A New Two-Dimensional Pulse Sequence for T2* Measurements of Protons in C Isotopomers

A new two-dimensional pulse sequence for T₂* measurement of protons directly coupled to ¹³C spins is proposed. The sequence measures the tranverse relaxation time of heteronuclear proton single-quantum coherence under conditions of free precession and is therefore well suited to evaluate relaxation losses of proton magnetization during preparation delays of heteronuclear pulse experiments in analytical NMR. The relevant part of the pulse sequence can be inserted as a “building block” into any direct or inverse detecting H,C correlation pulse sequence if proton spin–spin relaxation is to be investigated. In this contribution, the building block is inserted into a HETCOR as well as into a HMQC pulse sequence. Experimental results for the HETCOR-based sequence are given.     

Effects of L-spin longitudinal quadrupolar relaxation in heteronuclear recoupling and S-spin magic-angle spinning NMR

In experiments on S–L heteronuclear spin systems with evolution of the S-spin magnetization under the influence of a quadrupolar nucleus (L-spin), effects of longitudinal quadrupolar (T_1Q) relaxation of the L-spin coherence on the sub-millisecond time scale have been documented and explored, and methods for minimizing their effect have been demonstrated. The longitudinal relaxation results in heteronuclear dephasing even in the reference signal S₀ of S{L} REDOR, REAPDOR, RIDER, or SPIDER experiments, due to T_1Q-relaxation of the transiently generated S_yL_z coherence, reducing or even eliminating the observable dephasing ΔS. Pulse sequences for measuring an improved reference signal S₀₀ with minimal heteronuclear recoupling but the same number of pulses as for S₀ and S have been demonstrated. From the observed intensity ΔS₀ = S₀₀ − S₀ and the SPIDER signal ΔS/S₀, T_1Q can be estimated. Accelerated decays analogous to the dipolar S₀ curves will occur in T₂ measurements for J-coupled S–L spin pairs. Even in the absence of recoupling pulses, fast T_1Q relaxation of the unobserved nucleus shortens the transverse relaxation time T_2S,MAS of the observed nucleus, in particular at low spinning frequencies, due to unavoidable heteronuclear dipolar evolution during a rotation period. The observed spinning-frequency dependence of T_2S,MAS matches the theoretical prediction and may be used to estimate T_1Q. The effects are demonstrated on several ¹³C{¹⁴N} spin systems, including an arginine derivative, the natural N-acetylated polysaccharide chitin, and a model peptide, (POG)₁₀.     

Stretched exponential relaxation and dispersive conductivity behavior in lithium bismuth silicate glasses

Glasses having compositions xLi₂O∙(85 − x)Bi₂O₃∙15SiO₂ (x = 35, 40, and 45 mol%) were prepared by normal melt quenching technique. Electrical relaxation and conductivity in these glasses were studied using impedance spectroscopy in the frequency range from 20 Hz to 1 MHz and in the temperature range from 453 to 603 K. The ac and dc conductivities, activation energy of the dc conductivity and relaxation frequency were extracted from the impedance spectra. The dc conductivity increases with increase in Li₂O content providing modified glass structure and large number of mobile lithium ions. Similar values of activation energy for dc conduction and for conductivity relaxation time indicate that the ions overcome the same energy barrier while conducting and relaxing. The non-exponential character of relaxation processes increases with decrease in stretched exponential parameter ‘β’ as the composition parameter ‘x’ increases. The observed conductivity spectra follow a power law with exponent ‘s’ which increases regularly with frequency and approaches unity at higher frequencies. Nearly constant losses (NCL) characterize this linearly dependent region of the conductivity spectra. A deviation from the ‘master curve’ for various isotherms of conductivity spectra was also observed in the high-frequency region and at low temperatures, which supports the existence of different dynamic processes like NCL in addition to the ion hopping processes in the investigated glass system.     

μ+SR Study of Ordering Phenomena in the Heavy-Fermion State of Ce3Pd20Ge6

Magnetic and quadrupolar ordering phenomena in a Ce₃Pd₂₀Ge₆ single crystal have been investigated by muon spin rotation/relaxation (μ⁺SR) spectroscopy. We have observed spontaneous precession of muons in zero-field below T _N =0.7 K in the antiferromagnetic state. The precession frequency follows the power law: ν(T)=ν(0)(1−T/T _N ) ⁿ . The exponent n=0.43(2) is close to the mean-field value of 0.5. The muon longitudinal spin relaxation rate 1/T ₁ is found to be nearly independent of temperature in the range of 0.3 to 2 K, i.e., across either T _N or T _Q =1.2 K, the quadrupolar ordering temperature. Two likely mechanisms for the temperature independent behavior of 1/T ₁ are suggested. This revised version was published online in September 2006 with corrections to the Cover Date.     

Effect of impurities scattering potential on NMR relaxation rate in impure d-wave superconductors

The purpose of our research is to study the nuclear spin lattice relaxation rate of impure d-wave superconductors. We use the Green’s function method to derive the approximation equation of density of states including the impurity scattering potential. We can get the analytic equation of the nuclear spin lattice relaxation rate that contained the impurity scattering potential in case of weak scattering potential and strong scattering potential in the simple form as the power series of Δ(T) and T. The numerical calculations show that there is coherence peak in the weak impurity scattering potential but there is no peak in the strong impurity scattering potential.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Critical nuclear relaxation in cobalt metal

Nuclear magnetic resonance of cobalt metal was investigated in the paramagnetic and ferromagnetic states and in the critical region below T_c. The Knight shift and spin lattice relaxation times were measured in the paramagnetic phase in the solid and liquid states from 1578 K to 1825 K. The resonant frequency, spin-lattice and spin-spin relaxation times were measured in the ferromagnetic phase from room temperature to 1385 K. The main part of (T₁T)^-1 results from fluctuating orbital moments in both phases except near T_c where this process forms the background for critical spin relaxation. The critical exponents for T^-1₁ and for the magnetization in the ferromagnetic state were found to be n' = 0.96 ± 0.07 and β = 0.308 ± 0.012, respectively.     

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

A precise measurement of the spin-dependent neutron scattering length of 3He

The poor knowledge of the spin-dependent neutron scattering length of ³He has until now handicapped nuclear four body theory and the interpretation of excitations in the quantum liquid. We have measured, for the first time directly, the real part of the bound incoherent neutron scattering length, b_i′ of ³He. A neutron spin echo spectrometer was used to detect pseudomagnetic precession of polarised neutrons passing through polarised ³He gas. Any absolute calibrations of sample and beam parameters were avoided using simple transmission measurements with non-polarised neutrons. The only a priory information required was the spin-dependent neutron absorption cross section of ³He. The result is b_i′ = -2.365(20) fm, which reduces the prior uncertainty by a factor 30. The corresponding new value of the bound incoherent scattering cross section is σ_i = 1.532(12) barn. Including the known value of the coherent neutron scattering length, we obtain new values for the real parts of the free triplet and singlet neutron scattering lengths, a_-′ = 7.370(58) fm and a₊′ = 3.278(53) fm.     

Electronic structure and spectrum of Cr3+ in LiCaAlF6

The electronic structure and spectrum of Cr³⁺ in LiCaAlF₆ are investigated by using the discrete variatitional-local density functional (DV-LDF) method with embedded cluster model. The clusters (CrF₆)^3– withC ₃,D _3d andO _h point group symmetries embedded in the crystal are treated. The one-electron energy levels, densities of states, orbital populations, spin polarization splittings and energies of some terms are calculated. The results show that the relaxation of F^– ions around the Cr³⁺ impurity is inevitable, and that theD _3d andO _h (CrF₆)^3– clusters, with an extended bond-lengthR(Cr–F) chosen to be equal to 1.88 Å can represent this relaxation in a much better way. All the ligand-field transition energies, which are obtained from the transition-state energy and the Griffith parameters, as yielded by a restricted one-electron DV-LDF calculation, compare well with the experimental ones.     

Spin-dependent photoabsorption at theL-edges of ferromagnetic Gd and Tb metal

The spin-dependent absorption of circularly polarized x-rays is studied at theL-edges of ferromagnetic Gd and Tb metal. At theL ₁-edge a spin-dependent part of the absorption coefficient of 10^–3–10^–2 is observed. Strong resonance absorption known as white line occurs at theL ₂- andL ₃-absorption onset. Correlated with it one finds large spin-dependent absorption effects with amplitudes of a few percent. The spin-dependent absorption spectra reflect the profiles of the spin densities of the states populated in the absorption process. Thep-states show spin densities correlated with the first two flat bands above the Fermi level. The spin density of thed-like states is concentrated in the energy range of the white line. In Gd a splitting of (0.5–0.6) eV of the unoccupied 5d spin up and spin down bands is indicated for both spin-orbit partners. In Tb a large dependence of the 5d spin density on the spin-orbit configuration is observed. The experimental results on the spin densities in Gd are compared with band structure calculations for the ferromagnetic ground-state. The theoretical and experimental spin density profiles agree well for thep-states but not for thed-states. The discrepancy concerning thed-states may be attributed to core-hole polarization effects in the absorption process.     

Large spin corrections in SYM : Still a linear integral equation

Anomalous dimension and higher conserved charges in the sl(2) sector of SYM for generic spin s and twist L are described by using a novel kind of non-linear integral equation (NLIE). The latter can be derived under typical situations of the SYM sectors, i.e. when the scattering need not depend on the difference of the rapidities and these, in their turn, may also lie on a bounded range. Here the non-linear (finite range) integral terms, appearing in the NLIE and in the dimension formula, go to zero as s→∞. Therefore they can be neglected at least up to the O(s⁰) order, thus implying a linear integral equation (LIE) and a linear dimension/charge formula respectively, likewise the ‘thermodynamic’ (i.e. infinite spin) case. Importantly, these non-linear terms go faster than any inverse logarithm power (lns)⁻ⁿ, n>0, thus extending the linearity validity.     

Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

Relaxation times and line widths of isotopically-substituted nitroxides in aqueous solution at X-band

Optimization of nitroxides as probes for EPR imaging requires detailed understanding of spectral properties. Spin lattice relaxation times, spin packet line widths, nuclear hyperfine splitting, and overall lineshapes were characterized for six low molecular weight nitroxides in dilute deoxygenated aqueous solution at X-band. The nitroxides included 6-member, unsaturated 5-member, or saturated 5-member rings, most of which were isotopically labeled. The spectra are near the fast tumbling limit with T₁∼T₂ in the range of 0.50–1.1 μs at ambient temperature. Both spin–lattice relaxation T₁ and spin–spin relaxation T₂ are longer for ¹⁵N- than for ¹⁴N-nitroxides. The dominant contributions to T₁ are modulation of nitrogen hyperfine anisotropy and spin rotation. Dependence of T₁ on nitrogen nuclear spin state m_I was observed for both ¹⁴N and ¹⁵N. Unresolved hydrogen/deuterium hyperfine couplings dominate overall line widths. Lineshapes were simulated by including all nuclear hyperfine couplings and spin packet line widths that agreed with values obtained by electron spin echo. Line widths and relaxation times are predicted to be about the same at 250 MHz as at X-band.     

Limits on the neutrino magnetic moment from solar neutrino experiments

If neutrinos have non-vanishing mass and non-vanishing magnetic moments, then electron neutrinos emitted in nuclear reactions in the solar interior may undergo flavour oscillations, spin precession or resonant spin-flavour precession. Assuming equal values for the magnetic moments of all neutrino flavours and using the data from Homestake and SuperKamiokande we obtain an upper limit on the neutrino magnetic moment and find μ_νe ≤ (2.2 − 2.3) × 10⁻¹⁰μ_B, within four standard solar models. We also point out that this limit may be further reduced if the detector threshold energy for the ν_e,χe⁻ scattering is decreased.     

NMRON spin echo in a slowly varying magnetic field

Nuclear spin-spin relaxation of⁶⁰Co and⁵⁶Co in iron single crystals has been studied, using the three-pulse NMRON spin echo. A previously reported rapidT ₂ in⁶⁰CoFe is shown to have arisen from a modulation of the echo amplitude, caused by variations in the phase of the Larmor precession relative to the applied rf field. A lower limit ofT ₂∼0.2s is found in⁵⁶Co⁵⁶ Fe. Extension of this result to other CoFe samples is discussed.     

Numerical renormalization group studies of SU(4) Kondo effect in quantum dots

We theoretically study an enhancement of the Kondo effect in quantum dots with two orbitals and spin . The Kondo temperature and conductance are evaluated as functions of energy difference Δ between the orbitals, using the numerical renormalization group method. The Kondo temperature is maximal around the degeneracy point (Δ=0) and decreases with increasing |Δ| following a power law, T_K(Δ)=T_K(0)(T_K(0)/|Δ|)^γ, which is consistent with the scaling analysis. The conductance at T=0 is almost constant 2e²/h. Both the orbitals contribute to the conductance around Δ=0, whereas the current through the upper orbital is negligibly small when |Δ|T_K(0). These are characteristics of SU(4) Kondo effect.     

Mirror supersymmetry in the space of (super) extended Poincaré algebras p(p,q)

We classify extended Poincaré Lie superalgebras and Lie algebras of any signature (p, q), i.e. Lie superalgebras and ₂-graded Lie algebras g = g₀ + g₁, where g₀ = s₀(V) + V is the (generalized) Poincaré Lie algebra of the pseudo Euclidean vector space V = ^{p, q} of signature (p, q) and g₁ is a spin 1/2 s₀(V)-module extended to a s₀-module with kernel V.As a result of the classification, we obtain, if g₁ = S is the spinor module, the numbers L ⁺(n, s) (resp. L ^–(n, s)) of independent such Lie super algebras (resp. Lie algebras), which are periodic functions of the dimension n=p+q (mod 8) and the signature s=p–q (mod 8) and satisfy: L ⁺(–n, s)=L ^– (n, s).Supported by Max-Planck-Institut für Mathematik (Bonn).Supported by the Alexander von Humboldt Foundation, MSRI (Berkeley) and SFB 256 (Bonn University).     

μSR study of the S=1/2 triangular lattice antiferromagnet AgNiO2

AgNiO₂, a model compound of an S=1/2 triangular lattice, was studied by muon spin relaxation in addition to ac, dc susceptibility, electrical resistivity and neutron diffraction. The relaxation rate shows a sharp peak at around T_N=28 K followed by a sudden decrease of initial asymmetry indicating a magnetic ordering. Three internal fields ranging from 0.2 to 0.3 T were obtained from the muon precession period. However, a neutron diffraction experiment failed to detect any magnetic order at low temperatures. From these results, it was concluded that magnetic coherence is confined to small domain compared with the coherence length of neutron diffraction due to spin frustration. This revised version was published online in August 2006 with corrections to the Cover Date.