Low-energy electronic spin excitations between filling factors ν=1 and studied by optically detected nuclear magnetic resonance

We report measurements of the spin relaxation time (T_1n) for nuclei in the potential well confining a high-mobility two-dimensional electron system at a single GaAs–GaAlAs heterojunction. At low temperatures nuclear spin relaxation is dominated by electron–nuclear spin scattering: we find that T_1n displays sharp maxima at incompressible states throughout the hierarchy of the fractional quantum Hall effect. This behaviour is consistent with the existence of low-energy spin excitations only where the electron system is compressible. Our measurements also provide evidence for a gap in the spin excitation spectrum at .     

DIRECT MEASUREMENT OF TRANSVERSE RELAXATION TIME OF INTERMOLECULAR MULTIPLE QUANTUM COHERENCES IN NMR

A one-dimensional NMR method is presented for measuring the transverse relaxation time, T_2,n, of intermolecular multiple quantum coherences (IMQCs) of coherence order n in highly polarized spin systems. The pulse sequence proposed in this paper effectively suppresses the effects of radiation damping, molecular diffusion, inhomogeneity of magnetic field, and variations of dipolar correlation distance, all of which may affect quantitation of T_2,n. This pulse sequence can be used to measure not only IMQC transverse relaxation time T_2,n(n>1) quickly and directly, but also the conventional transverse relaxation time. Experimental results demonstrate that the quantitative relationship between T_2,n(n≥1) and T₂ is T_2,n≈T₂/n. These results will be helpful for understanding the fundamental properties and mechanisms of IMQCs.     

Characterization and Suppression Techniques for Degree of Radiation Damping in Inversion Recovery Measurements

Radiation damping is a phenomenon in which transverse nuclear magnetization couples with the current in a coil used in nuclear magnetic resonance experiments. This results in an additional magnetic field that increases the relaxation pathway for the magnetization, which then relaxes back to equilibrium more quickly. Radiation damping has been shown to affect longitudinal relaxation time (T₁) measurement in inversion recovery experiments. In this work, we demonstrate that the extent of radiation damping depends upon the T₁ of the sample. Radiation damping difference spectroscopy is used to characterize the severity of radiation damping, while gradient inversion recovery is used for radiation damping suppression in T₁ measurements. At field strength of 9.4 T, for the radiation damping characteristic time (T_rd) of 50 ms, these investigations show non-negligible radiation damping effects for T₁ values greater than T_rd, with severe distortions for T₁ longer than about 150 ms, showing reasonable agreement with the predicted T_rd. We also report a discrepancy between published expressions for the characteristic radiation damping time.     

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.     

14N pulsed nuclear quadrupole resonance. 3. Effect of a pulse train. Optimal conditions for data averaging

The calculations developed in this paper aim at determining the optimal conditions of a NQR experiment when a transition is monitored by means of a pulse train with pulses of identical duration and signal acquisition after each pulse; coherences are assumed to vanish by effective transverse relaxation prior to every new pulse. These calculations demonstrate that, as in NMR, a steady state is effectively reached for any value of the recycle time. However, by contrast with NMR, it is shown that, for optimal data averaging under steady state conditions, the recycle time T can be kept as low as possible (the only limitation is the acquisition time). Nutation curves (signal amplitude versus pulse length) calculated in the steady state case are shown to depend strongly on the ratio T/T ₁ (T ₁: longitudinal relaxation time). The signal growth as a function of T/T ₁under averaging of the first transients has been evaluated as well as the number of pulses necessary for reaching a steady state.     

Hydrogen bond dynamics in dodecanoic acid studied by QNS and NMR

The dynamics of hydrogen atoms in the hydrogen bonds of molecular dimers in dodecanoic acid (c phase) have been studied by quasi-elastic neutron scattering and pulsed nuclear magnetic resonance. Q-dependence measurements of the intensity of the quasi-elastic peak have established that the hydrogen atoms move along a line connecting the two oxygen atoms in the hydrogen bond. The correlation time for this motion has been studied by temperature dependence measurements of the width of the quasi-elastic line and of the proton spin-lattice relaxation time,T ₁. These studies reveal the quantum mechanical nature of the dynamics in the low temperature region. The dynamical parameters which characterise the motion have been determined by fitting the data to a model which invokes phonon assisted tunnelling. The frequency dependence ofT ₁ at low temperature is anomalous because the gradient of the ln(T ₁) vs 1/T curve is dependent on the applied magnetic field.     

Spin relaxation and magnetic shielding of 93Nb nuclei in [NbCl n Br6-n ]- anions

The temperature dependence of T ₁ and T ₂ relaxation times of ⁹³Nb nuclei in octahedral [NbCl _n Br_6-n ]^-(n = 0 to 6) complexes contained in acetonitrile solution is measured. The relaxation rate is found to be controlled by quadrupole interactions in all complexes except cis-[NbCl₃Br₃]^-. The relaxation mechanism in cis-[NbCl₃Br₃]^- anion depends on exchange processes associated with intramolecular cis?trans isomerization. Calculated values of the electric field gradient (EFG) tensor invariant g _φ ² agree qualitatively with experimental values of T _1,2 ^-1. For cis-[NbCl₃Br₃]^- g _φ ² = 0. On the basis of data for T ₁ and T ₂ the assignment of resonant signals to isomers has been established. The relative chemical shift of cis and trans isomers does not correspond to that evaluated by using a pairwise additivity model. The variations of diamagnetic Δσ^d and paramagnetic Δσ^p contributions to the shielding constant of ⁹³Nb nuclei with the composition of coordination sphere are calculated. Δσ^p contribution to the chemical shifts in the [NbCl _n Br_6-n ]^- is shown to be about 70 per cent.     

Field dependence of spin-lattice relaxation of Nd3+ ions in Y3Al5O12 crystals

Our studies involve measuring spin-lattice relaxation times for Nd³⁺ ions in yttrium-aluminum garnets over the temperature range 4–50 K at 9.25 and 36.4 GHz for different orientations of the external magnetic field in relation to the crystallographic axes. The temperature dependence of the relaxation rate is described by T ₁ ⁻¹ =AT ⁿ+b exp(−Δ/kT), where n varies from sample to sample, with n=1 for “perfect” samples (i.e., with the longest relaxation times). Here Δ is approximately 130 cm⁻¹, which is the energy of the excited Kramers doublet of the neodymium ion closest to the ground state, and this makes it possible to interpret the second term in T ₁ ⁻¹ as the contribution of two-stage relaxation proceeding through the intermediate level Δ. A strong field dependence of these processes has been discovered: when the frequency was increased fourfold, the relaxation rate increased by a factor of 10. The effect is a specific manifestation of the degeneracy of the excited level, breaking of the symmetry of the crystalline field due to lattice defects, and the prevalence of deformations of a certain type in the spin-lattice interaction. Zh. éksp. Teor. Fiz. 111, 332–343 (January 1997)     

Polar optical phonon limited energy and momentum relaxation of hot electrons in a GaAs-quantum well (QW)

The average energy loss rate, the energy- as well as the momentum relaxation time of hot electrons confined in a GaAs-square quantum well are calculated as a function of the external controllable parametersn _s (electron density),T (lattice temperature) andT _e (electron temperature) for the interaction of the charge carriers with bulk- and surface polar optical phonons. Analytical expressions are derived in the limit of vanishing quantum well width at non-degeneracy and degeneracy of the electron system. Both energy-and momentum relaxation time are found to be complicated functions of the ratiosT _D /T _e andT _D /T withT _D being the Debye-temperature of the polar optical phonon involved in the scattering. In a thick (very thin) QW the energy loss rate to bulk PO-phonons is found to be larger (smaller) than the corresponding loss rate to surface modes. The energy- (momentum-) relaxation times are found to be constant (increasing) functions ofn _s at non-degeneracy (degeneracy) of the electron system. Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Effect of oxygen on the NMR relaxation properties of crude oils

Nuclear magnetic resonance relaxation measurements of bulk fluids provide a sensitive probe of the dynamics of molecular motion. Dissolved oxygen can interfere with this technique as its paramagnetic nature leads to a reduction of the paramagnetic relaxation times of the fluids. We studied this effect for the relaxation properties of crude oils that are in general characterized by a distribution of relaxation times. The samples were stock tank oils that have been exposed to air. We comparedT ₁ andT ₂ relaxation time distributions and their correlation functions of the initial (oxygenated) samples with those from the deoxygenated samples. Oxygen was removed from the oils with a freeze-thaw technique. As expected, the effect of oxygen is most apparent in oils with long relaxation times. In these oils the effect of oxygen can be described by an additional relaxation rate 1/T _1,2 ^ox to the transverse and longitudinal relaxation rates that is sample dependent but does not vary within the relaxation time distribution of the oil. Values of 1/T _1,2 ^ox for different crude oils were found to be in the range of 2.5 to 8.3 s. For crude oils that have components with relaxation times less than 100 ms, no significant oxygen effect is observed.     

Joint Optimization of the Number of Pulses and the Relaxation Pause in the Combined Multiple-Pulse Spin-Locking Sequence for Detecting Explosives by NQR

The problem has been solved for the joint optimization of the number N of pulses and the relaxation pause t _p in the combined multiple-pulse spin-locking sequence, which is successfully used for detecting some explosives by nuclear quadrupole resonance (NQR). Initially, the formula is derived for the signal-to-noise ratio provided by this sequence. Using the condition that an explosive detection time T _det is constant (it is typical in practice), from this expression the set of two interrelated equations is obtained for optimum values of N and t _p, which provide the maximum signal-to-noise ratio. These values are determined by both effective transverse T _2e and longitudinal T ₁ relaxation times and sequence parameters, and do not depend on the number m of sequence repetitions. The m value is calculated as the quotient of T _det by the duration of the onefold sequence with optimum values of N and t _p. This set of equations is shown to be mutually compatible at all values of sequence parameters and relaxation times T ₁ and T _2e, which occur in actual practice. The results of the experiments, which have been carried out on cyclotrimethylene trinitramine (RDX) at a ¹⁴N NQR frequency of 3.41 MHz and temperatures of 26 and −3°C, are in good agreement with the theoretical ones.     

Dynamic light scattering in solid polymers

The viscosity of an amorphous polymeric solid above its glass transition [T _g (T,P)] increases as the temperature of the solid is decreased or the pressure is increased. Under changes in temperature or pressure, molecular subunits in the polymeric solid undergo configurational changes. Such changes or relaxations have a distribution of relaxation strengths and times. As the solid is cooled or as the hydrostatic pressure on the solid is increased, the relaxation strengths increase and the relaxation times increase. These changes in relaxation or dynamic properties are very dramatic as the empirical T _g is approached. Near T _g the polymeric solid is no longer in volume equilibrium; continued cooling or pressuring at a time rate faster than the average relaxation time will produce a polymeric glass. This glass is a nonequilibrium, amorphous solid. If the glass is held at a fixed temperature and pressure very close to, but below, T _g , the volume of the glass will be observed to relax to its equilibrium value. For temperatures and pressures well below T _g , equilibrium is a much more conjectural concept since the relaxation times become extremely long. It has been proposed^1,2 that there is a characteristic temperature T _g at which an amorphous polymer undergoes a second-order transition to an equilibrium glass with zero configurational entropy (i.e., a noncrystallizable solid).     

The kinetics of relaxation of magnetization fluctuations near the phase transition from paramagnetic state to ferromagnetic state with domain structure

The equations of motion describing relaxation of magnetization fluctuations in the paramagnetic state for a uniaxial ferromagnet have been solved. In the Landau-Ginzburg functional the demagnetization energy has been taken into account. The finite dimensions of a sample have been considered. It has been shown, that a phase transition is generated by fluctuations containing information about the period of the domain structure at the phase transition point T_c¹. The obtained formulae describe T_c¹ and the period of the domain structure. The results can be used both for bulk materials and thin films.     

Nuclear quadrupole resonance and thermally activated molecular mobility in solids: Reorientations of symmetric molecular species and pseudorotation in trigonal-bipyramidal molecules

The specific features revealed in the behavior of temperature dependences of the spin-lattice relaxation time t ₁ of quadrupole nuclei involved in different types of thermally activated motions in crystals have been analyzed under the assumption that there exists a temperature dependence of the activation energy of motion. An expression for the spin-lattice relaxation rate has been obtained. This expression includes the effect under consideration and provides an adequate explanation for numerous anomalies in the behavior of the experimental dependences t ₁(T), which were revealed in the case of the motion of molecular fragments with a relatively large volume. A nontraditional method for evaluating the activation energy of motion under these conditions has been proposed.     

Linewidth-Resolved N HSQC, a Simple 3D Method to Measure N Relaxation Times from T1 and T2 Linewidths

A three-dimensional approach for measuring ¹⁵N relaxation times is described. Instead of selecting particular values for the relaxation period, in the proposed method the relaxation period is incremented periodically in order to create a 3D spectrum. This additional frequency domain of the transformed spectrum contains the relaxation time information in the T₁ and T₂ linewidths, and thus the longitudinal and transverse ¹⁵N relaxation times can be measured without determination of 2D cross peak volumes/intensities and subsequent curve fitting procedures.     

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.     

Properties of (Bi1/9Na2/3)(Mn1/3Nb2/3)O3 analysed within dielectric permittivity,conductivity, electric modulus and derivative techniques approach

The (Bi_1/9Na_2/3)(Mn_1/3Nb_2/3)O₃ ceramics with perovskite structure were sintered. The XRD test proved that the samples are cubic (a?=?3.920?±?0.001?Å). Microstructure and atomic composition were determined with a SEM (JSM-5410) equipped with energy dispersion X-ray analyser (ISIS-300). The fluctuation in the chemical composition was found indicating on local disorder. Broadband dielectric spectroscopy in the range 10^?1–3?·?10⁷?Hz was applied within the range of 100–650?K. The real, ?′(f,?T), and imaginary, ?″(f,?T), parts of complex dielectric permitivity characteristics, both in the temperature and frequency domain, show relaxation processes partially covered by electric conductivity. At high temperatures the electric conductivity exhibits a thermally activated behaviour σ(f,?T)?∝?exp(?E _a/kT) but the variable range hopping (VRH) dependence σ?∝?exp[?(T ₀/T)^1/4] is manifested at low temperatures. The derivatives technique in the frequency (??log??/??log?ω) and temperature (??log??/?T) domain enabled various relaxation processes to be distinguished. The data converted to electric modulus representation, M*(f,?T)?=?1/?*, exhibited clearly resolved relaxation peaks. The relaxation times obtained from the peaks position show a slightly non-Arrhenius temperature behaviour with the activation energy varying in 0.4–0.6?eV range and characteristic time of the electric conductivity relaxation of the order of 10^?12?s. The relaxation times can be fitted at better accuracy with the VRH dependence where T ₀ are of the order of 10⁸?K. It is shown that the low frequency ac-conductivity converges to dc-conductivity and the relation σ(0)?～?ω_m?～?τ_m ^?1 typical for the disordered solids applies. The conduction current relaxation relationship behaves in accord with the VRH system: σ_dc?∝?(T/T ₀)^q (e ²/kT) ω_c, where ω_c?=?ν_ph exp[?(T ₀/T)^1/4] is valid for the locally disordered (Bi_1/9Na_2/3)(Mn_1/3Nb_2/3)O₃ compound.     

Single-Pulse Echo and Its Secondary Signals in Two-Level Spin Systems

The dependences of the amplitudes of single- and two-pulse spin echoes and their secondary signals in NMR (protons of glycerin in an inhomogeneous magnetic field) in the exciting-pulse repetition period T _r have been compared. The difference in origin of the primary and secondary signals of a single-pulse echo in a two-level spin system has been confirmed. It is shown that only a primary single-pulse echo observed when T _r > T ₁ (T ₁ is the spin lattice relaxation time) results from single-pulse excitation. The secondary single-pulse echo signals are observed for T _r < T ₁ and are due to the multiphase formation mechanism. The results obtained for magnetically ordered substances are analyzed. Based on these data, it was inferred earlier that primary and secondary single-pulse echo signals were formed by one and the same multiphase mechanism.     

The proton relaxation of methyl cyanide in the presence of Ni(II) ions,as studied by spin-echo techniques

The proton relaxation times (T ₁ and T ₂) of methyl cyanide, in the presence of Ni(II) ions, have been measured as a function of temperature and frequency by spin-echo techniques. The observed decay times (T ₂?) have also been measured as a function of the separation, t _ep, between the pulses in a Carr-Purcell train of echos. The results obtained in the limit of long pulse separation have been fitted to existing theories. The rotational correlation time of the Ni/MeCN complex, τ _R , the electron spin relaxation time, τ _S , and the distance of closest approach of the protons to the nickel have been estimated from the results. In addition the scalar coupling constant, the exchange rate τ _B and the activation energies for τ _B , τ _S and τ _R have been evaluated. The chemical exchange parameters obtained differ significantly from those obtained by previous workers. There is evidence from the pulse dependence experiments that the complex is a distorted octahedron.     

Temperature- and Concentration-Dependence of the Spin-Lattice Relaxation Time of Chromium Ions in GASH

Investigations of the temperature- and concentration dependence of the spin-lattice relaxation time T₁ in ferroelectric GASH (= Guanidinium aluminium sulfate hexahydrate) single crystals doped with Cr³⁺-ions are reported. The concentration-dependence found on the higher concentrated crystals C 0.1% Cr³⁺) as well as the observed cross-relaxation are explained in terms of spin-lattice relaxation via exchange pairs. Using the VAN VLECK formalism T₁ has been estimated for Cr³⁺: GASH by comparision of the present system and K-Cr-alum.