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.     

Influential Factors of Internal Magnetic Field Gradient in Reservoir Rock and Its Effects on NMR Response

Nuclear magnetic resonance (NMR) plays a significant role in porous media analysis and petroleum exploration, but its response is significantly influenced by the internal magnetic field gradient in fluid saturated porous medium, which obviously limits the accuracy of rock core analysis and logging interpretation. The influential factors of the internal magnetic field gradient in formation and its influences on NMR response are studied in this paper, based on NMR mechanism through one- and two-dimensional core NMR experiments. The results indicate that the internal magnetic field gradient is positively correlated with the static magnetic field strength and the magnetic susceptibility difference between pore fluid and solid grains, while it presents negative correlation with pore radius. The internal magnetic field gradient produces an additional diffusion relaxation in hydrogen relaxation system and accelerates the attenuation of magnetization vector. As a result, T₂ spectrum shifts to the left and NMR porosity and diffusion coefficient of the fluid could be inaccurate. This research sets a foundation for the NMR porosity correction and fluid distribution on T₂-G maps based on the internal magnetic field gradient correction.     

The stabilization of unusual conformers in guest-host systems: Solid-state NMR investigations of 2-methylhexadecane in urea and thiourea

Solid-state nuclear magnetic resonance (NMR) spectroscopy is employed for the first time on urea and thiourea inclusion compounds (UICs and TICs) containing branched alkyl chains. In the present work,²H and¹³C NMR as well as X-ray diffraction studies of two selectively deuterated 2-methylhexadecanes in UIC and TIC are presented. An analysis of the derivedT ₁ data reveals significant differences between UICs and TICs, which can be attributed to differences in the motional features of the guest species. It is found that four different motional contributions have to be considered, namely, chain rotation, chain wobbling,trans-gauche isomerization and methyl group rotation. 2-Methylhexadecane in UIC exists in an almost all-trans conformation (gauche amount not more than 5%) and undergoes fast chain rotation (6-site jump process, activation energyE _A=16.7 kJ/mol). The analysis of the²H NMR spectra of 2-methylhexadecane-1,1′,2-d₇ in urea proves that the branched chain end exists in an eclipsed conformation. TheT ₁ data of 2-methylhexadecane-3-d₂ in thiourea can be reproduced by an overall rotation (E _A=9.8 kJ/mol) and atrans-gauche isomerization with torsional jumps around the C-3-C-4 bond (E _A=11.0 kJ/mol,gauche population=15%). As for the corresponding UIC, the²H NMR spectra of 2-methylhexadecane-1,1′,2-d₇ in TIC can be only explained by the existence of an eclipsed conformation at the branched chain end.     

Spin-glass behavior as a function of concentration and local order by NMR in nearly random NiMn systems

Unidirectional anisotropy fields (H_A) in disordered Ni_{100 ? x}Mn_x (25 ? x ? 32) systems after field cooling are found by NMR (spin echo) to be very sensitive to the Mn concentration and to local order. The H_A increases by roughly a factor of 10 when the concentration increases 5%. The Mn NMR spectra show that all Mn have several first nearest Mn neighbours. For a given concentration, in the above range, the H_A are very sensitive to the annealing-quenching temperatures (T_AQ) and vanish when the sample is cooled down from 900°C in 2 h. The NiMn system can be tuned by heat treatments from spin-glass to a ferromagnet. The Mn NMR spectra with decreasing T_AQ show a clear metallurgical evolution tending to states where a Mn atom sees fewer first nearest Mn neighbours. We find evidence that the anisotropy has its roots in atomic randomness.     

Estimation of Permeability by Integrating Nuclear Magnetic Resonance (NMR) Logs with Mercury Injection Capillary Pressure (MICP) Data in Tight Gas Sands

It has been a great challenge to determine permeability in tight gas sands due to the generally poor correlation between porosity and permeability. The Schlumberger Doll Research (SDR) and Timur–Coates permeability models, which have been derived for use with nuclear magnetic resonance (NMR) data, also lose their roles. In this study, based on the analysis of the mercury injection experiment data for 20 core plugs, which were drilled from tight gas sands in the Xujiahe Formation of central Sichuan basin, Southwest China, two empirical correlations between the pore structure index ( $ \sqrt {{K \mathord{\left/ {\vphantom {K \varphi }} \right. \kern-0em} \varphi }} $ , defined by the square root of the ratio of rock permeability and porosity) and the R ₃₅ (the pore throat radius corresponding to 35.0 % of mercury injection saturation), the pore structure index and the Swanson parameter have been developed. To consecutively estimate permeability in field applications, based on the study of experimental NMR measurements for 36 core samples, two effective statistical models, which can be used to derive the Swanson parameter and R ₃₅ from the NMR T ₂ logarithmic mean value, have been established. These procedures carried out on the experimental data set can be extended to reservoir conditions to estimate consecutive formation permeability along the intervals with which NMR logs were acquired. The processing results of several field examples using the proposed technique show that the classification scale models are effective only in tight gas reservoirs, whereas the SDR and Timur–Coates models are inapplicable. The R ₃₅-based model is of significance in thin sands with high porosity and high permeability, but the predicted permeability curves in tight gas sands are slightly lower. In tight gas and thin sands, the Swanson parameter model is all credible.     

Optorelaxers: Achieving real-time control of NMR relaxation

We present an approach to increase the detection sensitivity of NMR by shortening the spin-lattice relaxation time using transient paramagnetic species created by light irradiation of “optorelaxer” molecules. In the ultimate implementation of this concept, not yet realized here, these transient species are absent during the detection period, thereby avoiding the loss of spectral resolution caused by inhomogeneous broadening from paramagnetic species. Real-time control of NMR relaxation by visible light is demonstrated with Fe(II)(ptz)₆(BF₄)₂, (ptz = 1-propyltetrazole), abbreviated FePTZ. Illumination of FePTZ at 30 K results in a decrease of the ¹H NMR spin-lattice relaxation time T₁ due to formation of a high spin photoexcited state. The ¹H NMR of polystyrene containing a low concentration of FePTZ molecules shows a similar reduction in T₁, establishing that FePTZ can act as an optorelaxer for the protons of a matrix. Numerical modeling of the spin-diffusion processes from the protons in a FePTZ core to those in a shell of polystyrene accounts for the observed T₁ effects under both dark and light conditions. Additionally, ¹H MAS (magic-angle spinning) NMR results for pure FePTZ provide information on the isotropic and anisotropic portions of the electron-nuclear hyperfine interactions.     

Multiple quantum NMR transitions of8Li (T 1/2=0.84 s) in single crystals and powders of LiTaO3, and the quadrupole moment of8Li

Multiple quantum nuclear magnetic resonance (NMR) transitions were observed on polarized⁸Li nuclei, which were produced by capture of polarized neutrons in a single crystal of LiTaO₃. The asymmetric⁸Liβ-radiation distribution was used for the detection of NMR. A quadrupole moment ratio ¦Q(⁸Li)/Q(⁷Li)¦=0.78(1) was determined. Saturation of multiple quantum transitions in nuclear radiation detected NMR may lead to a reduction in measuring time of up to two orders of magnitude, as compared to single quantum detection methods. The measured spectra agree well with an exact lineshape calculation. The same measurements were also performed on a LiTaO₃ powder sample. This was done to test a method to obtain quadrupole coupling constants from high field NMR multiple quantum powder patterns, which are easily detectable, also for higher nuclear spins. This latter method may be applicable also to conventional NMR detection techniques.     

Solid-state NMR/NQR and first-principles study of two niobium halide cluster compounds

Two hexanuclear niobium halide cluster compounds with a [Nb₆X₁₂]²⁺ (X=Cl, Br) diamagnetic cluster core, have been studied by a combination of experimental solid-state NMR/NQR techniques and PAW/GIPAW calculations. For niobium sites the NMR parameters were determined by using variable B_o field static broadband NMR measurements and additional NQR measurements. It was found that they possess large positive chemical shifts, contrary to majority of niobium compounds studied so far by solid-state NMR, but in accordance with chemical shifts of ⁹⁵Mo nuclei in structurally related compounds containing [Mo₆Br₈]⁴⁺ cluster cores. Experimentally determined δ_iso(⁹³Nb) values are in the range from 2400 to 3000 ppm. A detailed analysis of geometrical relations between computed electric field gradient (EFG) and chemical shift (CS) tensors with respect to structural features of cluster units was carried out. These tensors on niobium sites are almost axially symmetric with parallel orientation of the largest EFG and the smallest CS principal axes (V_zz and δ₃₃) coinciding with the molecular four-fold axis of the [Nb₆X₁₂]²⁺ unit. Bridging halogen sites are characterized by large asymmetry of EFG and CS tensors, the largest EFG principal axis (V_zz) is perpendicular to the X-Nb bonds, while intermediate EFG principal axis (V_yy) and the largest CS principal axis (δ₁₁) are oriented in the radial direction with respect to the center of the cluster unit. For more symmetrical bromide compound the PAW predictions for EFG parameters are in better correspondence with the NMR/NQR measurements than in the less symmetrical chlorine compound. Theoretically predicted NMR parameters of bridging halogen sites were checked by ^79/81Br NQR and ³⁵Cl solid-state NMR measurements.     

A Portable NMR Sensor Used for Assessing the Aging Status of Silicone Rubber Insulator

A portable nuclear magnetic resonance (NMR) sensor with an adjustable ‘clamp’ structure is constructed for the noninvasive measurement of the aging status of silicone rubber insulators used in the high-voltage power transmission. The Carr–Purcell–Meiboom–Gill sequence was employed to record the ¹H NMR transverse relaxation curves of silicone rubber insulators with different service times. The decay curves were fitted to mono-exponential and bi-exponential functions. Further data processing of the decay curves was performed with the inverse Laplace transformation for one-dimensional T ₂ distribution analysis, focusing on the mean lifetime of the long T ₂ component (T _{2long mean}). The results demonstrate that an increase in the aging level of the insulator clearly results in a decrease of T _{2long mean}. For comparison, the relative permittivity of the insulator was also measured. It shows the same trend as that of T _{2long mean}. This indicates that the T _{2long mean} relaxation time obtained from our portable NMR sensor can reliably be used as an index to reflect the aging status of silicone rubber insulator.     

On the representation theory of quantum Heisenberg group and algebra

We show that the quantum Heisenberg groupH _q (1) and its *-Hopf algebra structure can be obtained by means of contraction from quantumSU _q (2) group. Its dual Hopf algebra is the quantum Heisenberg algebraU _q (h(1)). We derive left and right regular representations forU _q (h(1)) as acting on its dualH _q (1). Imposing conditions on the right representation, the left representation is reduced to an irreducible holomorphic representation with an associated quantum coherent state. Realized in the Bargmann-Hilbert space of analytic functions the unitarity of regular representation is also shown. By duality, left and right regular representations for quantum Heisenberg group with the quantum Heisenberg algebra as representation module are also constructed. As before reduction of group left representations leads to finite dimensional irreducible ones for which the intertwinning operator is also investigated.     

Proton NMR relaxation study of the CsHSO4 solid acid system

At 141 °C the solid acid CsHSO₄ is known to undergo transition to a superprotonic phase that is characterized by dramatic (several-order-of-magnitude) increases in hydrogen ion conductivity. Proton NMR spin-spin relaxation time T₂ measurements reported here for CsHSO₄ also reveal substantial increases (factors of 20-30) in the vicinity of the transition temperature. In the temperature range just below the transition (70-136 °C), T₂ increases by a factor of order 10 relative to the rigid-lattice regime, suggesting motional narrowing of the NMR resonance line. In the regime of motional narrowing, the activation energy barrier to diffusion is 0.40 eV, as determined from the present T₂ results. NMR spin-lattice relaxation T₁ measurements also show behavior consistent with transition to a regime of rapid hydrogen motion. In particular, proton T₁'s decrease with temperature (from 80 to 120 °C), and then drop sharply near the transition temperature. Above the transition temperature, T₁ exhibits a minimum in which the correlation time is found to be ∼2 ns.     

Pb2MnF6: Antiferromagnet and superionic conductor

Measurements of the EPR linewidth versus temperature indicate Pb₂MnF₆ is an antiferromagnet with T_N = 30 ± 1 K. The disappearance of the low-field NMR lines at T_N confirms these results. The coalescence of the ¹⁹F NMR lines above 500 K show the anion conductivity to be comparable to PbF₂.     

Structural Nature of 7Li and 11B Sites by Static NMR and MAS NMR in Nonlinear Optical Material LiCsB6O10

The relationship between structure and nonlinear optical properties in LiCsB₆O₁₀ is characterized using single-crystal nuclear magnetic resonance (NMR) and magic-angle spinning (MAS) NMR. Although the quadrupole parameters for B(1) and B(2) sites were obtained using single-crystal NMR, the T ₁ values for these atomic sites could not be distinguished in this way. Thus, the structural nature of lithium and boron sites in LiCsB₆O₁₀ was investigated using MAS NMR. B(1) and B(2) sites could be distinguished based on the spectrum and T _1ρ obtained from ¹¹B MAS NMR. In addition, the T ₁ and T _1ρ values and activation energies for ⁷Li and ¹¹B are compared. No significant changes were seen in the T _1ρ at the lithium and boron nuclei in LiCsB₆O₁₀.     

NMR study of the quasi-one-dimensional compound BaCo2V2O8

We report the results of a ⁵¹V nuclear magnetic resonance (NMR) study on the single crystal BaCo₂V ₂O₈ at temperatures between 3 and 300 K. The NMR features for fields both parallel and perpendicular to the c-axis have been identified. We found no substantial changes in the NMR shift and line width at low temperatures as a constant field of 7.06 T was applied along the c-axis. The NMR observations thus indicate the absence of magnetic long-range ordering under this field, consistent with the specific heat result which showed the disappearance of the magnetic transition beyond an external field of 4 T in BaCo₂V ₂O₈.     

Electric field gradient,anisotropic shift,tetrahedral site occupation,and atomic motion in LixTiS2

New measurements of NMR lineshape parameters and relaxation rates have been made to characterize a carefully prepared set of samples of Li_xTiS₂, with x spanning the composition range from one-tenth to one. Electric quadrupole coupling constants are in general agreement with previous measurements, but display differences at the high end of the composition range and an unpredicted upturn as x tends toward zero. An anisotropic shift of the line has been discovered and its possible origins are discussed. An unexpected discontinuity in the linewidth-composition relation may be due to lithium occupation of tetrahedral sites at the level of a few percent. Lithium hopping rates derived from continuous wave NMR and pulsed NMR measurements are found to agree quite well with one another.     

Complex magnetic differentiation of cobalts in Na x CoO2 with 22 K Néel temperature

Single crystals of sodium cobaltates Na _x CoO₂ with x ≈ 0.8 were grown by the floating zone technique. Using electrochemical Na de-intercalation method we reduced the sodium content in the as-grown crystals down to pure phase with 22 K Néel temperature and x ≈ 0.77. The ⁵⁹Co NMR study in the paramagnetic state of the T _N = 22 K phase permitted us to evidence that at least 6 Co sites are differentiated. They could be separated by their magnetic behavior into three types: a single site with cobalt close to non-magnetic Co³⁺, two sites with the most magnetic cobalts in the system, and the remaining three sites displaying an intermediate behavior. This unusual magnetic differentiation calls for more detailed NMR experiments on our well characterized samples.     

Solid H2: Has the quadrupolar glass phase a well-defined transition?

We report measurements of the NMR lineshape, the second and fourth moments (M₂ and M₄), and of the longitudinal relaxation tine in H₂ single crystals. Although a sharp phase transition cannot be excluded, our results for ortho concentrations between 0.15 and 0.4 suggest rather a continuous freezing of rotational motion to a “glass state” as T decreases. In this regime; the NMR spectrum is found to be very nearly isotropic.     

Cross relaxation study on NaClO3 by NMR acoustic saturation

Cross relaxation rate between adjacent NMR lines of Na²³ in NaClO₃ was measured at room temperature by the NMR acoustic saturation method. When the angle φ between the [010] axis and H₀ in the (100) plane is 1.75°, two of the three NMR lines are superposed exactly. As φ is increased gradually, they split and they separate perfectly at φ = 2.75°. Cross relaxation probability between these two lines was measured as a function of the separation. The results are compared with the theory of overlap integral approximation. For small separation the theory reproduces fairly well the experimental results, but for larger separation disagreement appears, which may be due to the Gaussian approximation to the NMR line shape in the theory.     

NMR and NQR studies of spin dynamics and superconductivity in High-T c oxides

The magnetic and superconducting properties in the high-T _c cuprates have been investigated over a wide hole doping range by⁶³Cu,¹⁷O and²⁰⁵Tl NMR and NQR in the lightly-doped La_2?xSr_xCuO₄ (LSCO), the heavily-doped Tl₂Ba₂CuO_6+y (TBCO) and the Zn-doped YBa₂Cu₃O₇ (YBCO₇). In low doping region, the large antiferromagnetic (AF) spin correlation around the zone boundary (q=Q) causes the Curie-Weiss behavior of⁶³(1/T ₁ T) associated with that of the staggered susceptibility χ_O(T) in LSCO. In the vicinity of the hole content whereT _c has a peak, the AF spin correlation still survives, although the magnetic coherence length ξ_M is considerably short being presumably (ξ_M/a) ～ 1. The further doping destroys progressively the AF spin correlation, which is no longer present is non-superconducting TBCO compounds. These NMR evidences signify that there is an intimate relation between the presence of the AF spin correlation and the onset of the superconductivity. The local collapse of AF spin correlation is a primary cause for the unexpected strong reduction ofT _c in case of the substitution of Zn impurities into the CuO₂ plane. The superconducting properties clarified by NMR experiments cannot be accounted for by the conventional BCS model or other isotropic s-wave models. A d-wave model is applicable in interpreting consistently most of the NMR results, if the finite density of states at the Fermi level is taken into consideration and is associated with the pair breaking effect. There are increasing evidences that the magnetic mechanism for the superconductivity is promising in high-T _c cuprates.     

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.