on the spin susceptibility and on the structure of the vortex lattice is obtained. In addition, from the temperature behavior of the linewidth a motional narrowing related to flux melting is evidenced. The effective correlation time for the vortex motion is derived and it is discussed why μ⁺SR cannot detect it in view of the different rigid-lattice line broadening.     

Non-cyclic geometric phase of nuclear quadrupole resonance signals of powdered samples

The non-cyclic geometric phase of ¹⁴N and ³⁵Cl NQR signals induced by the character of trajectory of nuclear magnetization motion upon pulse r.f. excitation of powdered samples is studied. Analytical expressions for the geometric phases of NQR signals of the nuclei of spins I=1 and 3/2 upon nuclear magnetization rotation induced by means of r.f. pulses with frequency detuned from the resonance and for any impulse duration for a separate crystallite are obtained. It is shown that the geometric phase recorded for the signal from a powdered sample at Δω=0 can be different from zero and can oscillate upon changes in duration of the r.f. excitation pulse. An alternative variant of the nutation experiment aimed at obtaining the asymmetry parameter η from locations of frequency singularities in the nutation phase spectrum for nuclei of spin I=3/2 in powder substances is proposed.     

Ba nuclear resonance in YBa2Cu2Oy

The first observations of NMR and NQR of both isotopes¹³⁵Ba and¹³⁴Ba in isotopically enriched samples of YBa₂Cu₃O_y with oxygen concentrations y=6.0, 6.2, and 7.0 are described. The pure NQR frequencies and asymmetry parameter are in good agreement with theoretical predictions. The temperature dependence of the NQR frequency of Ba for y=7 is qualitatively similar to that for Cu(2) but much stronger. The temperature dependence of the longitudinal and transverse relaxation times opens new questions.     

Multiphoton transitions in a spin system driven by strong bichromatic field

EPR transient nutation spectroscopy is used to measure the effective field (Rabi frequency) for multiphoton transitions in a two-level spin system bichromatically driven by a transverse microwave (MW) field and a longitudinal radio-frequency (RF) field. The behavior of the effective field amplitude is examined in the case of a relatively strong MW field, when the derivation of the effective Hamiltonian cannot be reduced to first-order perturbation theory in ω₁/ω_rf(ω₁ is the microwave Rabi frequency, ω_rf is the RF frequency). Experimental results are consistently interpreted by taking into account the contributions of second and third order in ω₁/ω_rf evaluated by Krylov-Bogolyubov-Mitropolsky averaging. In the case of inhomogeneously broadened EPR line, the third-order correction modifies the nutation frequency, while the second-order correction gives rise to a change in the nutation amplitude due to a Bloch-Siegert shift.     

Two dimensional NQR separation of inhomogeneous and homogeneous lineshapes in disordered solids

A two-dimensional (2D) zero field NQR separation of inhomogeneous and homogeneous lineshapes technique is described. The nuclear spin Hamiltonian for spinsI>1/2 in zero magnetic field consists to a good approximation only of the electric quadrupole term. The 2D separation technique enables a separate spectroscopic observation of a static and a randomly time-fluctuating dynamic part of the quadrupole interaction. The separation is based on the fact that nuclear spin precession under a static quadrupolar Hamiltonian can be time-reversed whereas this can not be achieved under the action of a randomly time-fluctuaing Hamiltonian. The 2D spectrum displays in theω ₂-domain the inhomogeneously broadened lineshape, which is a convolution of the inhomogeneous static frequency distribution function and the homogeneous (adiabatic) lineshape. Theω ₁-domain shows the pure homogeneous lineshape. A deconvolution of the inhomogeneous lineshape with the homogeneous one yields a pure static inhomogeneous frequency distribution function which is characteristic and theoretically known for many different models of disordered solids like glasses and incommensurate systems. This technique is important in studies where both lineshapes have comparable widths. The 2D NQR separation technique has been applied to⁷⁵As in a proton glass Rb_0.98(NH₄)_0.02H₂AsO₄.     

199Hg and63,65Cu NMR studies of mercury based high-T c superconductors

Hg-oxide ceramic high temperature superconductors were studied by¹⁹⁹Hg and^63,65Cu NMR spectroscopy. Room temperature spectra, spin-spin and spin-lattice relaxation times of samples with different superconducting transition temperatures are presented. A spin-lattice relaxation time ofT ₁=35 msec and a spin-spin relaxation time ofT ₂=1.6 msec were found for the¹⁹⁹Hg NMR. All samples exhibit similar characteristic powder spectra caused by an axially symmetric¹⁹⁹Hg spin interaction. The isotropic value and the anisotropy of the tensor relative to solid HgCl₂ as a standard substance is estimated. Furthermore, results of^63,65Cu NMR measurements at a temperature of 4.2 K which exhibit a typical powder line shape (forI=3/2) are presented.     

Non-equilibrium population and slow relaxation of Fe2+ in57Co:LiNbO3 and57Co:LiTaO3 single crystals

The Fe²⁺ fraction observed in the Mössbauer emission spectra of⁵⁷Co:LiNbO₃ and⁵⁷Co:LiTaO₃ exhibits both slow electronic relaxation and nonthermal populations of them _s sublevels of the⁵A_lg orbital singlet ground state at low temperatures (T<15 K) in high magnetic fields. The relaxation rates depend on temperature and on the angle ? between the magnetic field and the crystallographicc-axis.     

Two-dimensional on- and off-resonance nutation FFT/MEM NQR spectroscopy

The new two-dimensional nuclear quadrupole resonance experiments based on the principle of nutation spectroscopy, which can be used to determine the asymmetry parameter, and thus the full quadrupolar tensor of spin-3/2 nuclei at zero applied magnetic field are discussed. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. Use of the MEM in 2D-NQR spectroscopy can lead to sensitivity improvement, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. The possibilities of off-resonance irradiation in nutation experiments are demonstrated experimentally and theoretically. It is shown that the off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments thus facilitating the determination of asymmetry parameters in multiple spectrum. The methods have been successfully demonstrated for the³⁵Cl on-and off-resonance 2D-nutation spectra in polycrystalline 2,4,6-trichloro-1,3,5-triazine.     

Two-dimensional nutation exchange NQR spectroscopy: direct determination of rotational angles

A new method for the direct determination of rotational angles based on 2-dimensional nutation exchange NQR spectroscopy is proposed. The method involves the detection of exchange processes through NQR nutation spectra recorded after the mixing interval. The response is analysed of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence with incrementing pulse widths. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively. It is shown that the 2D nutation exchange NQR spectrum exhibits characteristic ridges, which reveal the motional mechanism in a model-independent fashion. The angles through which the molecule rotates can be read directly from elliptical ridges in the 2D spectrum, which are also sensitive to the value of asymmetry parameter of the electric field gradient tensor.     

NQR study of spin-freezing in superconducting La2−x Sr x CuO4: the example ofx = 0.06

Nuclear quadrupole resonance (NQR)¹³⁹La and⁶³Cu spin-lattice relaxation rateT ₁ ^t-1 measurements in a La_1.94Sr_0.06CuO₄ single crystal are described. Slowing-down of Cu²⁺ spin fluctuations is evidenced through a dramatic increase of¹³⁹ T ₁ ^?1 on cooling. While the onset of diamagnetism occurs atT _c = 8 K,¹³⁹ T ₁ ^?1 has a peak atT _g ? 5 K, when the characteristic frequency of magnetic fluctuations reaches the NQR frequencyv _Q ? 9 MHz. In agreement with a number of previous studies, these results show that the so-called “cluster spin-glass” phase persists in the superconducting regime. Issues concerning the coexistence of the two phases are discussed.     

Electron spin resonance and longitudinal relaxation around phase transition in La0.9Ca0.1 MnO3

With original modulation technique, the longitudinal electron spin-relaxation timeT ₁ has been measured in the La_1-xCa_xMnO₃ manganite (x = 0.1) both in the paramagnetic state and around the temperature (T _c) of the ferromagnetic ordering. The data are compared with the evolution of the transverse relaxation time T₂ as determined from the electron spin resonance (ESR) linewidth. Well above T_c, theT ₁ =T ₂ equality was confirmed, whereas a steep slowing down ofT ₂ was observed asT _c was approached (theT ₁/T₂ ratio increased by two orders of magnitude). The temperature dependence ofT ₁ within the whole temperature range was found to be consistent with that ofT · χ(T), where χ(T) is the electron-spin susceptibility obtained from the ESR absorption area. The interpretation suggests that both the longitudinal and transverse electron-spin relaxation rates are governed by strong exchange interaction between the Mn ions, the ESR linewidth being inhomogeneously broadened in the vicinity of the phase transition.     

Structures and electronic states of photoexcited states in a system of two nitroxide radicals linked to fullerene studied by two-dimensional pulsed nutation and time-resolved electron paramagnetic resonance spectroscopy

Magnetic properties of fulleropyrrolidine adducts with two stable nitroxide radicals (2,2,6,6-tetramethylpiperidine-1-oxyl, TEMPO) were studied in toluene solution by continuous-wave time-resolved (TR) and pulsed electron paramagnetic resonance (EPR) spectroscopy in the ground and photoexcited states. Four isomers of the bisadduct,trans-1,trans-2,trans-3, and equatorial forms, having the second pyrrolidine ring at different [6-6] bonds were synthesized. In the ground states, the exchange interaction between two TEMPOs is so small that the spin state of the bisadduct is a doublet in nature. By means of spectral simulations of the EPR spectra in frozen solution at 70 K, the upper limit of the exchange interaction was estimated to be 5 MHz for thetrans-1 andtrans-2 and 10 MHz for thetrans-3 and equatorial isomers. The simulation was also made to determine relative positions of the two TEMPO groups with respect to the pyrrolidine ring. Photoexcited states of the bisadducts with excitation of the 532 nm laser pulse were studied in frozen toluene solution at 5–100 K by using two-dimensional (2-D) pulsed nutation EPR and TREPR. The spin multiplicity of the excited state was determined by the nutation frequency. All of the four bisadducts showed strong exchange couplings between two TEMPOs and fullerene triplet³C ₆₀ ^* , resulting in the generation of the excited quintet and triplet states. The excited triplet states have been observed and assigned for the first time in strongly coupled triplet-radical systems. The zero-field splittings of the quintet state determined from the 2-D nutation EPR spectra were analyzed as the sum of the spinspin interactions among the three paramagnetic centers, two TEMPOs and³C ₆₀ ^* . On the basis of these analyses, the spin distribution on the³C ₆₀ ^* part and the geometry of two TEMPOs are discussed.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.     

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)     

Relaxation phenomena and nuclear magnetic resonance of116In(T 1/2=14s) produced by capture of polarized neutrons in the indium III–V compounds

Polarized¹¹⁶In nuclei have been produced by capture of polarized thermal neutrons in several In compounds. At temperaturesT below 77 °K and magnetic field strengthsH ₀ of several kOe, asymmetries of a few percent of the β^? decay of the¹¹⁶In ground state could be observed in polycrystalline InP, InAs and InSb, thus indicating the nuclear polarization. Nuclear magnetic resonance signals have been measured with the result for the magnetic moment μ _i (¹¹⁶In)=2.7723 (10) nm (uncorrected). β^? decay asymmetry and spin lattice relaxation timeT ₁ have been studied as a function ofH ₀ andT. The effect ofH ₀ is to decouple the hyperfine interaction caused by the capture-γ recoil process. However,H ₀ has no influence uponT ₁, which demonstrates the absence of nuclear relaxation due to paramagnetic impurities.T ₁ is determined by quadrupolar relaxation. A quadrupole momentQ(¹¹⁶In)=0.09 (2) b was calculated by comparison of the¹¹⁶In relaxation rates with those of the stable¹¹⁵In isotope in the same compounds. Above 30 °K the temperature dependence of 1/T ₁ agrees with a recent theoretical investigation. Below 30 °K the relaxation rate shows an anomalous behaviour, which can be explained by resonance modes due to recoil lattice defects.